File: File_18
Title: Chronological Data Tables
Status: Inherited Final baseline retained; bounded September 18 2026 author-authorized SP Flood / Noah–Shem correction and cross-tradition Flood-Gear clarification applied; bounded September 13 2026 source-table / phase clarification applied (LXX Peleg/Reu/Serug copy-error correction; Aaron-before-Moses phase wording); September 8 2026 Lamech settlement clarified by author direction: attested LXX lifespan `753`, restored begetting `182`, calculated remainder `571`; the combined `182/753` biography is component-wise reconstructed. LXX `777` remains an MT-derived appendix overlay. The **September 8 Lamech wording clarification** changed no numerical table; the September 13 LXX triplet correction changes only the three author-confirmed §4.2 copy-error cells and their death labels. Focused verification only; no new full-file pressure test or separate re-Finalization.
Pressure-test status: Prior full and focused certifications remain historical to their source editions. The September 8 Lamech and September 18 SP/Flood amendments receive focused arithmetic, source-diff, guard, protected-region, and dependency verification only; no new full pressure test is claimed.
Focused correction verification status: Complete July 24 2026 — included in the File_63 Finalization package-level `176/176` verification PASS; no new full pressure test claimed
Reciprocal-routing verification status: Prior File_61/File_62 and File_69 routes remain retained. The August 20 2026 coordinated File_09/File_69 package adds one derived restored-Cainan/Apparent-Adam companion row and one reciprocal guard; focused package verification is complete; no pre-existing raw table row or Primary anchor is changed.
Register Agreement status: Lamech source hierarchy remains at State Vocabulary Register v1.54 §D.43 / current v1.55 inherited §D.43 and Restart Capsule v11.53 §10.30; September 13 corrections are registered at State Vocabulary Register v1.55 §D.44 and Restart Capsule v11.54 §10.31; the v1.53 / v11.52 numerical settlement is unchanged. Earlier Lamech-specific D.18/D.42 instructions remain superseded in scope. The September 18 SP/Flood correction is author-authorized in this file and the revised Report V / companion register; corresponding central Register and Restart Capsule updates remain pending. Unrelated inherited controls, nested Gears, Sothic amendments, and Primary anchors remain unchanged.
Publication-cleanup status: Public-clean Final Markdown; bounded reciprocal replacement included in the coordinated Final File_09/File_69 source/control package. Repository Change Archive, Publication Manifest, indexes, landing pages, deployment, and external archival recapture remain separate subsequent work.
Source-history status: Essential companion to all inquiries; Version 5.0
Entity: RAW CHRONOLOGICAL DATA
Classification: Foundational Tables / Lookup Reference
UUID: DATA_TABLES_CORE
Primary domain: Regular; Cumulative; Comparative; SKL; Calendar; Theological
Traditions: MT; SP; LXX; BJ / Jubilees; SKL; Berossus by dependency
Canonical source: Markdown
Primary anchors: 3899 BC; 4199 BC; 5279 BC; 1661 BC; 1876 BC; 1885–1878 BC; 1670/1663/1656 BC; AD 1656/1663/1670; 1936 BC; 1816 BC; 1846 BC; 1446 BC; 1406 BC; literal/precise United Monarchy `1050t/n→1010t/n→970t/n→930t/n BC`; Rounded United Monarchy `1051n→1011n→971n→931n BC`; 967/966 BC; 1016 BC; 586 BC; AD 29395; AD 29465; AD 29515; 14006 BC; 14466 BC; 4831 BC; 5291 BC; 5296–5289 BC; 4858–4851 BC; 4856 BC; 4398–4391 BC; 4396 BC; 4278–4271 BC; 4825–4818 BC; 3136 BC; 3921 BC; 3011 BC; 2551 BC; 2336 BC; 2091 BC; 6306 BC; 13398 BC; 14896 BC; 3856 BC; 2906 BC; 2856 BC; 20886 BC; 27366 BC; 452886 BC; 459366 BC
Related files: File_00; File_01; File_02; File_04; File_05; File_06; File_07; File_08; File_09; File_10; File_11; File_12; File_14; File_16; File_17; File_20; File_21; File_22; File_34; File_46; File_50c; File_51a; File_54; File_56; File_61; File_62; File_63; Restart Capsule v11.46; 490d Repository Style Guide v2.5; Project Procedures v3.5; State Vocabulary Register v1.47; File_69
Major operators: `+60 Terah`; `+215 Sojourn`; `+275`; `60 + 155 + 60`; `±215`; File_11 absolute Three-Gear `+0/+2/+4`; Shem-centered local `−2/0/+2`; SKL dilation `−720/0/+720`; nested local-on-macro subrails; regular restored 2nd Cainan `+130`; cumulative restored 2nd Cainan `+460`; 137 checksum `7 + 130`; proportional unit `1656 ÷ 12 = 138`; missing-four extension `4 × 138 = 552`; completed extension `16 × 138 = 2208`; Cainan-to-Moses lock `3450 = 138 × 25`; Kenan / Cainan reinforcement `1370 = 10 × 137`; Cainan lifespan-sum `910 + 460 = 1370`; Cainan macro-vector `2300`; Cainan / Famine envelope projection `2520`; cross-tradition Shelah `60`-multiple comparison `2400` / `2940`; `60 × 42`; `60 × 40`; `60 × 49`; `60 × 59`; `60 × 99`; `60 × 101`; `60 × 108`; `6 × 490`; `3540`; `5940`; `6060`; `6480`; inclusive companion `2307`; Enochian lower-bound vector `2730 = 7.5 × 364`; Daniel 12 sandwich `1260 → 1290 → 1260`; 360:1 SKL scale; `+6480`; selected macro `+720` member; `+30 Apparent Mode`; selected local `+2` member; bounded adjacent-macro `690/720/750`; File_21 SKL rounded mod-10 Mirror display `BC + AD − 2`; File_21 SKL Short / Long relation `6530 − 50 = 6480`; File_34 SKL-to-Berossus `2370` corridor by dependency; File_34 `30 + 20 + 30` restoration corridor by dependency; paired slash-display arithmetic by dependency; phase-chain arithmetic by dependency; `25/23`; `70/69`; `300/299`; `430`; `480`; `+50` Jubilee Offset; same-side BC subtraction; civil cross-axis span `BC + AD − 1` if opened; Lamech non-operative transmitted-`188` comparison; hypothesis-level gain-transfer; appendix triad deltas `+6 / −30 / −24`; `454 − 24 = 430`; LXX Exodus lock `299 × 45` by File_56 dependency; Flood Gears `3240 / 3238 / 3236` (`+215` frame) by File_11 dependency; downstream full clutch `T14(C) = C − 14`, half-clutch midpoint `H7(C) = C − 7`, and fixed-offset Joseph translation by corrected File_61 / Final File_62 dependency only
Major modal states: raw data source state; minimum baseline table state; Regular chronology; Cumulative chronology; MT Minimum-Regular; MT Standard-Normal; Abraham two-state / Terah four-state variant field; 2nd Cainan variant-boundary state; 12–8–4–2–0 generational variant-count ladder; multi-tradition Pentateuchal Funnel all-even structural harmony; restored/native 2nd Cainan 27-generation completion state; tebah / ark typological bridge state; 137 boundary checksum state; Shem dual-100 state; 16 × 8 expectation / cumulative-Cainan extension state; Kenan / Cainan tenfold reinforcement state; Cainan macro-vector state; Cainan / Famine envelope-to-envelope state; cross-tradition 60-multiple Shelah / Plenty-Famine alignment state; Mirror 60-spine / Terah-Cainan death-rail state; regular-Cainan 460-year cross-modal symmetry state; Cainan triple-target matrix state; Cainan-to-Exile Daniel 12 sandwich state; Cainan-sector branch-restraint state; SP Normal / G2; SP-local Noah/Shem primary–companion field; cross-tradition Flood Gear / start–close field; SP Ideal / Exclusive comparison; LXX Regular-Minimum; LXX Terah / Abraham `2 × 2` variant field; regular-localized Shem `±2`; cumulative-propagated Shem `±2`; absolute Three-Gear state; selected local `+2` member state; SKL centered `±720` dilation; nested local-on-macro subrail state; regular restored 2nd Cainan; cumulative restored 2nd Cainan; literal/precise United Monarchy state; Rounded Scaffold United Monarchy state; shared-`966` state; Kings dual-ledger state; Sumerian A / SKL Short; Sumerian B / SKL Long; SKL `+30 Apparent Mode`; selected SKL local `+2` member; selected SKL macro `+720` member; full nested `±2 / ±720` Three-Gear control; File_21 SKL Unified Protocol dependency state; File_34 post-final dependency state; File_34 SKL-to-Berossus `2370` corridor dependency state; File_34 `30 + 20 + 30` restoration corridor dependency state; SKL rounded mod-10 Mirror display-state; Jachin / Boaz Temple-Time Pillar coordinate state; providential multi-tradition system state; LXX component-wise `182/753` main-chain state; non-operative transmitted-`188` comparison state; Key-of-23 crossover hypothesis; appendix-only LXX `777` overlay state; `430`-alignment justification state; Flood-marker convention set; Kohath / Amram silence state; corrected File_61 / Final File_62 downstream half-/full-clutch table-routing state; File_62 Joseph inherited-translation and fixed-Joshua `216` comparison state by dependency
Revision basis: 490d Repository Style Guide v2.5; Restart Capsule v11.46; State Vocabulary Register v1.47 Part D §D.38; Project Procedures v3.5; prior finalized File_18 source; Files 11, 21, 34, and 50c; retained monarchy, File_63, File_61/File_62, File_09/File_69, and File_69 routes; August 25 2026 bounded nested Three-Gear control correction; Repository_Change_Archive and Publication Manifest retained as non-controlling prior publication records.
Current refresh note: Prior monarchy, File_63, File_61/File_62, and File_09/File_69 table-source boundaries remain unchanged. The August 25 2026 bounded correction clarifies only the SKL rail ontology: the printed `+2` and `+720` rows are selected members of the complete centered `−2/0/+2` and `−720/0/+720` wheels, with optional local subteeth nested inside admitted macro members. The `+30 Apparent Mode` remains orthogonal, and no new raw date row or proof-bearing equation is introduced.

September 8 2026 Lamech correction: the former regular-`777` / cumulative-`753` split is superseded by `182/753` in both main reconstructions. Regular Lamech death changes from `3028` to `3052 BC` in the minimum frame; the birth chain and all cumulative chain values remain fixed. `188` remains non-operative but may be examined as a qualified Key-of-23 transmission hypothesis; LXX `777` examples move to Appendix B.

Current pressure-test note: The June 28 2026 File_18 pressure test verified current control alignment, table-source boundaries, Machine Guards, dependency routing, no-comma Markdown formatting, and visible arithmetic / table arithmetic. The pass changed only stale trust-status and dependency-status wording; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries were changed.

Bounded monarchy-correction note: The July 24 2026 amendment is independently focused-verified but is not a new full pressure test. The prior June 28 2026 full-pressure-test baseline remains historical control for all unaffected material.

September 18 2026 SP/Flood correction: in the native SP frame, G2 Lamech is `3545→2893`, `653` inclusive; Noah primary/companion is `3493/3492`; Flood start→close is `2893→2892`; fixed Arphaxad remains `2891`. Add `215` for the reports’ equalized SP frame: `3760→3108`, Noah `3708/3707`, Flood `3108→3107`, Arphaxad `3106`. Ordinary Flood Gears and each Gear’s one-year event span apply to MT, LXX, and SP; the adjacent `−1` person-station rail applies only to SP Noah/Shem. The native-LXX comparison remains Cainan ON: G2 Creation `5494`, Flood `3238→3237`, Arphaxad `3236`. §§0, 2.2.1, and 3, Appendix A, and clarification note 10 carry the bounded correction; cumulative and SKL data are unchanged.

# File_18 — Chronological Data Tables

## Related Repository Files

| File | Function for `File_18` |
|---|---|
| `File_00` | Axiom Engine, structural variators, source-map discipline, civil / Mirror / inverse firewalling, and source-control rules. |
| `File_01` | Abraham entity data and `1876 BC` convergence year-label where Abraham rows are used. |
| `File_02` | Flood terminology; MT Minimum-Regular / MT Standard-Normal distinction; SP Normal / G2 with the September 18 local correction; LXX Regular-Minimum; SKL Short / Long terminology; Shem `±2` state distinction. |
| `File_04` | Jacob, Entry, LXX `33 + 397`, Levi death-state handling, and the `1876 BC` shared year-label. |
| `File_05` | Primary `1446 BC` Exodus state; subordinate `1231 BC` Ramesside state; Sojourn 215 / Exodus 215 firewall. |
| `File_07` | Creation-week endpoint / Year-6 distinction, restored Cainan `+130` / `+460`, and Creation microstructure. |
| `File_08` | Controls the literal/precise and Rounded United-Monarchy state split, historical `966 BC`, schematic `1016 BC`, David’s exact/rounded reign states, and Fall of Jerusalem date-state controls. |
| `File_09` | Controls the cumulative Creation–Cainan–Enoch substrate, including the derived restored-Cainan/Apparent-Adam companion `14501–14494 BC`; File_18 remains the raw-table controller and admits that state only as an explicitly derived companion. |
| `File_10` | External validation, Smith / Rudd source-control, SKL / Berossus witness framing, and providential multi-tradition system language. |
| `File_11` | Three-Gear Protocol, `299 → 300`, `300/299`, and Residue Protocol distinction. |
| `File_12` | Calendrical physics, Enochian `300/299`, Solar / Enochian year display, `7` / `7.5`, and residue controls. |
| `File_14` | Biological-fractal terminology where variant-gap, `275`, `276`, `280`, and LXX Maximum states are opened by dependency. |
| `File_16` | `1876 BC` Nexus, Cainan convergence, Triple `430`, `+50` Jubilee Offset, and Bullseye claim-status discipline. |
| `File_17` | Prophetic span-component terminology and exact-ratio controls. |
| `File_21` | Controls the SKL Unified Protocol as an application layer: `360:1` scalar, four-state SKL matrix, SKL rounded mod-10 Mirror display-state, Residue Protocol `6480.25`, Projective Boundary / Temple-Time Pillar coordinates, and Jachin / Boaz spelling control. It does not replace `File_34` for full SKL / Berossus derivation. |
| `File_22` | Decimal Bridge and cumulative / Aaron-Moses dependency where exact cumulative tables are opened. |
| `File_61` | Uses the unchanged §6A Jacob, Levi, Kohath, Amram, and Moses/Aaron rows to derive the bounded `T14(C)=C−14` and `H7(C)=C−7` rails and Joseph's fixed-offset collateral portions. File_18 remains the table source; none of the derived clutch coordinates is inserted as a new File_18 row. |
| `File_62` | Controls the detailed half-clutch birth-law interface, inherited Joseph translations, Mosaic phase carrier, dual-`490` closure, BJ comparative warrant, and fixed-Joshua `216` comparison. It consumes File_18 source rows through Files 61–62 but does not reclassify its derived coordinates as File_18 table data. |
| `File_34` | Full SKL / Berossus derivation, precessional envelope, `6480` tier logic, Berossus computational-anchor state, SKL-to-Berossus `2370` corridor, `30 + 20 + 30` restoration corridor, paired slash-display arithmetic, and phase-chain / Pillar cross-axis controls. |
| `File_51a` | Controls the Rounded Scaffold, including the Rounded United-Monarchy companion rail and `560`-year Aaron/Moses checks. |
| `File_54` | State-register, File map, Machine Guard, claim-status, Mirror / inverse restraint, and later-file style precedent. |
| `File_63` | Downstream Final carrier synthesis requiring the literal/Rounded monarchy table split and retaining File_18 as table source. |

File_69 Cainan-count reciprocal note:
Final File_69 uses File_18's restored/native second-Cainan `27`-generation Adam-to-Moses inventory as the internal reverse fingerprint of its external `14+13` schematic spacing. File_18 remains the raw-table and count controller.

Machine Guard [FILE_18 FILE_25 FILE_69 CAINAN-FINGERPRINT ROUTING]:
Final File_69 may use File_18's restored/native-second-Cainan `27`-generation Adam-to-Moses inventory and File_25 / File_29's same-name Kenan–Cainan `70+840=910` corroboration to state the external `14+13` / internal `13+14` reverse fingerprint. File_18 remains the raw table and count controller; File_25 remains the Decimal Invariance / `910` reference controller. In LXX, do not add another `+130` to native Cainan. The `26/27/28` states alter attribution or the figurative bookend only and do not move the fixed date grid.

File_69 Jeconiah–Cainan reciprocal note:
Final File_69 now compares Jeconiah's forwarded `70+840=910` row with first Kenan and compares Jeconiah's `41↔42` slot operation with second Cainan's `26↔27` retention/expunction. This is a bounded analogy, not an identity of persons, texts, curses, or chronologies.

Machine Guard [FILE_18 FILE_25 FILE_29 FILE_53 FILE_69 JECONIAH–CAINAN ROUTING]:
Final File_69 may compare Jeconiah's six-year-forwarded row with first Kenan's `70+840=910` anatomy and may compare Jeconiah's `41↔42` overlap with second Cainan's `26↔27` retention/expunction as analogous one-position count-clutches. File_18 retains the raw table and Adam-to-Moses count states; File_25 retains Decimal Invariance and the `910` reference field; File_29 retains the `7/13` theological grammar; File_53 retains Cainan-expunction and BJ claim-status control. Analogy does not create identity, and native LXX Cainan receives no additional `+130`.

### Final File_09/File_69 cumulative-substrate reciprocal note

Final File_09 derives the restored-Cainan/Apparent-Adam companion by applying the already controlled `+460` cumulative Cainan translation to the base Apparent-Adam row, equivalently by applying localized `+30` Apparent Age to the restored-Cainan Creation row. Final File_69 uses that companion only by dependency inside its cumulative-substrate synthesis. File_18 records the row as **derived companion data**, not as an independently transmitted chronology row.

Machine Guard [FILE_18 FILE_09 FILE_69 RESTORED-CAINAN / APPARENT-ADAM ROUTING]:
`14501–14494 BC`, Moses-side center `14496 BC`, Aaron whole-year node `14499 BC`, and Aaron phase-resolved node `14499.5 BC` are derived companion values generated from File_18 source rows under `+460` and localized `+30`. They are not inherited raw data, do not revise the base Apparent-Adam or restored-Cainan Creation rows, and are not repository Primary anchors. Final File_09 controls their cumulative derivation; Final File_69 controls only the downstream genealogical interpretation.

## 0. File-function

`File_18` contains the raw chronological data required to verify calculations and apply axioms defined in `File_00` through `File_17`. It is the repository's number source paired with the rule source supplied by the axiom and entity files.

Three data systems are always required for any inquiry:

| Data system | Legacy term | Function |
|---|---|---|
| Regular chronologies | Short chronologies | Historical / begetting-age timeline for MT, SP, and LXX. |
| Cumulative chronologies | Long chronologies | Theological / schematic lifespan-added timeline. |
| Sumerian Integration | Cosmic timeline | SKL / Sumerian 360:1 day-year scale. |

Design principle:
Tables present minimum baseline dates. All variants are derived by applying the documented mechanisms, especially `+60 Terah`, `+215 Sojourn`, or both.

Modal-state rule:
A shared date-label, number, span, or tradition does not create identity unless state, node-class, tradition, and operator agree.

Source-control note:
LXX chronology is materially active in this file. Henry B. Smith Jr.'s reconstruction of the LXX Genesis 5 and 11 chronology is therefore an important external source-reconstruction witness for the LXX layer. Smith is not the source of this file's harmonic interpretation, SKL / Berossus integration, providential synthesis, or theological reading.

Publication-cleanup note:
This public-clean source preserves the Final, post-final pressure-tested, focused-amendment, later cross-file-update, and current post-equalization full pressure-test status in the header. Detailed pass logs, pressure-test records, bounded update ledgers, pointer-refresh history, and replacement-workflow notes are archived rather than repeated in the public body.

Nested Three-Gear correction note:
The August 25 2026 update is a state/guard correction only. It changes no table datum and adds no chronology row.

### 0.1 Working state register

The following states are active in `File_18`. They are simultaneous, non-competing states unless a local section explicitly narrows the working state.

| State | Primary values / forms | Node-class / function | Handling in `File_18` |
|---|---:|---|---|
| Raw data source state | whole file | table-source / lookup-reference file | `File_18` supplies baseline values and verification tables. It does not locally re-prove every operator it tabulates. |
| Minimum baseline table state | `3899 BC`; `4199 BC`; `5279 BC`; `1661 BC` | minimum display rows | Baseline rows are forward-most table values. Variant rows are generated by stated operators rather than by silently altering the baseline. |
| Regular chronology state | begetting ages | historical / genealogical timeline | Use for MT, SP, and LXX begetting-age rows. Do not collapse with cumulative lifespan stacking. |
| Cumulative chronology state | lifespans added end-to-end | theological / schematic deep-time timeline | Use for §6 tables. Do not treat cumulative dates as ordinary historical birth dates unless a local dependency opens that node-class. |
| Restored-Cainan/Apparent-Adam derived companion state | `14501–14494 BC`; Moses `14496 BC`; Aaron whole-year `14499 BC`; Aaron exact `14499.5 BC` | derived companion row / cumulative interface | Generated by `+460` from the base Apparent-Adam row, equivalently `+30` from restored-Cainan Creation. It is not an inherited raw chronology row or Primary anchor. |
| Literal Creation-week state | 7 days | literal Genesis 1 week | Converges with the figurative week at the displayed Creation endpoint. |
| Figurative Creation-week state | 7 years | day-year Creation-week | Converges with the literal week at the displayed endpoint. The Year-6 / Adam state remains distinct from the endpoint. |
| Creation endpoint state | `3899 BC`; `4114 BC`; `4174 BC`; `5279 BC`; related endpoints | Day 7 / Year 7 complete | Do not collapse Creation endpoint states with Year-6 / Adam states such as `3900 BC` or cumulative `14006 BC`. |
| MT Minimum-Regular state | `3899 BC`; `2243 BC`; `1661 BC` | forward-most MT regular baseline | Active in §2. No `+60 Terah` or `+215 Sojourn` is applied unless the section names it. |
| MT Standard-Normal / `+215 Sojourn` state | `4114 BC`; `2458 BC` by dependency | full-430 Egypt / normative MT state | Distinct from MT Minimum-Regular. `4114 BC` is not a correction of `3899 BC`; it is `3899 + 215`. |
| MT `+60 Terah` state | `3959 BC` from `3899 + 60` | Terah-only variant | Applies to Adam → Terah field where opened. Does not alter fixed Aaron-forward rows. |
| MT maximum / `+275` state | `4174 BC` from `3899 + 275` | combined `+60 Terah` and `+215 Sojourn` | Preserve the source's combined position while also preserving sequential `60 + 155 + 60` anatomy. |
| Epoch-boundary state | Adam → Terah; Abraham → Levi / Joseph; Aaron onward | variant-scope boundary | Abraham through Levi / Joseph admits two positions through the `±215` Sojourn fork. Terah opens the `+60 Terah` fork and doubles the field to four positions from Terah back to Adam in the normal no-2nd-Cainan table state. If restored 2nd Cainan is explicitly inserted, Terah through 2nd Cainan remains four-position, while Arphaxad / Flood through Adam becomes eight-position. Aaron onward is fixed. |
| Abraham → Levi / Joseph `±215` field | Abraham `1951/2166 BC`; Entry `1661/1876 BC`; Jacob / Joseph / Levi rows | Sojourn-position fork | Events from Levi / Joseph back to Abraham have two possible dates because of the `215`-year Sojourn variant. Do not apply `+60 Terah` until the Terah boundary. |
| Terah four-position field | Terah births `2021/2081/2236/2296 BC`; Terah deaths `1816/1876/2031/2091 BC`; Abraham births `1951/2166 BC` | `±215 × +60 Terah` hinge | Author-clarified. Abraham has two birth states, `1951 BC` and `2166 BC`. Terah has four birth/death states because `+60 Terah` doubles the Abraham field. Restored 2nd Cainan does not make 2nd Cainan itself eight-position; 2nd Cainan remains in the four-position Terah-to-Shelah field. The eight-position field begins with Arphaxad / Flood and propagates back to Adam only when restored 2nd Cainan is explicitly opened. |
| 2nd Cainan variant-boundary state | Shelah births `2481/2421 BC` and `2266/2206 BC`; 2nd Cainan births `2611/2551 BC` and `2396/2336 BC`; 2nd Cainan deaths `2151/2091 BC` and `1936/1876 BC` | restored regular 2nd Cainan boundary | Author-clarified. 2nd Cainan has four possible date states, like Terah. His father Arphaxad, whose birth is synonymous with the Flood / Ark-exit conception boundary, is the first row to absorb the additional restored-Cainan hinge and therefore becomes eight-position, with that eight-position state propagating back to Adam. |
| Multi-tradition Pentateuchal Funnel all-even structural harmony | Generation-count ladder `12 → 8 → 4 → 2`; possible-date ladder `8 → 4 → 2 → 0` when the Cainan hinge is active, whether restored in MT / SP or native / explicitly toggled in LXX | structural inference / Pentateuchal macro-architecture across MT, SP, and LXX | Author-clarified. The variant-boundary pattern is not merely a list of boundary lines and is not local to MT. MT, SP, and LXX encounter the same structural fork sequence at the same genealogical locations: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary. The tradition-specific status differs: MT / SP restore Cainan when that state is opened; LXX already contains Cainan in the baseline and uses removal / expunction only as a theoretical state. The pattern maps onto Creation → Flood; Flood → Abraham; Abraham → Entry into Egypt; Egypt → Conquest / death of Moses. The `+215` fork is held open by the Kohath / Amram silence: no begetting ages are given for Kohath or Amram, so no strict chain caps the Egypt span (Kohath / Amram silence state; the associated seven-multiple minimum / maximum locks remain an explicitly deferred author item). Claim-status: structural inference, with theological / providential significance available where the local argument opens it. |
| Restored/native 2nd Cainan 27-generation completion state | `12 + 8 + 4 + 2 + 1 = 27 = 3 × 3 × 3` | secondary generation-count completion / structural keystone | Author-clarified and pressure-tested. With restored 2nd Cainan opened in MT / SP, or native 2nd Cainan retained in LXX, the Pentateuchal generation count from Adam to Moses completes at `27`. This state is secondary to the primary `12–8–4–2–0` variant-count ladder and must not obscure the main 8-date / 4-date / 2-date / 0-date block logic. Without restored/native 2nd Cainan, the count drops to `26`, the 2nd Cainan → Terah block becomes `7` rather than `8`, and the all-even funnel no longer has the same structure. Claim-status: arithmetic fact for the count; structural inference for its architectural role. |
| Tebah / ark typological bridge state | Noah's ark; Moses' ark/basket; `8` souls; Moses as final deliverer | typological note / theological bridge | The Hebrew `tebah` ark motif links the Flood boundary and Moses narrative by typological correspondence. The `8`-generation post-Flood block and the `8` souls saved through Noah's ark provide a theological / typological explanation of the numeric structure, but do not carry the arithmetic burden. |
| `137 = 7 + 130` boundary checksum state | Adam → Seth; Flood / Arphaxad; Abraham / Sarah; Levi / Amram; Aaron terminal imprint where opened | boundary checksum / theological note | The value `137` may be read as `7 + 130`, joining the completion / Sabbath register to the mortal-line / curse-register. Treat the meaning as typological / theological support, not as a chronological operator. |
| Shem dual-`100` state | Noah-bound `100`; Arphaxad-bound `100` | Shem `±2` modal state | Shem is `100` at the Flood when bound to Noah's `500 → 600` chronology, and `100` at Arphaxad's birth when bound to Genesis 11:10. Both states are retained, analogous to Terah's `70/130` begetting-state display. |
| `16 × 8` expectation / cumulative-Cainan extension state | expected `16 × 8`; actual `12 × 8`; `4 × 138 = 552`; `4854/4856/4858 BC` | structural diagnostic / cumulative comparison | The visible funnel remains `12 × 8`; the idealized `16 × 8` expectation is a diagnostic only. The missing-four extension lands on the MT Cumulative + 2nd Cainan Cainan field when the restored regular Flood Gear rails are extended by `2208 = 16 × 138`. |
| Kenan / Cainan tenfold reinforcement state | 1Kenan `3921 BC`; son `3851 BC`; 2nd Cainan `2551 BC`; `1370 = 10 × 137`; Cainan lifespan-sum `910 + 460 = 1370`; `910 + 460 + 460 = 1830` | Cainan-sector support note | This state reinforces the `137` checksum at 10x scale. It supports the bounded File_18 amendment but does not open the full Cainan-sector branch. |
| Cainan macro-vector state | `4858–4851 BC`; `4398–4391 BC`; `2300`; `2520`; `2730`; `2307`; `1260 → 1290 → 1260` | File_16 dependency / Funnel support state | `File_18` supplies the table-source values and state controls. `File_16` controls the Nexus argument, Category B classification, and Bullseye Protocol use. |
| Cainan / Famine envelope-to-envelope state | `4398–4391 BC → 1878–1871 BC`; selected core `4396 BC → 1876 BC` | cumulative-to-historical envelope projection | Uses `2520 = 7 × 360` as a macro-prophetic projection by `File_16` dependency. This does not change the MT `430` Egypt state or make the cumulative Cainan death itself a regular-history event. |
| Cross-tradition 60-multiple Shelah / Plenty-Famine alignment state | MT `4398–4391 BC → 1878–1871 BC` by `60 × 42`; SP `4278–4271 BC → 1878–1871 BC` by `60 × 40`; LXX `4825–4818 BC → 1885–1878 BC` by `60 × 49` | table-source support / structural inference | `File_18` preserves the comparative source coordinates. `File_16` controls the Nexus interpretation. The common `60` factor is not a table-generation operator and does not collapse the Plenty window with the Famine window. |
| Mirror 60-spine / Terah-Cainan death-rail state | `1885n/1878n/1871n BC`; `1670n/1663n/1656n BC`; AD-side reversed mirror labels `AD 1656n/1663n/1670n`; `3540 = 60 × 59`; `1936n BC → 1876n BC → 1816n BC` | table-source support / Mirror corroboration | `File_18` preserves the date labels and arithmetic controls only. `File_16` controls the Nexus interpretation. The constant `3540` requires civil cross-axis arithmetic and reversed endpoint order on the AD side; it is not a table-generation operator. |
| Regular-Cainan `460` cross-modal symmetry state | `2551–2091 BC`; `2336–1876 BC` | regular restored 2nd Cainan lifespan members compared with cumulative `+460` | These are same-side 460-year regular spans. They may mirror the cumulative `+460` value, but they do not substitute cumulative lifespan insertion for the regular `+130` begetting-age operator. |
| Cainan triple-target matrix state | `2091 BC`; `1876 BC`; `1661 BC` | macro-vector alignment to Call / Super-Anchor / lower-bound Entry states | `2300`, `2520`, and `2730` point from the cumulative Cainan / Shelah field to three distinct target node-classes. The targets must remain state-labeled and non-collapsed. |
| Cainan-to-Exile Daniel 12 sandwich state | `4396 BC → 3136 BC → 1846 BC → 586 BC`; companion `1876 BC → 586 BC` | macro-prophetic witness by File_16 dependency | Classify as Category B / macro-prophetic witness. It does not turn `1846 BC` into Entry or `1876 BC` into Affliction start. |
| Cainan-sector branch-restraint state | `8970`; `9100`; `130 + 330`; `7800`; `2300`; `6900` by dependency | restraint / dependency-control state | Deeper Cainan-sector branches remain controlled by File_11, File_16, File_22, or later Cainan-sector files unless explicitly opened. |
| Fixed epoch state | Aaron birth; Moses birth; Exodus; Conquest | fixed post-variant anchor field | Values from Aaron onward are fixed unless another file explicitly opens a subordinate state. |
| `1876 BC` shared year-label state | `1876 BC` | Entry / Call / return / convergence year-label by dependency | In `File_18`, `1876 BC` may mark Entry under MT `430`, Abraham Call / Death of Terah under Sojourn-division paths, or another dependency-controlled convergence label. Do not collapse node-classes. |
| Primary Exodus state | `1446 BC` | primary Exodus anchor | Governs the tables unless a subordinate Ramesside state is explicitly opened by dependency. |
| Conquest / Moses-death state | `1406 BC` | Conquest / Moses endpoint anchor | Active in regular and cumulative tables. Do not collapse with Joshua death `1296 BC` in SP cumulative state. |
| Literal/precise United-Monarchy state | `1050t/n→1010t/n→970t/n→930t/n BC` | primary royal phase rail | Preserve as author-clarified chronology. Same-phase reigns equal `40`; David’s exact cross-phase reign equals `40.5`. |
| Rounded Scaffold United-Monarchy state | `1051n→1011n→971n→931n BC` | mod-5 comparison rail | File_51a-controlled; not literal/precise chronology. |
| Shared-`966` state | literal `1446n→966n=480`; Rounded `1526n→966n=560` | Temple / Rounded comparison | Shared label; distinct origin, node-class, and operator. |
| Kings dual-ledger state | `966 BC`; `1016 BC`; `+50` | historical Temple ledger versus schematic Triple-`430` ledger | Preserve both ledger states in §2.5. `1016 BC` does not replace historical `966 BC`. |
| Fall of Jerusalem endpoint state | `586 BC` | Kings / exile endpoint | In `File_18`, `586 BC` remains the displayed endpoint unless another dependency opens adjacent `587/586 BC` date-states. |
| SP Normal / G2 state | Creation `4199 BC`; Flood start `2893 BC`, close `2892 BC` | SP native regular frame | §3 retains the preferred chain head and applies interval-specific inclusive/completed counts. The legacy Toggle ON label does not license a global one-year shift. |
| SP Ideal / Exclusive comparison | `4200 BC` | legacy uncompressed / harmonic comparison | Does not replace the preferred §3 chain head `4199`; is not generated by the localized Noah/Shem companion rail. |
| SP Arphaxad-bound post-Flood state | Shem `2991 BC`; Arphaxad `2891 BC`; subsequent rows | fixed-Gear suffix / ordinary begetting intervals | At held Sojourn, Terah, and Cainan settings, Arphaxad onward does not move with ordinary Gear or inherit the SP Noah/Shem companion rail. |
| SP Noah/Shem adjacent field / Shem Superposition | G2 Noah `3493/3492`; G2 Shem `2993/2992`; G1 Shem `2991/2990` | primary / lower companion, with binding named | Only Noah/Shem receive the SP `−1` companion. Ordinal `599+` and conventional cardinal `600` are interval-specific readings. No backward propagation to Adam and no forward propagation into the fixed Arphaxad suffix. See §3.2.1 for paired deaths. |
| Flood Gear / event-year state | MT `2460/2458/2456`; native LXX `3240/3238/3236`; SP `3110/3108/3106`, full-430 frame | G3/G2/G1 starts; every close = start−1 | Ordinary three-Gear transport in all three traditions; each start→close is an event span. No Flood companion rail is generated by SP Noah/Shem. See §3.1.4. |
| SP Terah dual-lock state | `145`; `205`; `2021 BC`; `1876 BC`; `1951 BC` | textual lifespan / architectural lifespan pair | Author-clarified. SP text gives Terah's official lifespan as `145`, landing death at Abram's call; the architectural `205` mirrors MT/LXX and shows that the same Terah problem remains as a swapped lifespan / begetting-age issue. In SP cumulative tables, `145` remains the official span. |
| BJ / Jubilees comparison state | `3856 BC`; `343`; 7 Jubilees | external comparative witness | Used as SP / BJ alignment witness. Do not turn BJ into the SP table itself. |
| LXX Regular-Minimum state | `5279 BC`; `3023 BC`; native 2nd Cainan | LXX regular comparison state | Active in §4. Smith is an external LXX reconstruction witness, not the source of the repository interpretation. |
| LXX component-wise Lamech reconstruction | `182` restored begetting; `753` attested LXX lifespan; `571` calculated remainder; minimum `3805–3052 BC` | main Regular/Cumulative source selection | `753` is retained as the author-preferred original LXX lifespan; that judgment is distinct from its textual attestation. Only the combined `182/753` biography lacks identified joint attestation. `188` is non-operative; LXX `777` is an MT-derived Appendix B overlay. See §4A. |
| LXX Terah / Abraham `2 × 2` variant field | Abraham `1951/2166 BC`; Terah `2021/2081/2236/2296 BC` | independent `+215 Sojourn` and `+60 Terah` variant field | Author-clarified. Abraham has two birth labels because the `+215 Sojourn` state applies from Levi / Joseph back to Abraham. Terah has four birth labels because `+60 Terah` activates at Terah and doubles that two-date field. If restored 2nd Cainan is inserted, 2nd Cainan remains four-position; the eight-position effect begins at Arphaxad / Flood and propagates backward to Adam. |
| LXX cumulative source-table state | `14896 BC`; `5745 BC`; Cainan `5280 BC`; Peleg `3856 BC`; Lamech `753`; Nahor `208` | cumulative LXX table state | Lamech shares the main `753` lifespan selection with Regular execution; cumulative values remain unchanged. The row-local `777` overlay is preserved only in Appendix B.2 and must not propagate. |
| Regular-localized Shem `±2` state | Noah / Shem binding and qualified cross-Gear comparisons | local regular anomaly | Distinct from coherent Gear transport of other admitted biographies and the Flood. Arphaxad remains fixed under Gear at held variant settings; see §3.1.4. |
| Cumulative-propagated Shem `±2` state | `2 + 3 + 2`; 7-year margin | chain-wide cumulative anomaly | Generates cumulative envelopes; do not reduce to the regular-localized anomaly. |
| Regular restored 2nd Cainan state | `+130` | begetting-age insertion | Applies to regular MT/SP restoration only. LXX already includes Cainan. |
| Cumulative restored 2nd Cainan state | `+460` | lifespan insertion | Applies to cumulative MT/SP restoration only. Do not substitute `+130`. |
| LXX native 2nd Cainan state | LXX includes Cainan | native LXX baseline | No adjustment is applied in LXX regular or cumulative baseline. Theoretical LXX removal remains non-standard. |
| Theoretical LXX Cainan removal state | `5279 − 130 = 5149 BC` | theoretical removal / non-standard table state | Retained as architecturally valid but not tracked in standard tables. |
| MT cumulative Moses / Nisan trunk | `14006 BC`; `4831 BC`; `1526 BC` | primary cumulative trunk | Nisan / Spring line. |
| MT cumulative Aaron / Tishri trunk | `+3.5`; `.5` labels | secondary cumulative trunk | Tishri / Fall line. Preserve exact `.5` labels as display-state values. |
| Cumulative apparent birth / Year-6 +30 state | `14036 BC`; `14039.5 BC`; span `14041–14034 BC` | apparent-age cumulative overlay | Overlay only; does not replace the Adam Year-6 row. |
| Restored cumulative 2nd Cainan Flood Week | `5296–5289 BC`; `5291 BC` | restored cumulative Flood envelope | Controlled by §6B and `File_09` / `File_02` dependencies. |
| SP cumulative square state | `13398 BC`; `12100 = 110 × 110`; Joshua death `1296 BC` | SP cumulative square / Joshua target | Distinct from SP regular chronology and from MT cumulative trunk. |
| LXX cumulative / BJ Peleg state | `3856 BC` | LXX cumulative Peleg / BJ Creation correspondence | Comparative witness state; does not make BJ the LXX table. |
| MT cumulative Peleg phase-resolved Mirror state | `3501n–3494n BC`; parallel `3502t–3495t BC`; Mirror AD `1399t/1400n–1406t/1407n` | cumulative Peleg / Conquest Mirror coordinate-completion | Author-clarified. The Peleg envelope mirrors the Conquest / land-rest envelope by File_09 phase-resolved suffix inversion. Component spans equal `4900 = 70 × 70 = 100` Jubilees. |
| Sumerian A / SKL Short state | `2906 BC`; `20886 BC`; `452886 BC`; `17980` | primary SKL Short whole-year state | Preserve as Sumerian A / SKL Short. |
| Sumerian B / SKL Long state | `2856 BC`; `27366 BC`; `459366 BC`; `24510`; `+6480` | alternate SKL Long whole-year state | Preserve as Sumerian B / SKL Long. |
| SKL appended month/day datum state | `3 months and 3.5 days` | SKL textual-datum / dependency-controlled calendar detail | Retained as source datum. Whole-year local arithmetic remains separate unless `File_34` / `File_12` opens granular execution. |
| SKL `+30 Apparent Mode` state | `+30`; examples `2936/2886 BC` by dependency; bounded adjacent-macro `690/720/750` comparison | orthogonal apparent-age rail | Apply after Gear selection. Do not collapse with local or macro Gear units. |
| SKL local centered `±2` Three-Gear state | absolute `+0/+2/+4`; relative `−2/0/+2`; examples `2908/2858 BC` as selected members | ordinary-year fine-tooth wheel | Printed `+2` rows expose one member only. The full field is active when §D.38 or a local section opens it. |
| SKL centered `±720` Three-Gear dilation | `−720/0/+720`; `720 = 2 × 360`; examples `262086/262806 BC` as center/selected member | cosmic years-of-years wheel | Exact `360:1` dilation of the local field. Distinct units; not a floating adjustment. |
| SKL nested local-on-macro subrail state | for admitted macro member `M`, coordinate field `M−2/M/M+2` | small teeth within large teeth | Open only under declared phase, Mirror, or rail-closure work. It does not add source rows or evidence. |
| Precessional envelope / Berossus state | `6480`; `12960`; Berossus by `File_34` dependency | SKL / Berossus unification field | Preserved as dependency-controlled; §7 does not fully rederive it. |
| File_34 post-final dependency state | `2370`; `30 + 20 + 30`; `568/566 BC`; `538/536 BC`; `518/516 BC`; `488/486 BC` | post-final SKL / Berossus citation-control state | `File_18` may register these as File_34-controlled dependency labels. It does not rederive the corridor or change local SKL table rows. |
| Same-side BC span state | higher BC minus lower BC | same-axis chronology span | Main arithmetic display in §8. Arithmetic verification is recorded in §0.8 and §8. |
| Civil cross-axis span state | `BC + AD − 1` | BC/AD span | Active where AD targets are opened, including the author-clarified MT cumulative Peleg / Conquest Mirror component checks. |
| Residue / conceptual residual-display state | `300/299`; legacy `299/300`; `365.24`; `365.2422`; `7.5 days`; physical `299/40 = 7.475 days` | Enochian ratio / residue-control field | Author-clarified. File_17 controls the exact `300/299` operator, File_12 controls legacy `299/300` wording and true-solar display, and File_11 controls physical-residue versus conceptual residual-display language. |
| Providential multi-tradition system state | MT; SP; LXX; BJ / Jubilees; SKL; Berossus | interpretive synthesis state | Preserve distinct textual / chronological witness states. Do not overstate demonstrable scribal intent. |
| Formal Mirror state | not active in main `File_18` table source | inactive protocol | Mirror / inverse material remains dependency-controlled unless explicitly opened by a later pass or file. |

### 0.1a Node-class and display-state register

| Date / value / display | Node-class | Active state | Do not collapse with |
|---|---|---|---|
| `3899 BC` | Creation endpoint / Adam table baseline | MT Minimum-Regular | MT Standard-Normal `4114 BC`; Year-6 `3900 BC`; cumulative Adam `14006 BC` |
| `3906–3899 BC` | figurative Creation-week wrapper | MT Minimum-Regular | literal seven-day Creation week by itself |
| `3900 BC` | figurative Year-6 / Adam-as-year display | MT Minimum-Regular | endpoint `3899 BC` |
| `4114 BC` | Creation endpoint under `+215 Sojourn` | MT Standard-Normal | `3899 BC`; Year-6 anchors in `File_07`; rounded MT `4106 BC` |
| `3959 BC` | Terah-only Creation endpoint | MT `+60 Terah` | `3899 BC`; `4114 BC`; `4174 BC` |
| `4174 BC` | maximum Creation endpoint | MT `+275` | Year-6 `4176 BC`; LXX Maximum node-labels in `File_14` |
| `4199 BC` | SP Normal Creation endpoint / preferred chain head | SP Normal / G2 | legacy SP Ideal `4200 BC`; MT `3899 BC`; separately typed Creation-week / Adam-Day nodes |
| `4206–4199 BC` | SP Creation-week wrapper | SP Normal / G2 | SP Ideal wrapper if separately opened |
| `2991/2990 BC` | Shem G1 primary / companion births | SP-local person-station pair | G2 Shem `2993/2992`; Flood start/close pairs; name the Noah-bound or Arphaxad-bound relation |
| `2893→2892 BC` | Flood start→close | SP Normal / G2, native frame | Noah/Shem primary→companion; fixed Arphaxad `2891` |
| `5279 BC` | LXX Creation endpoint | LXX Regular-Minimum | File_13 LXX actual `5494 BC`; File_54 rounded `5486 BC` |
| `5286–5279 BC` | LXX Creation-week wrapper | LXX Regular-Minimum | LXX cumulative Adam `14896 BC` |
| `3023 BC` | LXX Regular-Minimum Flood | LXX corrected Lamech state | LXX cumulative Flood `5745 BC` |
| `1661 BC` | minimum Entry into Egypt | minimum / Sojourn-division state | `1876 BC` shared year-label; `1843 BC` LXX `33 + 397` by dependency |
| `1876 BC` | shared year-label | Entry / Call / convergence by active state | a single event-node |
| `1446 BC` | primary Exodus anchor | fixed epoch | subordinate `1231 BC` Ramesside state by dependency |
| `1406 BC` | Conquest / Moses death | fixed epoch and cumulative anchor | Joshua death `1296 BC` in SP cumulative state |
| `966 BC` | historical Temple foundation | Kings dual-ledger | schematic `1016 BC` |
| `1016 BC` | schematic Triple-`430` Temple pivot | Kings dual-ledger | historical `966 BC` |
| `586 BC` | Fall of Jerusalem endpoint | Kings / Triple-`430` endpoint | adjacent `587/586 BC` states unless opened by dependency |
| `14006 BC` | MT cumulative Adam / Year-6 center | cumulative Moses / Nisan trunk | regular MT Creation endpoint `3899 BC`; apparent `14036 BC` |
| `14009.5 BC` | MT cumulative Adam on Aaron / Tishri trunk | cumulative Aaron line | integer Moses line `14006 BC` |
| `14011–14004 BC` | MT cumulative Adam envelope | cumulative 7-year span | one single date |
| `14036 BC` | cumulative apparent birth | Year-6 +30 overlay | Adam Year-6 `14006 BC` |
| `4831 BC` | MT cumulative Flood / Arphaxad table label | cumulative MT | regular G2 Flood-start rows `2243 BC`, `2893 BC`, `3023 BC` |
| `5291 BC` | restored cumulative Cainan Flood / Arphaxad label | cumulative restored 2nd Cainan | regular restored Cainan `+130` state |
| `5296–5289 BC` | restored cumulative 2nd Cainan Flood Week | cumulative envelope | LXX Creation endpoint `5279 BC`; LXX cumulative Cainan `5280 BC` |
| `4858–4851 BC` | MT Cumulative + 2nd Cainan Cainan envelope | cumulative restored 2nd Cainan | regular restored Cainan `+130`; LXX cumulative Cainan `5280 BC` |
| `4856 BC` | rounded / control coordinate inside the cumulative Cainan field | `16 × 8` expectation / cumulative-Cainan extension state | ordinary regular Cainan birth rows; Protocol 1 Mirror targets |
| `4398–4391 BC` | extended death-window / Shelah convergence envelope | cumulative restored 2nd Cainan; Cainan / Famine envelope-to-envelope state | ordinary regular death rows; the `1878–1871 BC` Famine window unless the `2520` projection is active |
| `4278–4271 BC` | SP cumulative Shelah envelope | cross-tradition 60-multiple Shelah / Plenty-Famine alignment state | MT Cainan / Shelah envelope; LXX Shelah envelope; inactive unless SP cumulative comparison is opened |
| `4825–4818 BC` | LXX cumulative Shelah envelope | cross-tradition 60-multiple Shelah / Plenty-Famine alignment state | MT and SP Shelah envelopes; inactive unless LXX cumulative comparison is opened |
| `1885–1878 BC` | seven years of Plenty | Joseph / Plenty target window by File_16 dependency | Famine window `1878–1871 BC`; the shared `1878 BC` boundary must not collapse Plenty and Famine into one event |
| `1670/1663/1656 BC` | `−215` companion triad to the Plenty / Famine labels | Mirror 60-spine / Terah-Cainan death-rail state | AD-side Mirror labels `AD 1656/1663/1670`; same-order pairing if the constant `3540` is being asserted |
| `1936n BC → 1876n BC → 1816n BC` | Terah / regular restored 2nd Cainan death-date rail | Mirror 60-spine / Terah-Cainan death-rail state | a single event-node or identity of Terah and Cainan |
| `4396 BC` | Cainan death-window member | cumulative restored 2nd Cainan / File_16 dependency | ordinary regular Cainan death rows unless the cumulative state is active |
| `4391 BC` | lower member of the extended Cainan / Shelah convergence envelope | cumulative restored 2nd Cainan; Daniel 8 / Enochian lower-bound comparison by dependency | regular death at `2091 BC`; minimum Entry `1661 BC`; do not collapse without active vector operator |
| `2551–2091 BC` | regular restored 2nd Cainan lifespan member | regular restored 2nd Cainan; `2300` Cainan vector | cumulative Cainan envelope `4858–4851 BC`; the `2336–1876 BC` minimum-span member |
| `2336–1876 BC` | regular restored 2nd Cainan minimum lifespan member | regular-Cainan `460` cross-modal symmetry state | MT Entry node-class at `1876 BC`; cumulative `+460` operator; Cainan death-window state |
| `3921 BC`; `3011 BC`; `2551 BC` | 1Kenan birth, 1Kenan death, and restored 2nd Cainan birth by dependency | Kenan / Cainan tenfold reinforcement state | ordinary MT Minimum-Regular Kenan row unless Gear 3 / restored Cainan is active |
| `6306 BC` | LXX missing-four extension coordinate | LXX Maximum node-label comparison state | LXX Regular-Minimum Creation `5279 BC`; LXX cumulative Adam `14896 BC` |
| `14466 BC` | MT cumulative Adam with restored Cainan | cumulative `+460` | regular restored Cainan `4029 BC`; `1446 BC` Exodus label resemblance |
| `13398 BC` | SP cumulative Adam | SP cumulative square state | SP regular Creation `4199 BC` |
| `1296 BC` | SP Joshua death target | SP cumulative state | Conquest / Moses-death anchor `1406 BC` |
| `14896 BC` | LXX cumulative Adam | LXX cumulative source-table state | LXX regular Creation endpoint `5279 BC` |
| `3856 BC` | LXX cumulative Peleg / BJ Creation correspondence | LXX cumulative / BJ comparative state | LXX regular Peleg; BJ table itself |
| `2906 BC` | Tower / SKL Short base | Sumerian A / SKL Short | SKL Long `2856 BC`; local `+2`; `+30`; `+720` states |
| `2856 BC` | Tower / SKL Long base | Sumerian B / SKL Long | SKL Short `2906 BC` |
| `20886 BC` | SKL Short Flood | Sumerian A / SKL Short | cumulative Floods; SKL Long `27366 BC` |
| `27366 BC` | SKL Long Flood | Sumerian B / SKL Long | SKL Short `20886 BC` |
| `452886 BC` | SKL Short Pre-Creation | Sumerian A / SKL Short | SKL Long Pre-Creation `459366 BC`; +720 rail by dependency |
| `459366 BC` | SKL Long Pre-Creation | Sumerian B / SKL Long | SKL Short Pre-Creation `452886 BC` |
| `262086/262806 BC` | Adam / Alulim center and selected `+720` member | SKL centered `±720` Three-Gear dilation | complementary `261366 BC` macro member; nested local `±2` subteeth; regular Adam rows |

### 0.1b Operator and sign-convention register

| Operator or sign convention | Active form | Scope in `File_18` | Guard |
|---|---|---|---|
| Same-side BC subtraction | higher BC date minus lower BC date | §8 and visible verification rows | Main arithmetic display; locally executable visible rows check under stated operators. |
| Civil cross-axis span | `BC + AD − 1` | Only where AD targets are opened | Not Mirror protocol and not inverse-number logic. |
| `+60 Terah` | add 60 years backward beginning at Terah | regular variant matrix | Doubles the Abraham `±215` field from two states to four states at Terah and then propagates back toward Adam. Does not affect the Abraham → Levi / Joseph field before Terah or the Aaron-forward fixed epoch. |
| `+215 Sojourn` | add 215 years backward where full 430 Egypt position is opened | variant matrix and Entry field | Distinct from Exodus 215 / subordinate Ramesside shift. |
| `+275` | `+60 + 215`; also sequential `60 + 155 + 60` display | four-position variant matrix | Preserve both combined and sequential displays. |
| `±215` | Sojourn-position fork | Abraham → Levi / Joseph field | Produces two date states for Abraham through Levi / Joseph. Not a generic global adjustment and not identical to `+60 Terah`. |
| Shem `±2` | localized bindings in regular; propagated in cumulative | Noah / Shem comparisons; cumulative envelope | Name active mode; do not use localized binding scope to deny ordinary coherent Flood Gears. |
| SP Noah/Shem companion | primary minus one | SP Noah/Shem person-stations only | Count the distinction once per admitted local path; no upstream birth shift and no Flood companion. |
| Flood start→close | start minus one | each ordinary Gear in MT, LXX, and SP | Event-year boundary, independent of the SP Noah/Shem operator. |
| SP inclusive cap capacity | birth−Flood start+1 = birth−Flood close | Adam through Lamech, with declared lifespan count | Inclusive count does not give the nine rows a Noah/Shem companion rail; Noah is excluded from the cap. |
| Regular restored 2nd Cainan | `+130` | regular MT/SP restoration | Begetting-age insertion only. |
| Cumulative restored 2nd Cainan | `+460` | cumulative MT/SP restoration | Lifespan insertion only. |
| `137` checksum | `7 + 130` | boundary checksum where completion and patriarchal `130` states are both opened | Diagnostic only; not a new chronological operator. |
| `138` proportional unit | `1656 ÷ 12 = 138` | `16 × 8` expectation diagnostic | Arithmetic diagnostic only; do not replace the actual `12–8–4–2–0` table-source pattern. |
| Missing-four extension | `4 × 138 = 552` | proportional pre-Adamic extension | Structural diagnostic; does not add four patriarchs. |
| Completed extension | `16 × 138 = 2208` | extension from restored regular Flood Gear rails to cumulative Cainan field | Same-side BC extension only. |
| Cainan-to-Moses lock | `4856 − 1406 = 3450 = 138 × 25` | cumulative Cainan to Moses-death / Conquest terminus | Same-side BC subtraction; not Mirror protocol. |
| Cainan / Famine `2520` projection | `4398/4396/4391 BC − 2520 = 1878/1876/1871 BC` | cumulative Cainan / Shelah envelope to Famine window by `File_16` dependency | Category B pattern-vector witness only; not an alteration of the MT `430` Egypt state. |
| Cross-tradition Shelah `60`-multiple comparison | MT `2520 = 60 × 42`; SP `2400 = 60 × 40`; LXX `2940 = 60 × 49 = 6 × 490` | comparative Shelah-envelope support in §1.3.8 and §6B note | Structural inference / providential synchronization only. MT and SP target the Famine window; LXX targets the Plenty window. Do not collapse target windows or add Category A event nodes. |
| Mirror 60-spine companion | `3540 = 60 × 59`; `3540 + 2400 = 5940 = 60 × 99`; `3540 + 2520 = 6060 = 60 × 101`; `3540 + 2940 = 6480 = 60 × 108` | Mirror companion to cross-tradition Shelah `60`-multiple comparison | Civil cross-axis arithmetic only where AD targets are explicitly opened. The `3540` component requires reversed AD-side endpoint order: `1885 ↔ AD 1656`, `1878 ↔ AD 1663`, `1871 ↔ AD 1670`. Not a table-generation operator. |
| Cainan Daniel 8 `2300` vector | `4851 − 2300 = 2551`; `4391 − 2300 = 2091` | cumulative Cainan envelope to regular restored Cainan lifespan member | Same-side BC subtraction; `2300` does not replace regular `+130` or cumulative `+460`. |
| Inclusive companion `2307` | `4858 − 2551 = 2307`; `4398 − 2091 = 2307` | sanctuary / Hanukkah-style inclusive companion where later dependency opens it | Retained as exploratory / audit companion. It is not promoted to a File_18 operator. |
| Enochian lower-bound `2730` vector | `4391 − 1661 = 2730`; `2730 = 7.5 × 364` | cumulative envelope to minimum Entry lower-bound where EnvSpread / Enochian state is active | Dependency-controlled by File_12 / File_17 / File_16. The solar companion remains audit-controlled. |
| Daniel 12 sandwich | `1260 → 1290 → 1260`; total `3810` | Cainan-to-Exile macro-prophetic witness by File_16 dependency | Same-side BC subtraction; Category B macro-prophetic witness, not a table-generation operator. |
| Kenan / Cainan tenfold relation | `1370 = 10 × 137`; `1370 − 460 = 910`; `910 + 460 = 1370` | Cainan-sector support note | Dependency-controlled by Gear 3 / restored-Cainan state. |
| Aaron/Moses phase offset | `+3.5` | cumulative Aaron / Tishri line | Exact display state; not rounded to `3` or `4`. |
| Apparent age overlay | `+30` | cumulative and SKL apparent modes | Overlay only unless a local section says it propagates. |
| SKL scale | `360:1` | Sumerian Integration | Scale-state; do not use as ordinary biblical-year chronology. |
| SKL `+6480` | variant tier separation | SKL Short / Long and Berossus relation | Full derivation controlled by `File_34`. |
| SKL `+720` | `2 × 360` | scaled Shem `±2` state | Distinct from local `+2`. |
| SKL local `+2` | literal-year local rail | SKL Tower / anchor fine-tuning | Distinct from scaled `+720`. |
| `25/23`; `70/69`; `300/299` | exact-rational operators by dependency | Key-of-23, prophetic, Enochian contexts | Do not decimalize or invert without naming the active state. |
| Residue Protocol | physical / residual display only where opened | 299/300 residue audit line | Not ordinary Key-of-23 whole-year conversion. |
| Literal/precise monarchy rail | `1050→1010→970→930`; each step `40` | United Monarchy chronology | Distinct from Rounded and schematic ledgers. |
| Rounded monarchy rail | `1051→1011→971→931`; each step `40` | File_51a mod-5 comparison | Distinct from literal chronology. |
| Rounded Moses/Aaron links | `1531−971=560`; `1526−966=560` | Rounded Scaffold comparison | Does not redefine literal `966 BC`. |
| Kings `+50` Jubilee Offset | `1016 − 966 = 50` by dependency | Kings dual-ledger state | Does not change historical `966 BC`. |

### 0.1c Slash-pair, range, envelope, and display-state register

| Form | Type | Active state | Handling |
|---|---|---|---|
| `3906–3899 BC`; `4206–4199 BC`; `5286–5279 BC` | Creation-week wrapper ranges | regular Creation endpoint states | Ranges / blocks, not single anchors. |
| `70/130` | Terah begetting-age slash-pair | MT regular table | Ordered source display for Terah's dual begetting logic; not a range. |
| `2991/2990 BC`; `2391/2390 BC` | SP Shem G1 primary / companion pairs | SP Shem Superposition, native frame | First members pair together, and second members pair together; each lifespan is `600`. Name the binding. G2 is `2993/2992` and `2393/2392`. |
| `145 (205)` | SP Terah lifespan pair | SP Terah dual-lock | Textual / architectural pair; preserve both. |
| `.5` labels | half-year display | Aaron / Tishri cumulative track | Exact display states; do not floor unless a display operator is named. |
| `14011–14004 BC`; `4836–4829 BC`; `5296–5289 BC` | cumulative 7-year envelopes | cumulative MT / restored Cainan | Envelopes with internal members; not one date. |
| `4716–4709 BC`; `14901–14894 BC` | cumulative comparison envelopes | SP / LXX cumulative | Preserve as table envelopes. |
| `1878–1871 BC` by dependency | famine-window envelope | File_16 dependency | Not locally tabulated as a main File_18 anchor unless opened by dependency. |
| `4398–4391 BC → 1878–1871 BC` by dependency | projected envelope-to-envelope relation | Cainan / Famine macro-vector state | Uses `2520`; component labels must remain distinct and non-collapsed. |
| `1050t/n→1010t/n→970t/n→930t/n BC` | literal/precise monarchy phase rail | Kings / File_08 dependency | Compact `t/n` means phase-admissible same-year alternatives, not a Mirror slash-pair or uncertainty range. |
| `1051n→1011n→971n→931n BC` | Rounded monarchy rail | File_51a dependency | Mod-5 comparison state; not literal chronology. |
| `587/586 BC`; `967/966 BC` by dependency | adjacent date-state slash-pairs | Kings / File_08 / File_14 dependencies | Preserve as adjacent states if opened; File_18 uses `966 BC` and `586 BC` as primary displayed anchors. |
| `2906/2856 BC`; `20886/27366 BC`; `452886/459366 BC` | SKL Short / Long paired states | Sumerian A / B | Paired states, not ordinary uncertainty ranges. |
| `262086/262806 BC` | SKL +720 rail pair | scaled Shem `±2` | Scale-state pair, not local `±2`. |
| `3658/3656/3608/3606 BC` | SKL fine-tuning display cluster | +720 / +30 / +2 dependency field | Source-retained display cluster; full derivation remains `File_34`-controlled. |
| `599+` / conventional `600` | ordinal / cardinal counting distinction | SP Noah/Shem local paths | Qualify each interval; not a Flood uncertainty range. Each Gear has an independently typed Flood start→close year. |
| `3 months and 3.5 days` | SKL textual-datum display | Sumerian B / SKL Long dependency | Month/day datum is preserved separately from whole-year local arithmetic. |

### 0.1d Modal-state processing rules

1. `File_18` is a table-source file. A table value should be read under its local state before it is used as proof in another file.
2. Regular and Cumulative chronologies are different methods. Regular uses begetting ages; Cumulative stacks lifespans.
3. A shared date-label does not create identity. This is especially important for `1876 BC`, `1406 BC`, `4831 BC`, `5291 BC`, and `3856 BC`.
4. Creation endpoint states and Year-6 / Adam states remain distinct. Endpoint rows mark Day 7 / Year 7 completion; Year-6 / Adam rows are separate node-classes.
5. The MT Minimum-Regular, MT Standard-Normal / `+215 Sojourn`, MT `+60 Terah`, and MT `+275` positions are simultaneous variant states, not corrections of one another.
6. The Abraham → Levi / Joseph `±215` field gives two possible date states. Terah then opens the `+60 Terah` hinge, doubling the field to four states in the normal no-2nd-Cainan Adam-to-Terah field. If restored 2nd Cainan is explicitly inserted, 2nd Cainan through Terah remains four-position, while Arphaxad / Flood through Adam becomes eight-position.
7. The `12–8–4–2–0` shorthand must be read as a structural funnel: generation-count blocks `12 → 8 → 4 → 2`, paired with possible-date states `8 → 4 → 2 → 0` when restored 2nd Cainan is explicitly opened. It is not a mere boundary list.
8. The restored/native 2nd Cainan 27-generation completion state extends the Pentateuchal Funnel to Moses: `12 + 8 + 4 + 2 + 1 = 27 = 3 × 3 × 3`. This is a secondary generation-count / typological layer. Do not let it overshadow the primary `12–8–4–2–0` variant-count ladder or the operative 8-date / 4-date / 2-date / 0-date block logic. Do not use this theological / structural state to add dates to Kohath, Amram, Aaron, or Moses, and do not erase the ordinary fixed-anchor rule from Aaron / Moses onward.
9. The fixed epoch from Aaron onward uses fixed anchors unless a dependency explicitly opens another state.
10. SP Noah/Shem alone receive the adjacent `−1` companion rail. Flood start→close is an independent event-year span within ordinary three-Gear transport in MT, LXX, and SP. SP cap counts are inclusive to Flood start. With other variant settings held, Arphaxad onward remains fixed under Gear and the SP companion mechanism.
11. The September 8 2026 ruling uses Lamech `182/753` in the main LXX Regular and Cumulative reconstructions. `571` is calculated only; `188` is non-operative transmitted data; LXX `777` and its dependent comparisons are appendix-only. See §4A and Appendix B.
12. Regular restored 2nd Cainan uses `+130`; cumulative restored 2nd Cainan uses `+460`; LXX native Cainan requires no restoration.
13. Cumulative `.5` labels belong to the Aaron / Tishri trunk and must not be silently rounded.
14. Cumulative 7-year spans are envelopes. A stated upper, lower, or internal member must be preserved as a member-label. The MT cumulative Peleg row has a Nisan envelope `3501n–3494n BC` and a parallel Tishri envelope `3502t–3495t BC`; its Mirror relation to the Conquest / land-rest envelope must be evaluated component-wise.
15. Sumerian A / SKL Short, Sumerian B / SKL Long, `+30 Apparent Mode`, the selected local `+2` member, the full local `−2/0/+2` wheel, the selected macro `+720` member, the full SKL `−720/0/+720` dilation, and `+6480` variant-tier logic must remain distinct by unit and state.
16. The SKL appended `3 months and 3.5 days` datum is preserved as a textual / dependency-controlled state, not as a local whole-year operator.
17. The Cainan macro-vector state is a File_16 dependency layer, not a new File_18 table-generation operator. `2300`, `2307`, `2520`, `2730`, and `1260 → 1290 → 1260` may be cited from File_18 table values only when the active vector state and target node-class are named.
18. No broad Mirror protocol or inverse-number operator is active in the main body of `File_18`. The author-clarified MT cumulative Peleg row opens a bounded File_09-style phase-resolved Mirror coordinate-completion state only for that Peleg / Conquest relation. Mirror, civil cross-axis span, `10x` scaling, and inverse-number reversal must still be named separately.
19. The 299 / 300 residue line is now author-clarified as a dependency-controlled residue / conceptual residual-display state. The active Enochian ratio is `300/299`; legacy `299/300` wording is source-history / inverse-caption language; physical residue and conceptual residual-display must remain distinct.
20. The literal/precise United Monarchy is `1050t/n→1010t/n→970t/n→930t/n BC`. The Rounded Scaffold United Monarchy is `1051n→1011n→971n→931n BC`. The old mixed `1011→971/970→931 BC` row must not be restored as Actual / Historical.
21. `966 BC` is a shared year label: literal cardinal Temple foundation from `1446 BC`, and Rounded `560`-year landing from Moses `1526n BC`. Shared label does not collapse state or operator.

### 0.2 File map

| Section | Function | Active state / operator |
|---|---|---|
| §0 | File-function, audited modal-state register, current amendment hierarchy, node-class / display-state register, operator register, File map, terminology controls, Machine Guards, source-control notes, and argument controls | file-level controls; non-collapse guards; claim-status controls |
| §0A | Fractal Self-Constraint Principle | vertical scale-state / multi-witness framework |
| §1 | Variant mechanism, Pentateuchal Funnel, `137` checksum, bounded cumulative-Cainan extension, and Cainan macro-vector controls | `+60 Terah`; `+215 Sojourn`; `+275`; Shem `±2`; Cainan `+130` / `+460`; `137 = 7 + 130`; `16 × 8` diagnostic; `4 × 138 = 552`; `2300`; `2520`; `2730`; Pentateuchal Funnel state; File_16 dependency |
| §2 | MT Regular baseline | MT Minimum-Regular; Kings dual-ledger dependency |
| §3 | SP Regular baseline | SP Normal / G2; ordinal/completed local paths; inclusive cap; universal Flood Gears; Noah/Shem companion field and named bindings |
| §4 | LXX Regular baseline | LXX Regular-Minimum; Smith source-reconstruction witness; native 2nd Cainan; Abraham / Terah `2 × 2` variant field |
| §4A | Common LXX Lamech reconstruction and bounded transmission hypothesis | main `182/753`; cross-Gear `69/529/598`; generated `+6` comparisons; source distinction |
| §5 | Source-numbering note | supplied source has no Section 5 |
| §6 | Cumulative chronology matrix | cumulative MT; cumulative 2nd Cainan; SP cumulative; LXX cumulative |
| §7 | SKL Integration | Sumerian A / SKL Short; Sumerian B / SKL Long; `+6480`; `+720`; `+30`; `+2`; File_21 application controls |
| §8 | Arithmetic verification table and argument-control notes | same-side BC subtraction; exact spans checked where locally executable; claim-status controls |
| §9 | Cross-reference index | dependency tracking |
| Appendix A | Website table adjustments | source-history conversion notes |
| Appendix B | LXX `777` preservation and subsidiary comparisons | non-propagating overlay; Smith reconstruction; supporting arithmetic only |
| Audit notes | Retains unresolved dependency and audit controls | audit notes; dependency boundaries |
| Unresolved issues | Lists retained non-blocking controls | source-history and dependency controls |


### 0.2A Current amendment hierarchy

This table states the current hierarchy for the post-final Cainan / Funnel material. It governs how §§1.3.1–1.3.7 should be read.

| Layer | Material | Claim-status / state | Handling |
|---|---|---|---|
| Primary table-source layer | Regular, cumulative, and SKL baseline tables | Governing table-source layer | Baseline rows remain the controlling data source. Variants require named operators. |
| Primary variant-count layer | `12–8–4–2–0` ladder and `8–4–2–0` possible-date countdown | Governing structural layer when restored/native 2nd Cainan is active | Controls the Pentateuchal Funnel and variant-date countdown. |
| Secondary completion layer | `12 + 8 + 4 + 2 + 1 = 27 = 3 × 3 × 3` | Arithmetic fact when restored/native 2nd Cainan is active; structural inference for its architectural role | Must not obscure the primary `12–8–4–2–0` table mechanics. |
| Typological bridge | Noah / Moses `tebah`; `8` souls; Moses as final deliverer | Typological / theological note | Explains meaning but does not create a chronological operator. |
| Diagnostic checksum layer | `137 = 7 + 130`; Shem dual-`100`; `16 × 8`; `4 × 138 = 552`; `16 × 138 = 2208` | Structural diagnostic / providential synchronization where invoked | Does not alter the genealogy, does not add four patriarchs, and does not replace the visible `12 × 8` pattern. |
| Cainan-sector reinforcement | 1Kenan / 2nd Cainan `1370 = 10 × 137`; `910 + 460 = 1370` | Structural reinforcement | Supports the bounded File_18 amendment only; deeper Cainan-sector branches remain dependency-controlled. |
| Cainan macro-vector layer | `2300`; `2520`; `2730`; `2307`; `1260 → 1290 → 1260` from the cumulative Cainan / Shelah field | Category B macro-prophetic witness by File_16 dependency | Supports the Pentateuchal Funnel / 1876 BC Nexus relation. It does not alter table rows, variant-count mechanics, or Cainan `+130` / `+460` operators. |

### 0.3 Terminology controls

| Source form | Public-clean handling |
|---|---|
| `FILE_18`; `FILE_00`; etc. | Normalized to `File_18`, `File_00`, etc. |
| `MT Minimum`; `MT min` | Normalized where needed to `MT Minimum-Regular`; source-history wording retained where the source explicitly explains legacy usage. |
| `MT Standard`; `MT +215` | Normalized where needed to `MT Standard-Normal / +215 Sojourn`. |
| `Terah +60` | Normalized to `+60 Terah`. |
| `Sojourn +215` | Normalized to `+215 Sojourn`. |
| `Regular (Short)` | Preserved as Regular chronology with Short as legacy term. |
| `Cumulative (Long)` | Preserved as Cumulative chronology with Long as legacy term. |
| `SP Normal`; legacy `Toggle ON` | Preferred `SP Normal / G2`; use interval-specific counting and SP-local Noah/Shem primary/companion labels. Legacy Toggle language does not authorize a whole-chain shift. |
| `SP Ideal`; exclusive reckoning | Preserved as `SP Ideal / Exclusive`. |
| `LXX Minimum` | Normalized to `LXX Regular-Minimum`. |
| `Sumerian`, primary rail | Normalized to `Sumerian A / SKL Short` where the 17980-year state is active. |
| `Sumerian`, +6480 rail | Normalized to `Sumerian B / SKL Long` where the 24510-year state is active. |
| `±30`; local `±2`; macro `±720` in SKL | Label `+30 Apparent Mode` separately; use full centered local `−2/0/+2` and SKL `−720/0/+720` when the wheel is active; retain `+2` / `+720` only for selected-member rows. |
| Comma-form numbers | Normalized to no-comma format, e.g. `6480`, `14466`, `453600`. |

### 0.4 Machine Guards for `File_18`

Machine Guard [FILE_18 RAW DATA SOURCE]:

`File_18` supplies table values and baseline dates. It must not silently promote a baseline row into a proof of a later file's full argument. Where another file controls the argument or operator, retain the row as a data dependency.

Machine Guard [FILE_18 REGULAR / CUMULATIVE CAINAN]:

Regular restored 2nd Cainan uses `+130`. Cumulative restored 2nd Cainan uses `+460`. LXX already includes 2nd Cainan in the relevant baseline. Do not feed the regular `+130` insertion into cumulative lifespan arithmetic.

Machine Guard [FILE_18 SHEM ±2]:

In Regular chronology, the localized Shem `±2` anomaly governs Noah/Shem bindings and qualified endpoint comparisons. Ordinary coherent Gear transport also applies to the Flood and other admitted pre-Flood biographies; see §3.1.4. At held variant settings, Arphaxad onward remains fixed under regular Gear. In Cumulative chronology, the anomaly propagates through the cumulative chain and creates the 7-year margin. Keep these mechanisms and domains distinct.

Machine Guard [FILE_18 KINGS DUAL LEDGER]:

`966 BC` is the historical Temple foundation anchor. `1016 BC` is the schematic Triple-`430` pivot generated by the `+50` Jubilee Offset. Do not let either ledger overwrite the other.

Machine Guard [FILE_18 LITERAL / ROUNDED MONARCHY NON-COLLAPSE]:

The literal/precise United Monarchy is `1050t/n→1010t/n→970t/n→930t/n BC`. The Rounded Scaffold rail is `1051n→1011n→971n→931n BC`. Do not label the Rounded rail Actual / Historical, and do not move the precise phase rail backward by one year.

Machine Guard [FILE_18 966 SHARED-LABEL]:

`966n BC` may function as the literal cardinal Temple foundation and as the Rounded `1526n→966n=560` landing. Shared year label does not create identity of source state, origin, or operator.

Machine Guard [FILE_18 SKL NESTED THREE-GEAR RAILS]:
File_11's ordinary Three-Gear field is `+0/+2/+4` in absolute notation and `−2/0/+2` when centered on Gear 2 / Shem. Under the SKL `360:1` scalar, the centered field is `−720/0/+720`. Sumerian A / SKL Short, Sumerian B / SKL Long, `+30 Apparent Mode`, the local and macro wheels, and `+6480` remain distinct states and units. Existing `+2` and `+720` table rows are selected-member displays, not the complete topology; each admitted macro member may carry a nested local `−2/0/+2` subrail only when explicitly opened. No nested subrail creates a new raw table row, source witness, or Primary anchor.

Machine Guard [FILE_18 CREATION ENDPOINT / YEAR-6]:

Creation endpoint rows mark Day 7 / Year 7 completion. Year-6 / Adam states are related but distinct node-classes. Do not use `3899 BC`, `4114 BC`, `4174 BC`, or `5279 BC` as if they were the same node-class as Year-6 / Adam states such as `3900 BC`, `4116 BC`, or cumulative `14006 BC`.

Machine Guard [FILE_18 TERAH FOUR-POSITION FIELD]:

Abraham has two birth states, `1951 BC` and `2166 BC`, generated by the `±215` Sojourn fork. Terah has four birth/death states because `+60 Terah` doubles that field: `2021–1816 BC`, `2081–1876 BC`, `2236–2031 BC`, and `2296–2091 BC`. Do not force a single Terah begetting-age display across all four states. The no-`+60` rows use the `70` begetting-state; the `+60 Terah` rows use the `130` begetting-state. Restored 2nd Cainan may double Arphaxad / Flood through Adam only where explicitly opened; it does not make 2nd Cainan itself eight-position.

Machine Guard [FILE_18 1876 YEAR-LABEL]:

`1876 BC` is a shared year-label. Depending on active state, it may mark Jacob's Entry under MT `430`, Abraham's Call / Death of Terah under Sojourn-division paths, Jacob's return from Haran under LXX `33 + 397` by dependency, or another convergence witness. Do not collapse these node-classes.

Machine Guard [FILE_18 SP NOAH/SHEM LOCALITY + FLOOD GEAR SEPARATION]:

The SP companion operator is primary minus one for Noah/Shem person-stations only. Native G2 Noah is `3493/3492`, Shem `2993/2992`, Noah death `2543/2542`, and Shem death `2393/2392`. G1 Shem `2991/2990` with deaths `2391/2390` remains available under named bindings; only `2991→2891` is the displayed full-100 Arphaxad-bound relation. Do not propagate the companion into Adam through Lamech or Arphaxad onward, and do not transfer it to MT/LXX. Native G2 Lamech is `3545→2893`, `653` inclusive. Flood `2893→2892` is a start→close event pair, not a companion pair. All three traditions retain ordinary Flood Gears and independent one-year Flood spans; §3.1.4 supplies the exact table. LXX is native Cainan ON in that comparison. Keep the G2 `654+654` midpoint to fixed Arphaxad separate from the G1 Lamech-death / Flood-start / Arphaxad coordinate convergence.

Machine Guard [FILE_18 CUMULATIVE ENVELOPES]:

Cumulative 7-year spans such as `14011–14004 BC`, `4836–4829 BC`, and `5296–5289 BC` are envelopes. They are not single anchors, and `.5` labels in the Aaron / Tishri line must not be silently rounded or converted into ordinary Nisan labels.

Machine Guard [FILE_18 MT CUMULATIVE PELEG MIRROR]:

The MT cumulative Peleg row must preserve both the Nisan span `3501n–3494n BC` and the parallel Tishri span `3502t–3495t BC`. The Conquest / land-rest counterpart is `1406n–1399n BC` and `1407t–1400t BC`. Under File_09 phase-resolved Mirror suffix inversion, the AD-side display is `AD 1399t/1400n–1406t/1407n`. Component checks use `BC + AD − 1` and equal `4900`; do not treat `3495t` as an error or as an ordinary upper-member label.

Machine Guard [FILE_18 LXX REGULAR / CUMULATIVE]:

The main LXX reconstruction retains the attested/transmitted LXX lifespan `753` (Genesis 5:31) with restored operative begetting age `182` in both Regular and Cumulative execution. `753` itself is not reconstructed; its retention as the preferred original LXX lifespan is the author-adopted textual/structural judgment of §4A.1. The remainder `571 = 753 − 182` is calculated, not an identified manuscript reading. No surviving joint `182/753` attestation has been identified in the reviewed sources; this qualification concerns the combined biography, not the attestation of `753`. Regular begetting paths and cumulative lifespan paths remain distinct methods, but Lamech's selected lifespan no longer changes between them. LXX use of MT `777` is an appendix overlay confined to Appendix B and appendix-routed downstream comparisons; its cumulative overlay is row-local and must not propagate into the `753` chain. MT `777` and Nahor's controlled LXX `208` remain unchanged. The transmitted `188` is non-operative: its possible Key-of-23 origin is a structural/transmission hypothesis, not an admitted main-chain variant.

Machine Guard [FILE_18 LAMECH KEY / TRANSMISSION]:

File_18 §4A records exact arithmetic within declared chronological states and an author-favored Key-of-23 crossover hypothesis. Neither harmonic compatibility nor a generated `+6` endpoint proves a historical scribal sequence or a joint `182/753` manuscript. The continuous LXX `3336 → 3267 → 2738 BC` comparison is cross-Gear (`69 + 529 = 598`), not a replacement of Shem's `600`-year lifespan. The MT `3127 → 3058 BC = 69` and `3056 → 2458 BC = 598` are separately located intervals; their relationship must not be presented as one attested continuous MT three-node partition. Gain-transfer, anchored expansion, and whole-biography translation must be distinguished. `188`-based comparison outputs remain non-operative, and applying `188` to the otherwise unchanged birth chain does not preserve its `1656` total.

Machine Guard [FILE_18 RESIDUE / KEY-OF-23]:

Ordinary Key-of-23 whole-year conversion is distinct from the Residue Protocol. The active Enochian ratio is `300/299`. Legacy `299/300` wording remains only source-history / inverse-caption language. The displayed `365.24` form does not by itself yield `7.5` days; File_12's true-solar reference yields `7.4178` days, while File_11 classifies the `7.5 days` value as Enochian conceptual residual-display and distinguishes it from physical residue. Do not feed day-display residue values into civil-year arithmetic unless a local Residue Protocol or calibration operator is explicitly opened.

Machine Guard [FILE_18 137 CHECKSUM]:

The `137` recurrence is a boundary checksum, not a new chronological operator. It may be cited as `7 + 130` where a seven-year completion field and a `130` patriarchal hinge are both active. Do not use `137` to create additional birth-date states for Kohath, Amram, Aaron, or Moses. Do not collapse explicit lifespan `137` values with `7 + 130` begetting-wrapper values unless the active state is named.

Machine Guard [FILE_18 SHEM DUAL-100 STATE]:

Do not force Shem's `100` into a single chronological state. Shem is `100` at the Flood in the Noah-bound / Flood-bound state, and `100` at Arphaxad's birth in the Arphaxad-bound / text-bound state. The repository preserves both as valid modal states, analogous to Terah's `70/130` begetting-state display. Do not use either state to erase the other.

Machine Guard [FILE_18 16-EXPECTATION RESTRAINT]:

The `16 × 8` expectation is a structural diagnostic, not a revision of the File_18 table-source pattern. The visible funnel remains `12 × 8`, and the `12` has its own Pentateuchal logic. The proposed missing-four extension must not be used to add four patriarchs before Adam or to alter the regular genealogy. Its function is proportional: `4 × 138 = 552`, producing a pre-Adamic extension that lands on the cumulative 2nd Cainan field. Classify the result as structural inference / providential synchronization unless later proof promotes it.

Machine Guard [FILE_18 EXTENSION / OPERATOR FIREWALL]:

The `137`, `138`, `552`, `2208`, `3450`, and `4856 BC` relations are diagnostics and structural checks. They do not become new operators. Regular restored Cainan still uses `+130`; cumulative restored Cainan still uses `+460`; civil cross-axis spans still use `BC + AD − 1`; same-side BC spans still use subtraction.

Machine Guard [FILE_18 CAINAN-SECTOR RESTRAINT]:

The 1Kenan / 2nd Cainan reinforcement is included only to support the `137` checksum and the `16 × 8 / 552 → cumulative Cainan` extension. Do not expand File_18 into every Cainan-sector branch. Relations such as `8970`, `9100`, `130 + 330`, `7800`, `2300`, and `6900` remain controlled by File_11, File_16, File_22, or later Cainan-sector files unless explicitly opened.

Machine Guard [FILE_18 CAINAN MACRO-VECTOR FIELD]:

`File_18` supplies the cumulative Cainan table-source values used by the File_16 Cainan macro-vector: `4858–4851 BC`, `4398–4391 BC`, selected member `4396 BC`, regular Cainan lifespan members `2551–2091 BC` and `2336–1876 BC`, and lower-bound Entry `1661 BC`. The macro-vector calculations are Category B pattern-vector material by File_16 dependency. They do not alter the primary `12–8–4–2–0` Pentateuchal Funnel, do not add new table rows, and do not replace regular `+130` or cumulative `+460` Cainan handling.

Machine Guard [FILE_18 SHELAH MIRROR 60-SPINE]:

The Mirror `3540 = 60 × 59` companion is table-source support only. It uses civil cross-axis arithmetic with reversed endpoint order: `1885n BC ↔ AD 1656n`, `1878n BC ↔ AD 1663n`, and `1871n BC ↔ AD 1670n`. Same-order pairing of `1885/1878/1871 BC` with `AD 1670/1663/1656` does not yield a constant `3540`. The Terah / Cainan death rail `1936n BC → 1876n BC → 1816n BC` preserves variant death-date labels only; it does not identify Terah and Cainan as the same node-class and does not create a File_18 proof operator.

Machine Guard [FILE_18 2307 / SOLAR AUDIT]:

The `2307` inclusive companion and the solar `7.5 × 365` comparison are retained as audit-controlled companion notes unless a later sanctuary / Hanukkah / phase-resolved calendar file opens the operator explicitly. The exact executable Enochian lower-bound line in this file is `4391 − 1661 = 2730 = 7.5 × 364`.

Machine Guard [CANONICAL MARKDOWN / DERIVED AI FORMATS]:

This source remains canonical Markdown. RAG metadata, Knowledge Graph records, JSON, JSONL, prompt-response pairs, and embedding metadata are derived extraction layers and must not replace the source file's arithmetic, modal states, operators, node-classes, claim-status labels, or dependency boundaries.

## 0A. The Fractal Self-Constraint Principle

Source status:
Master Axiom.

Claim-status note:
This subsection states the file's architectural axiom. It is preserved as structural inference and theological / methodological framing. It does not replace table arithmetic, local state labels, or dependency-controlled derivations.

### 0A.1 Core statement

Under this source axiom, patterns established at one scale are not isolated. They propagate both upward to cosmic scales and downward to historical / literal scales. The claim is methodological and architectural: local values must remain compatible with the broader scale-state framework.

### 0A.2 Implication for methodology

Under the Fractal Self-Constraint Principle, dates and values are treated as discovered within the source's pattern constraints rather than freely chosen. Local consistency therefore remains subordinate to global state consistency.

Example:
The `720`-year span from Days 6–7 at the Creation-week level is treated by the source as requiring corresponding expressions at other active scales:

| Scale | Expression |
|---|---:|
| Historical scale | 720 days = 2 years |
| Cosmic scale | 720 years |
| Ultra-cosmic scale | 259200 years = `720 × 360` |
| Fine-tuning layer | `±2` at every scale, e.g. `2886/2888 BC`, `3606/3608 BC` |

### 0A.3 Test of authenticity

Claim-status:
Structural inference and theological / methodological axiom.

A proposed date or value is treated as weak if it solves a local table problem while breaking the stated pattern at another active scale. A proposed date or value is treated as stronger when it remains compatible across the relevant scale states, traditions, and operators. The source's design language is preserved as the theological interpretation of that multi-scale constraint.

### 0A.4 Relationship to the multi-witness principle

Under the source's multi-witness framework, MT, LXX, SP, and SKL are expected to harmonize horizontally across traditions and vertically across scale states. This is preserved as structural inference and providential-synchronization language, not as a claim that every alignment proves direct scribal intent.

### 0A.5 Predictive power

The source uses this principle to propose candidate values before verification. A candidate value becomes argumentatively useful only after the relevant table, state, operator, or dependency check supports it.

## 1. The Variant Mechanism

### 1.1 The `60 + 155 + 60` pattern

Active state:
Regular chronology; four-position variant matrix.

All three manuscript traditions share this fork structure from Adam to Terah's death.

| Position | Applied variants | Gap from previous | Example, MT Adam |
|---|---|---:|---:|
| Minimum | Neither | — | 3899 BC |
| `+60` only | `+60 Terah` | +60 | 3959 BC |
| `+215` only | `+215 Sojourn` | +155 | 4114 BC |
| Maximum | Both `+60 Terah` and `+215 Sojourn` | +60 | 4174 BC |

Note:
The `+155` gap occurs because `215 − 60 = 155` when variants are applied sequentially.

### 1.2 Inter-tradition gaps

Active state:
Literal versus harmonic gap comparison.

The shift of the SP baseline to `4200 BC` creates literal integer gaps, `301` and `1079`, that differ from the harmonic ideals, `300` and `1080`, by exactly 1 year. These are resolved through Gear 2 and reckoning mechanisms.

| Gap vector | Literal gap | Harmonic goal | Resolution mechanism |
|---|---:|---:|---|
| MT → SP | 301 years | 300 years | Spider Gear `299 → 300`: the gap between SP `4200 BC` and MT Gear 2 `3901 BC` is 299 years. This converts to 300 Enochian years through the Key of 23. |
| SP → LXX | 1079 years | 1080 years | Reckoning differential: `1079` exclusive → `1080` inclusive. This matches the `3 × 360` prophetic cycle. |
| MT → LXX | 1380 years | 1380 years | Invariant total: `301 + 1079 = 1380 = 3 × 460`. |

#### 1.2.1 The 7.5-day Creation residue

Active state:
Residue / Enochian comparison after Arithmetic Pass; audit-controlled.

The 299-year solar interval, derived from the 301-year literal gap through Gear 2, generates a specific residue when converted to the 300-year harmonic.

Source-retained math:

```markdown
(299 × 365.24) − (300 × 364) ≈ 7.5 days
```

Source-retained result:
Claim-status: structural inference / residue-display claim.
The source interprets the gap as generating the Full Creation Week, `7` days plus `0.5` straddle, thereby supporting the 301-year distance once the active residue-display state is named.

Arithmetic note:
Arithmetic-control checking verified that the displayed source expression does not produce `7.5` days by ordinary arithmetic: `(299 × 365.24) − (300 × 364) = 6.76` days. Using the true-solar reference named by `File_12`, `(299 × 365.2422) − (300 × 364) = 7.4178` days. Current source-state control classifies the source's `≈ 7.5 days` as conceptual residual-display / calibration language rather than ordinary arithmetic from the abbreviated `365.24` display. Current dependency controls identify `File_17` for the exact `300/299` ratio, `File_12` for legacy `299/300` wording and true-solar display, and `File_11` for physical-residue versus conceptual residual-display distinctions. The supplied source also cites `File_28`, Section 1, which remains a legacy dependency not needed to proceed with the current File_18 revision.

Cross-reference:
Gear logic: `File_11`, §3. Exact ratio: `File_17`; legacy 299/300 wording and true-solar display: `File_12`; physical-residue / conceptual residual-display distinction: `File_11`, Appendix B; legacy source also cites `File_28`, §1.

### 1.3 Epoch structure and Cainan / Funnel control module

Active state:
Variant-application epochs; restored/native 2nd Cainan state where named.

This section contains the primary variant-count architecture and its bounded secondary diagnostics.

Hierarchy rule:
The primary File_18 pattern is the `12–8–4–2–0` variant-count ladder and its corresponding `8–4–2–0` possible-date countdown. The 27-generation completion, tebah / ark typology, `137` checksum, Shem dual-`100`, `16 × 8` expectation, cumulative-Cainan extension, and 1Kenan / 2nd Cainan reinforcement are subordinate layers. They may support the architecture, but they must not alter the table-source mechanics.

| Tier | Subsections | Function |
|---|---|---|
| Primary epoch boundary | §1.3 overview | Establishes where variants begin and stop. |
| Primary variant mechanics | §§1.3.1–1.3.2 | Abraham / Terah / 2nd Cainan boundary and Pentateuchal Funnel. |
| Secondary completion | §1.3.3 | 27-generation completion and tebah / ark typological bridge. |
| Diagnostic checksum and extension | §§1.3.4–1.3.6 | `137`, Shem dual-`100`, `16 × 8`, and cumulative-Cainan extension. |
| Reinforcement and restraint | §1.3.7 | 1Kenan / 2nd Cainan tenfold reinforcement; branch restraint retained. |
| Macro-vector dependency layer | §1.3.8 | Cumulative Cainan / Shelah envelope used as File_16 source field for `2300`, `2520`, `2730`, and Daniel 12 sandwich vectors. |

Primary epoch map:

| Epoch | Date range | Variants | Mechanism |
|---|---|---:|---|
| Adam → Terah's death | Creation to approximately 1816 BC | 4 in the no-2nd-Cainan table state; 8 upstream from Arphaxad / Flood where restored/native 2nd Cainan is active | Full `60 + 155 + 60` matrix; Cainan hinge where named. |
| Abraham → Levi / Joseph | 1951–1567 BC, minimum | 2 | `±215` only. |
| Aaron's birth onward | 1529 BC → | 1 | Fixed; no variants. |

#### 1.3.1 Abraham / Terah / 2nd Cainan variant multiplication

Author clarification:
From Levi / Joseph back to Abraham, the active field has two possible dates because of the `215`-year Sojourn variant. Terah introduces the next variant, `+60 Terah`, doubling the field from two to four. In the ordinary no-2nd-Cainan regular table, those four positions extend from Terah back to Adam. When the 2nd Cainan hinge is active, the boundary changes: 2nd Cainan himself still has four possible dates, like Terah; Arphaxad / Flood and every patriarch back to Adam absorb the additional 2nd-Cainan hinge and therefore become eight-position.

Tradition-scope clarification:
This multiplication is not MT-local. MT, SP, and LXX encounter the fork sequence at the same genealogical locations: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary. The arithmetic status differs by tradition. MT / SP receive Cainan by restoration when that state is opened. LXX already contains Cainan in its regular baseline, so the LXX form is a native-Cainan boundary state unless a theoretical removal / reinsertion state is explicitly opened.

| Epoch / boundary | Active variants | Possible explicit date states | Handling |
|---|---|---:|---|
| Adam → Arphaxad / Flood | `±215 Sojourn × +60 Terah × restored 2nd Cainan` where opened | eight states | Active only if restored 2nd Cainan is explicitly inserted. Arphaxad is synonymous with the Flood / Ark-exit conception boundary and is the first upstream row to absorb the Cainan hinge. |
| 2nd Cainan → Terah | `±215 Sojourn × +60 Terah` | four states | 2nd Cainan, Shelah, Eber, Peleg, Reu, Serug, Nahor, and Terah remain four-position. |
| Abraham → Joseph / Levi | `±215 Sojourn` only | two states | Abraham birth `1951/2166 BC`. |
| Kohath → Amram | no direct regular-date anchor | zero explicit pivot states | These generations float inside the Sojourn envelope because the repository uses the global `430/215` spans rather than daisy-chaining overlapping lifespans. |
| Aaron / Moses onward | none in this table | fixed anchors | Fixed anchors such as `1446 BC` and `1406 BC`; Aaron / Moses are unaffected by the regular Abraham / Terah / 2nd Cainan variant multiplication. |

Restored 2nd Cainan dates under the four-position downstream field:

| Shelah birth state | 2nd Cainan birth | 2nd Cainan death | Active variant-state |
|---:|---:|---:|---|
| 2481 BC | 2611 BC | 2151 BC | `+275`; `+60 Terah` and `+215 Sojourn` active |
| 2421 BC | 2551 BC | 2091 BC | `+215 Sojourn` active; no `+60 Terah` |
| 2266 BC | 2396 BC | 1936 BC | `+60 Terah` active; minimum Sojourn state |
| 2206 BC | 2336 BC | 1876 BC | minimum; no `+60 Terah`; no `+215 Sojourn` |

Terah begetting-age display:

| Terah state | Birth / death | Begetting state | Abraham birth produced |
|---|---|---:|---:|
| Minimum, no `+60`, no `+215` | `2021–1816 BC` | 70 | 1951 BC |
| `+60 Terah`, no `+215` | `2081–1876 BC` | 130 | 1951 BC |
| `+215 Sojourn`, no `+60` | `2236–2031 BC` | 70 | 2166 BC |
| `+275`, both variants | `2296–2091 BC` | 130 | 2166 BC |

#### 1.3.2 Pentateuchal Funnel and all-even structural harmony

When the 2nd Cainan hinge is active, the regular-chronology variant mechanics form a structural funnel. The pattern is not only a set of boundary lines and is not local to MT. It aligns the number of generations and the number of possible date states with the four major Pentateuchal narrative arcs as the chronology approaches the fixed Exodus and Conquest anchors. MT, SP, and LXX each come to the same fork points: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary.

| Pentateuchal arc | Generational block | Variant-date field | Active hinges |
|---|---|---|---|
| Creation → Flood | Adam through Arphaxad / Flood, 12 generations inclusive | 8 possible dates per patriarch / event where the Cainan hinge is active | Sojourn `±215`; `+60 Terah`; 2nd Cainan `+130`, restored in MT / SP and native or theoretically toggled in LXX |
| Flood → Abraham | 2nd Cainan through Terah, 8 generations inclusive | 4 possible dates per patriarch | Sojourn `±215`; `+60 Terah` |
| Abraham → Entry into Egypt | Abraham, Isaac, Jacob, Joseph / Levi, 4 patriarchal nodes | 2 possible dates per patriarchal node | Sojourn `±215` only |
| Egypt → Conquest / Moses death | Kohath and Amram as 2 floating gap generations; Aaron / Moses fixed downstream | 0 direct regular pivot dates for Kohath / Amram | global Sojourn envelope; fixed `1446 BC` Exodus and `1406 BC` Conquest / Moses-death anchors |

Tradition-specific handling:

| Tradition | Fork sequence location | Cainan-state handling | Guard |
|---|---|---|---|
| MT | Sojourn / Egypt-position `+215`; `+60 Terah`; restored 2nd Cainan `+130` | Cainan is absent from the ordinary MT baseline and is inserted only when restored 2nd Cainan is explicitly opened. | Do not treat the restored state as the ordinary MT baseline. |
| SP | Sojourn / Egypt-position `+215`; `+60 Terah`; restored 2nd Cainan `+130` | Cainan is absent from the ordinary SP baseline and is inserted only when restored 2nd Cainan is explicitly opened. | Preserve SP Terah `145 (205)` and SP Shem Superposition as distinct local states. |
| LXX | Sojourn / Egypt-position `+215`; `+60 Terah`; native 2nd Cainan `+130` boundary | Cainan is already present in the LXX baseline. The fork is structural / boundary-based unless theoretical Cainan removal is explicitly opened. | Do not add `+130` to active LXX baseline rows. |

Claim-status: the generation counts and variant-date fields are structural data of the table state. The mapping of those counts to the four Pentateuchal arcs is a structural inference. The cross-tradition recurrence in MT, SP, and LXX is shared-tradition evidence / providential synchronization where the theological meaning is invoked. Where the pattern is interpreted as evidence of providential design, classify it as providential synchronization rather than as an unqualified proof of direct scribal intent.

Machine Guard [FILE_18 PENTATEUCHAL FUNNEL]:
Do not collapse the `12–8–4–2–0` variant-count ladder into a mere boundary note or an MT-only phenomenon. When the 2nd Cainan hinge is active, the ladder forms an all-even structural funnel that maps onto Creation → Flood, Flood → Abraham, Abraham → Entry into Egypt, and Egypt → Conquest / Moses death across MT, SP, and LXX. Also do not give 2nd Cainan eight possible dates. 2nd Cainan remains in the four-position block; Arphaxad / Flood is the first upstream eight-position row. In LXX, Cainan is native to the baseline; do not add `+130` to the active LXX baseline unless a theoretical removal / reinsertion state is explicitly opened.

#### 1.3.3 27-generation completion and the tebah / ark bridge

Active state:
Restored/native 2nd Cainan 27-generation completion state.

When restored 2nd Cainan is explicitly opened in MT / SP, or when native 2nd Cainan is retained in LXX, the Pentateuchal Funnel completes as a 27-generation structure from Adam to Moses. This is not a new date operator. It is a generation-count and typological state layered onto the variant-boundary structure already defined in §§1.3.1–1.3.2.

Hierarchy guard:
The primary File_18 pattern remains the `12–8–4–2–0` variant-count ladder and its possible-date countdown: 8 date states, 4 date states, 2 date states, then 0 direct regular pivot dates. The `12 + 8 + 4 + 2 + 1 = 27` pattern is a secondary generation-count completion state that includes Moses as the final deliverer generation. It must not be used to obscure or replace the primary date-state mechanics.

| Structural block | Count | Function in the funnel | Typological / narrative note |
|---|---:|---|---|
| Adam → Arphaxad / Flood | 12 | Primeval root block; first block with eight possible date states when the Cainan hinge is active | Culminates in the Flood / ark boundary. |
| 2nd Cainan → Terah | 8 | Post-Flood block with four possible date states | The count `8` corresponds typologically to the eight souls saved through Noah's ark. |
| Abraham → Joseph / Levi | 4 | Patriarchal block with two possible date states | The family-stage patriarchal arc narrows toward Egypt. |
| Kohath → Amram | 2 | Floating Egypt block with zero direct regular pivot dates | The generations float inside the global Sojourn envelope. |
| Moses | 1 | Final deliverer generation; fixed downstream anchor field | Moses is the second major `tebah` / ark figure by typological correspondence. |

Arithmetic fact:

```markdown
12 + 8 + 4 + 2 + 1 = 27
27 = 3 × 3 × 3
```

Structural inference:
The sequence reads backward from Moses as a narrowing / doubling structure: `1`, `2 = 1 + 1`, `4 = 2 + 2`, and `8 = 4 + 4`, with the 12-generation Adam-to-Arphaxad / Flood block serving as the primeval root block. This supports the Pentateuchal Funnel as a structured countdown into the fixed Exodus / Conquest anchors rather than as a mere list of boundary lines.

2nd Cainan keystone rule:
Without restored/native 2nd Cainan, the count from Adam to Moses is `26`, not `27`. The post-Flood block becomes seven generations rather than eight, and the `8`-generation / `8`-soul ark correspondence is not present in the same form. Therefore restored 2nd Cainan is required in MT / SP to obtain the 27-generation structure; in LXX the structure is already present because 2nd Cainan is native to the source-table baseline.

Typological note:
The Hebrew `tebah` ark motif connects Noah and Moses: Noah's ark saves eight souls through the waters of judgment, and Moses' ark / basket preserves the single deliverer who will lead Israel through the waters of judgment and deliverance. This typological bridge explains why the `8` and `1` endpoints of the funnel are theologically meaningful. It does not carry the arithmetic burden.

Theological note:
The structure is compatible with the Genesis multiplication theme: the movement from `1` to `2` to `4` to `8`, joined to the 12-generation primeval root, functions as a numerical expression of multiplication as the timeline moves from Adam through the Flood toward Moses. Claim-status: structural inference and providential synchronization where the theological interpretation is invoked.

Machine Guard [FILE_18 27-GENERATION / TEBAH PATTERN]:
Do not cite the 27-generation pattern unless restored/native 2nd Cainan is active. In MT / SP, restored 2nd Cainan is required for `27 = 3 × 3 × 3`; without it the count is `26`. In LXX, Cainan is already native, so do not add another `+130`. The tebah / ark correspondence is typological and theological; it explains meaning but does not replace the arithmetic count or create a new chronological operator. This secondary `12 + 8 + 4 + 2 + 1` completion layer must not overshadow the primary `12–8–4–2–0` variant-count ladder or the 8-date / 4-date / 2-date / 0-date table-source mechanics.


#### 1.3.4 The `137 = 7 + 130` boundary checksum

Tier: diagnostic checksum layer.

Active state:
Restored/native 2nd Cainan Pentateuchal Funnel, with the figurative Creation-week state opened only where named.

The value `137` functions as a boundary checksum:

```markdown
137 = 7 + 130
```

The `7` belongs to the completion / Sabbath / Creation-week register. The `130` belongs to the mortal-line, curse, exile, or unresolved-humanity register. Joined together, `7 + 130` may be read as a reconciliation / atonement checksum. This theological meaning does not replace the arithmetic; it explains why the recurrence of `137` is structurally meaningful.

| Boundary | Active state | Expression | Claim-status |
|---|---|---:|---|
| Adam → Seth | seven-year Creation-week wrapper plus Adam's begetting age | `7 + 130 = 137` | arithmetic fact under Creation-week state |
| Flood / Arphaxad boundary, MT | Noah-bound Shem `100`; Arphaxad born two years after Flood; Arphaxad begets at `35` | `100 + 2 + 35 = 137` | conditional arithmetic fact |
| Flood / native Cainan boundary, LXX | LXX native 2nd Cainan state | `2 + 135 = 137` | arithmetic fact under LXX source-table state |
| Abraham / Sarah | Sarah-Eve typological boundary | Sarah lifespan `127`; Abraham is 10 years older; `127 + 10 = 137` | arithmetic fact; typological note |
| Ishmael | Abrahamic side witness | lifespan `137` | collateral arithmetic witness |
| Levi | end of Abraham → Entry block | lifespan `137` | arithmetic fact |
| Levi / Kohath / Amram | hidden Egypt-era generations | Levi `137`; Kohath `133`; Amram `137` | arithmetic fact; structural frame |

Typological note:
Sarah functions as an Eve-like companion figure at the Abrahamic boundary. Sarah's own lifespan is `127`, but because Sarah is 10 years younger than Abraham, her death occurs when Abraham is `137`. As Eve derives from Adam's side while remaining distinct from Adam, Sarah's death-date is measured both from her own birth and from Abraham's birth. The arithmetic is direct; the Adam/Eve reading is typological.

Aaron terminal imprint:
Aaron does not directly live to `130`; he dies at `123`. The Conquest / land-rest process supplies the missing seven years as a priestly terminal imprint:

```markdown
123 + 7 = 130
```

In Nisan-state display this may be stated as `1529n BC → 1399n BC = 130`. In the phase-resolved Tishri-state display it may be stated as `1530t BC → 1400t BC = 130`. This does not alter Aaron's lifespan. It identifies the priestly atonement imprint reaching completion at the land-rest boundary.

Claim-status:
The boundary values are arithmetic facts or conditional arithmetic facts under their named states. The meaning “reconciliation / atonement” is a theological / typological note. The recurrence of `7 + 130` at the boundary points of the Pentateuchal Funnel is a structural inference and must not be promoted to a new chronological operator.

#### 1.3.5 Shem dual-`100` state

Tier: diagnostic modal-state support.

Active state:
Regular chronology; Shem `±2`; Noah-bound and Arphaxad-bound Shem states.

Shem carries two valid `100` states.

| Shem state | Textual basis | Meaning | Handling |
|---|---|---|---|
| Noah-bound / Flood-bound `100` | Noah is `500` when Shem is born; Noah is `600` at the Flood | Shem is `100` at the Flood | Valid harmonic / structural state |
| Arphaxad-bound / text-bound `100` | Genesis 11:10: Shem is `100` when he begets Arphaxad two years after the Flood | Shem is `100` at Arphaxad's birth | Valid textual state |

These states are not corrections of one another. They function like the Terah `70/130` begetting-state field: both readings are retained under named modal states.

The two-year difference is the Shem `±2` binding hinge. In Regular chronology this local binding distinction concerns Noah/Shem; ordinary coherent Flood Gear transport remains separately available (§3.1.4). In Cumulative chronology the anomaly may propagate through the cumulative chain where that state is opened.

#### 1.3.6 The `16 × 8` expectation and the cumulative Cainan extension

Tier: diagnostic extension layer.

Active state:
Regular restored/native 2nd Cainan Pentateuchal Funnel, with MT Cumulative + 2nd Cainan opened only as a comparison register.

The visible File_18 funnel gives:

```markdown
12 × 8
8 × 4
4 × 2
2 × 0
```

The `12` is meaningful in its own right. Adam → Arphaxad / Flood supplies the first 12-name block. The following `8 + 4` blocks form another 12-name movement toward Jacob's family entering Egypt and the emergence of the 12 tribes. Thus the `12` is not a defect.

Yet the backward doubling pattern also suggests an idealized head-block:

```markdown
16 × 8
8 × 4
4 × 2
2 × 0
```

Therefore the visible head-block is short by four proportional units:

```markdown
16 − 12 = 4
```

The expected `16` is not supplied by adding four hidden patriarchs. It appears as a proportional extension.

If the MT pre-Flood span `1656` represents the 12-name Adam → Arphaxad / Flood field, then:

```markdown
1656 ÷ 12 = 138
```

The missing four units are:

```markdown
4 × 138 = 552
```

The completed sixteen-unit extension is:

```markdown
16 × 138 = 2208
```

Using the restored regular Flood Gear rails with `+60 Terah` and regular restored Cainan `+130` opened:

```markdown
2646/2648/2650 BC + 2208 = 4854/4856/4858 BC
```

These values land inside the MT Cumulative + 2nd Cainan field, especially the cumulative Cainan span `4858–4851 BC` and the rounded / control value `4856 BC`.

This does not add four missing patriarchs. It identifies a proportional pre-Adamic extension that lands on the cumulative 2nd Cainan register.

The `4856 BC` coordinate is not isolated. From cumulative Cainan to the Moses-death / Conquest terminus:

```markdown
4856 − 1406 = 3450
3450 = 138 × 25 = 138 × 5 × 5
```

The coordinate is further reinforced by Key-of-23 and Danielic values:

```markdown
3450 = 3 × 1150
3450 × 70/69 = 3500
4856 + 50 = 4906 BC
4906 − 6 = 4900
```

Cainan's death also preserves the `130` signal:

```markdown
4856 − 460 = 4396 BC
4396 − 1406 = 2990 = 23 × 130
```

LXX corroboration:
The same missing-four logic appears in the LXX. LXX Regular-Minimum Creation to Flood is:

```markdown
5279 − 3023 = 2256
2256 ÷ 3 = 752
```

Extending the LXX Maximum node `5554 BC` by the missing fourth unit gives:

```markdown
5554 + 752 = 6306 BC
6306 − 1406 = 4900
```

This LXX route does not depend on the MT `1656 ÷ 12 = 138` calculation. It supplies an independent corroboration that the missing-four extension can land on a major Conquest-facing `4900` structure.

Claim-status:
The arithmetic checks are exact under the named states. The interpretation that the missing-four extension is intentionally answered by the cumulative Cainan coordinate is structural inference / providential synchronization. No formal probability model is supplied here.

#### 1.3.7 1Kenan / 2nd Cainan tenfold reinforcement

Tier: reinforcement and branch-restraint layer.

Active state:
Regular restored 2nd Cainan under Gear 3; Kenan / 2nd Cainan sector by File_11 dependency.

The 1Kenan / 2nd Cainan sector reinforces the same `7 + 130` pattern at 10x scale.

In Gear 3, 1Kenan is born at `3921 BC`. Kenan begets his son at age `70`:

```markdown
3921 − 70 = 3851 BC
```

Regular 2nd Cainan, the same Hebrew name in the restored line, is born at `2551 BC`.

Thus the span from the birth of 1Kenan to the birth of 2nd Cainan is:

```markdown
3921 − 2551 = 1370
1370 = 70 + 1300
1370 = 10 × 137
```

From Kenan's son to 2nd Cainan is:

```markdown
3851 − 2551 = 1300 = 10 × 130
```

Since 1Kenan lives `910 = 7 × 130`, and since:

```markdown
1370 − 460 = 910
```

the death of 1Kenan occurs `460` years before the birth of 2nd Cainan:

```markdown
3921 − 910 = 3011 BC
3011 − 2551 = 460
```

2nd Cainan then lives `460` years:

```markdown
2551 − 2091 = 460
```

The two same-name Cainan / Kenan lifespans also total `1370`:

```markdown
910 + 460 = 1370
1370 = 10 × 137
```

This is a lifespan-sum witness distinct from the birth-to-birth `1370` span. It helps conceptualize the consistent use of `137` around the Cainan variants at 10x scale.

Thus the same-name Kenan / Cainan sector gives the larger sequence:

```markdown
910 + 460 + 460 = 1830
```

This agrees with the established Gear-3 Cainan-sector control and reinforces the `7 + 130` checksum at 10x scale:

```markdown
1370 = 10 × (7 + 130)
```

Claim-status:
The arithmetic is direct once the Gear-3 restored-Cainan state is opened. The same-name Kenan / Cainan interpretation, the two-lifespan sum `910 + 460 = 1370`, and the 10x `137` reinforcement are structural inference. This note supports the `137` checksum and cumulative Cainan extension but should not be expanded into a separate Cainan-sector proof inside File_18.

Audit / scope note:
The deeper Cainan-sector branches involving `8970`, `9100`, `130 + 330`, and related expanded fields are arithmetically coherent but are not needed for the present File_18 funnel amendment. They should remain outside the main argument unless a later Cainan-sector file opens them directly.

#### 1.3.8 Cumulative Cainan macro-vector to `2091 BC`, `1876 BC`, and `1661 BC`

Tier: macro-vector dependency layer.

Active state:
MT Cumulative + 2nd Cainan table-source state, regular restored 2nd Cainan comparison state, and File_16 `1876 BC` Nexus dependency.

`File_18` supplies the table-source values. `File_16` controls the Nexus argument, Category B classification, Bullseye Protocol use, and theological synthesis.

The MT Cumulative + 2nd Cainan table places Cainan at `4858–4851 BC` and the downstream Shelah convergence envelope at `4398–4391 BC`. These values are table-source values. They may be used as macro-vector source coordinates only when the active vector state is named.

| Vector state | Source coordinate | Operator | Target coordinate | Handling |
|---|---:|---:|---:|---|
| Daniel 8 birth-side vector | 4851 BC | −2300 | 2551 BC | regular restored 2nd Cainan birth member |
| Daniel 8 death-side vector | 4391 BC | −2300 | 2091 BC | regular restored 2nd Cainan death / Abraham Call member by dependency |
| Daniel 9 Famine envelope, upper member | 4398 BC | −2520 | 1878 BC | Famine-window commencement by File_16 dependency |
| Daniel 9 Famine envelope, core member | 4396 BC | −2520 | 1876 BC | Super-Anchor / Famine Year-2 / Entry hinge by File_16 dependency |
| Daniel 9 Famine envelope, lower member | 4391 BC | −2520 | 1871 BC | Famine-window termination by File_16 dependency |
| Enochian lower-bound vector | 4391 BC | −2730 | 1661 BC | minimum Entry lower-bound; EnvSpread / Enochian state required |
| Daniel 12 sandwich | 4396 BC → 3136 BC → 1846 BC → 586 BC | 1260 → 1290 → 1260 | 586 BC | Cainan-to-Exile macro-prophetic witness by File_16 dependency |

Arithmetic ledger:

```markdown
4851 − 2300 = 2551
4391 − 2300 = 2091
4398 − 2520 = 1878
4396 − 2520 = 1876
4391 − 2520 = 1871
4391 − 2730 = 1661
2730 = 7.5 × 364
4396 − 1260 = 3136
3136 − 1290 = 1846
1846 − 1260 = 586
1260 + 1290 + 1260 = 3810
4396 − 3810 = 586
1876 − 1290 = 586
```

Regular-Cainan `460` cross-modal symmetry:

```markdown
2551 − 2091 = 460
2336 − 1876 = 460
```

Cross-tradition `60`-multiple Shelah / Plenty-Famine comparison:

| Tradition | Cumulative Shelah / Arphaxad-Cainan boundary envelope | Operator | Historical seven-year target | Handling |
|---|---:|---:|---:|---|
| MT + 2nd Cainan | 4398–4391 BC | `−2520 = 60 × 42` | 1878–1871 BC | Famine window; File_16 B6 dependency |
| SP | 4278–4271 BC | `−2400 = 60 × 40` | 1878–1871 BC | Famine window; comparative table-source support |
| LXX | 4825–4818 BC | `−2940 = 60 × 49 = 6 × 490` | 1885–1878 BC | seven years of Plenty; comparative table-source support |

Arithmetic check:

```markdown
4398 − 2520 = 1878
4391 − 2520 = 1871
2520 = 60 × 42

4278 − 2400 = 1878
4271 − 2400 = 1871
2400 = 60 × 40

4825 − 2940 = 1885
4818 − 2940 = 1878
2940 = 60 × 49 = 6 × 490
```

Claim-status note:
This row is collaborative structural evidence for design alignment among MT, SP, and LXX cumulative Shelah fields. It is not a new File_18 table-generation operator. `File_16` controls any Bullseye Protocol use. The direct `+60 Terah` state remains a separate regular-chronology fork that also intersects the `1876 BC` year-label.

Mirror `60`-spine companion:

The Plenty / Famine triad `1885n/1878n/1871n BC` has a `−215` companion triad `1670n/1663n/1656n BC`.

Same-side companion relation:

```markdown
1885 − 215 = 1670
1878 − 215 = 1663
1871 − 215 = 1656
```

When the `−215` triad is placed on the AD side in reversed endpoint order, each civil cross-axis component is `3540 = 60 × 59`:

| BC-side Plenty / Famine label | AD-side `−215` Mirror label | Civil cross-axis span |
|---:|---:|---:|
| 1885n BC | AD 1656n | `1885 + 1656 − 1 = 3540 = 60 × 59` |
| 1878n BC | AD 1663n | `1878 + 1663 − 1 = 3540 = 60 × 59` |
| 1871n BC | AD 1670n | `1871 + 1670 − 1 = 3540 = 60 × 59` |

Audit note:
The constant `3540` requires reversed endpoint order on the AD side. Same-order pairing of `1885/1878/1871 BC` with `AD 1670/1663/1656` does not produce `3540` in all three rows.

Combined Mirror span display:

```markdown
3540 + 2400 = 5940 = 60 × 99
3540 + 2520 = 6060 = 60 × 101
3540 + 2940 = 6480 = 60 × 108
6480 = 25920 ÷ 4
```

The same `60` register also appears in the Terah / regular restored 2nd Cainan death-date rail around `1876n BC`:

```markdown
1936 − 1876 = 60
1876 − 1816 = 60
```

State-control note:
The `1936n BC → 1876n BC → 1816n BC` display is a death-date variant rail. It does not identify Terah and Cainan as the same node-class. `File_18` preserves the source values and arithmetic controls; `File_16` controls the Nexus interpretation.

State-control note:
The two regular `460` spans may mirror the cumulative `+460` Cainan lifespan value, but they do not replace the regular restored 2nd Cainan `+130` begetting-age insertion. The active regular operator remains `+130`; the active cumulative operator remains `+460`.

Claim-status:
The same-side arithmetic is direct under the named states. The classification of the `2520`, `2300`, `2730`, and Daniel 12 sandwich relations as a macro-prophetic witness belongs to `File_16`. In `File_18`, the material is table-source support plus structural dependency notation.

Audit note:
The inclusive companion relation checks as same-side arithmetic:

```markdown
4858 − 2551 = 2307
4398 − 2091 = 2307
```

This `2307` companion is retained as sanctuary / Hanukkah-style exploratory material unless a later dependency opens the inclusive operator explicitly.

Audit note:
The solar companion is not promoted as an exact File_18 operator. The visible same-side span is:

```markdown
4398 − 1661 = 2737
```

The comparison with `7.5 × 365` or true-solar `365.2422` requires a phase-resolved calendar state and should remain audit-controlled unless `File_12` or a future calendar-control file opens the exact operator.

### 1.4 Deriving any date

1. Find the patriarch in the appropriate baseline table, §§2–4.
2. Identify which epoch the date falls within.
3. Apply the appropriate variant:
   - Adam → Terah: add `60`, `215`, or `275` as needed.
   - Abraham → Levi / Joseph: add `215` if using the 430-in-Egypt position.
   - Terah: preserve all four states when needed: `2021–1816 BC`, `2081–1876 BC`, `2236–2031 BC`, and `2296–2091 BC`.
   - Aaron onward: use the date as given.

### 1.5 The Shem `±2` anomaly

Active state:
Regular-localized Shem `±2` and cumulative-propagated Shem `±2` distinguished.

Genesis 11:10 creates a two-year ambiguity at Shem, Arphaxad, and the Flood.

- In Regular chronology, this binding anomaly is local to Noah/Shem. Ordinary coherent Gear transport of the Flood and other admitted pre-Flood biographies is separately retained; it does not move the Arphaxad-forward suffix at held variant settings (§3.1.4).
- In Cumulative chronology, the same anomaly propagates through the entire chain and creates the 7-year cumulative margin, `2 + 3 + 2`.

### 1.6 The 2nd Cainan switch

Active states:
Regular restored 2nd Cainan and cumulative restored 2nd Cainan.

The 2nd Cainan, Luke 3:36 and LXX Genesis 11:12–13, is native to LXX and intentionally omitted from MT / SP. When restoring Cainan to MT / SP, the adjustment value depends on the chronological method used.

#### 1.6.1 Why two different values

| Method | What is added | Cainan's value | Basis |
|---|---|---:|---|
| Regular | Begetting ages | +130 years | Age when Shelah was born. |
| Cumulative | Full lifespans | +460 years | Total years lived. |

This is a general principle applying to all patriarchs, not a value unique to Cainan.

| Patriarch | Begetting age | Lifespan | Difference |
|---|---:|---:|---:|
| 2nd Cainan | 130 | 460 | 330 |
| Shelah | 130 | 460 | 330 |
| Eber | 134 | 504 | 370 |
| etc. | — | — | — |

#### 1.6.2 Application by tradition

| Tradition / method | Handling |
|---|---|
| LXX Regular | Cainan is already in the baseline. `5279 BC` Adam minimum includes his `130` begetting years. No adjustment is needed. |
| MT / SP Regular | To restore Cainan, insert 2nd Cainan by adding the `+130` begetting-age hinge between Arphaxad and Shelah. Shelah and the downstream Terah field remain four-position; Arphaxad / Flood through Adam shift by `+130` and become eight-position where the restored-Cainan state is explicitly opened. MT with Cainan: `3899 + 130 = 4029 BC`. SP with Cainan: `4199 + 130 = 4329 BC`. |
| LXX Cumulative | Cainan is already in the baseline. His `460`-year lifespan is included in the chain. No adjustment is needed. |
| MT / SP Cumulative | To restore Cainan, insert the `+460` lifespan hinge between Arphaxad and Shelah. In the cumulative table this shifts Adam through Arphaxad / Flood by `+460`; Shelah and downstream rows remain unchanged. MT cumulative with Cainan: `14006 + 460 = 14466 BC`, Moses line center. |
| LXX theoretical removal | LXX could have Cainan removed: `5279 − 130 = 5149 BC`, Regular. This is not tracked in standard tables but remains architecturally valid. |

AI-processing rules:

| Rule | Handling |
|---|---|
| Regular chronology | Cainan = `+130` years, begetting age. |
| Cumulative chronology | Cainan = `+460` years, full lifespan. |
| LXX | Cainan already included; no adjustment. |
| MT / SP | Add the appropriate value to restore Cainan. |
| Method distinction | The `130` / `460` difference reflects method, not variant ambiguity. |

Cross-reference:
Data table: `File_18`, §6B for MT Cumulative + 2nd Cainan tables; §§6C–6D for SP and LXX cumulative comparison. Convergence logic: `File_16`, §3. Axiom definition: `File_00`, 2nd Cainan Switch.

## 2. MT Regular Baseline

Active state:
MT Minimum-Regular baseline.

Anchor:
Exodus `1446 BC`; Entry into Egypt `1661 BC`, 215 years in Egypt.

Website adjustment:
From the 490d.com table state, subtract `215` years from Adam through Levi to recover this minimum baseline.

### 2.1 Creation to Flood: MT Minimum-Regular

#### 2.1.1 Dual-scale Creation Week

The Creation Week functions at two scales simultaneously, as Daniel's 70th week may function as both 7 days and 7 years.

| Scale | MT Minimum-Regular, Nisan | Span |
|---|---:|---|
| Literal, 7 days | 3899 BC | Adar 25 – Nisan 2 |
| Figurative, 7 years | 3906–3899 BC | Year 1 – Year 7 |

Both scales converge on `3899 BC`. The Adam row represents:

- the year containing the literal Creation week, with Adam created on Day 6;
- the endpoint of the figurative Creation week, with Year 7 complete.

For figurative Year 6, Adam's creation as a year:

```markdown
3899 + 1 = 3900 BC
```

For the start of the figurative week, Year 1:

```markdown
3899 + 7 = 3906 BC
```

The same dual-scale principle applies at all variant positions: `+60 Terah`, `+215 Sojourn`, and `+275`.

#### 2.1.2 MT terminology clarification

| Common term | Repository state | Date | Variants |
|---|---|---:|---|
| MT Standard, traditional | MT Standard-Normal / `+215 Sojourn` | 4114 BC | `+215 Sojourn` |
| — | MT Minimum-Regular | 3899 BC | None |

The `215`-year difference is the Sojourn variant, 215 years in Canaan before Egypt.

Both `3899 BC`, minimum, and `4114 BC`, `+215`, mark the end of Creation Week: the completion of Day 7 / Year 7. The literal seven-day Creation and figurative seven-year Creation converge at these endpoints.

| Derivation from `3899 BC` | Result | State |
|---|---:|---|
| `3899 + 215` | 4114 BC | MT Standard-Normal / `+215 Sojourn` |
| `3899 + 60` | 3959 BC | `+60 Terah` only; also the 4000-to-Christ position by source claim |
| `3899 + 275` | 4174 BC | Maximum; both variants |

AI-processing note:
When external sources reference MT Creation at `4114 BC`, this corresponds to the MT Standard-Normal / `+215 Sojourn` position in this repository's nomenclature. Always verify which variant position is being used.

#### 2.1.3 MT Minimum-Regular table

| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |
|---|---:|---:|---:|---:|
| Creation Week | 3906 | 3899 | 7 | — |
| Adam | 3899 | 2969 | 930 | 130 |
| Seth | 3769 | 2857 | 912 | 105 |
| Enosh | 3664 | 2759 | 905 | 90 |
| Kenan | 3574 | 2664 | 910 | 70 |
| Mahalalel | 3504 | 2609 | 895 | 65 |
| Jared | 3439 | 2477 | 962 | 162 |
| Enoch | 3277 | 2912 | 365 | 65 |
| Methuselah | 3212 | 2243 | 969 | 187 |
| Lamech | 3025 | 2248 | 777 | 182 |
| Noah | 2843 | 1893 | 950 | 500 |
| Flood | 2243 | 2242 | 1 | — |

### 2.2 Post-Flood to Patriarchs: MT Minimum-Regular

| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |
|---|---:|---:|---:|---:|
| Shem | 2341 | 1741 | 600 | 100 |
| Arphaxad | 2241 | 1803 | 438 | 35 |
| Shelah | 2206 | 1773 | 433 | 30 |
| Eber | 2176 | 1712 | 464 | 34 |
| Peleg | 2142 | 1903 | 239 | 30 |
| Reu | 2112 | 1873 | 239 | 32 |
| Serug | 2080 | 1850 | 230 | 30 |
| Nahor | 2050 | 1902 | 148 | 29 |
| Terah | 2021 | 1816 | 205 | 70/130 |

#### 2.2.1 Noah and Shem `±2` anomaly

Active state:
Regular-localized Shem `±2`.

Genesis 11:10 supplies the two-year distinction used in the regular Noah/Shem binding comparisons. This localized comparison permission does not restrict ordinary coherent Gear transport of the Flood; see §3.1.4. In Cumulative chronology, the `±2` propagates through the chain; see §6 and `File_02`.

| Patriarch | Literal, in table | Idealistic `±2` | Source direction label |
|---|---|---|---|
| Noah | 2843–1893 BC | 2841–1891 BC | Earlier |
| Shem | 2341–1741 BC | 2343–1743 BC | Later |

The literal dates represent the minimum baseline. The idealistic dates represent the alternative reading of Genesis 11:10. Both are valid.

For LXX, retain the independently sourced `±2` comparisons at its own native-Cainan positions:

| Tradition | Patriarch | Literal | Idealistic `±2` |
|---|---|---|---|
| LXX | Noah | 3623–2673 BC | 3621–2671 BC |
| LXX | Shem | 3121–2521 BC | 3123–2523 BC |

The corrected SP field additionally has a local one-year companion. Its native-frame G2 pairs are:

| SP person | G2 primary biography | G2 lower-companion biography |
|---|---|---|
| Noah | 3493–2543 BC | 3492–2542 BC |
| Shem | 2993–2393 BC | 2992–2392 BC |

These columns differ by one year and must not be labelled `±2`. The ordinary SP G1 Shem biography `2991–2391` remains the displayed Arphaxad-bound row, distinct from G2 `2993–2393` by two years. §3.2.1 gives all three Gears and the named bindings. MT and LXX do not inherit this SP-only adjacent rail.

Cross-reference:
Axiom definition: `File_00`, Shem `±2`. Entity logic: `File_02`, Shem `±2` anomaly.

### 2.3 Patriarchal period: MT Minimum-Regular; `±215` fork begins

| Patriarch / event | Birth BC | Death BC | Lifespan | Key events |
|---|---:|---:|---:|---|
| Abraham | 1951 | 1776 | 175 | Call `1876 BC`; `+215 → 2091`. |
| Sarah | 1941 | 1814 | 127 | — |
| Isaac | 1851 | 1671 | 180 | — |
| Jacob | 1791 | 1644 | 147 | Entry `1661 BC`; `+215 → 1876`. |
| Joseph | 1700 | 1590 | 110 | Stood before Pharaoh at age 30, Gen 41:46. |
| Levi | 1704 | 1567 | 137 | Last patriarch death before fixed epoch. |

Note:
Joseph, born `1700 BC`, is born 4 years after Levi, born `1704 BC`, but Joseph dies 23 years before Levi, `1590 BC` versus `1567 BC`, because Levi lived 137 years while Joseph lived 110.

### 2.4 Fixed epoch: MT; no variants

| Event / person | Date BC | Notes |
|---|---:|---|
| Aaron birth | 1529 | 3 years historical / 3.5 years harmonic; see `File_22`, §6B.5 by source reference. |
| Moses birth | 1526 | — |
| Joshua birth | 1476 | — |
| Exodus | 1446 | Fixed anchor. |
| Tabernacle | 1445 | — |
| Aaron death | 1407 | Summer. |
| Moses death | 1406 | Winter. |
| Conquest begins | 1406 | — |
| Six years' war | 1406–1400 | Source-retained range; stray source brace removed as formatting residue. |
| First Sabbath | 1399 | First Sabbath year of rest. |
| Joshua death | 1366 | 110 years old. |

Note:
Aaron's date can optionally shift 0.5 years back to Tishri / Fall, which cascades back through all dates to Adam. Nisan / Spring remains the primary New Year season used in this baseline.

### 2.5 Kings of Judah baseline: literal, Rounded, and schematic ledgers

Active states:
literal/precise United Monarchy; Rounded Scaffold United Monarchy; post-Solomon conventional table; Kings `+50` schematic ledger.

Anchor:
Fall of Jerusalem `586 BC` for the broader Kings table; Exodus `1446 BC` for the Temple foundation.

#### 2.5.1 Literal / precise United Monarchy

The literal royal phase fields are:

```text
Nisan:  1050n → 1010n → 970n → 930n BC
Tishri: 1050t → 1010t → 970t → 930t BC.
```

| King | Textual reign | Precise accession | Precise transition / terminus | Handling |
|---|---:|---:|---:|---|
| Saul | `40` | `1050t/n BC` | `1010t/n BC` | Same-phase `40`. |
| David | `40`; exact `40.5` | `1010t/n BC` | `970t/n BC` | Same-phase `40`; exact diagonal `1010n→970t=40.5`, matching `7.5+33`. |
| Solomon | `40` | `970t/n BC` | `930t/n BC` | Same-phase `40`; `970n→970t` is a precise half-year joint whose co-rule interpretation remains proposed downstream. |

Checks:

```text
1050−1010=40
1010−970=40
970−930=40
1010n→970t=40.5.
```

#### 2.5.2 Rounded Scaffold United Monarchy

The mod-5 companion rail is:

```text
1051n → 1011n → 971n → 931n BC.
```

| King | Rounded accession | Rounded terminus | Span |
|---|---:|---:|---:|
| Saul | `1051n BC` | `1011n BC` | `40` |
| David | `1011n BC` | `971n BC` | `40` |
| Solomon | `971n BC` | `931n BC` | `40` |

The rounded Aaron/Moses comparisons are:

```text
1531n−971n=560=14×40
1526n−966n=560=14×40.
```

The Rounded rail is a File_51a state. It is not the literal / precise monarchy.

#### 2.5.3 Post-Solomon conventional Kings table

The one-year royal state split is not automatically propagated through every later king. The division boundary remains an adjacent `931n/930t/n BC` field: `931n BC` belongs to the Rounded/conventional accession display, while `930t/n BC` closes the precise Solomonic rail.

| King | Verbatim | Conventional accession BC | Conventional end / death BC | Logic / chronological anchor |
|---|---:|---:|---:|---|
| Rehoboam | 17 | `931/930` | 913 | Division-of-kingdom adjacent boundary. |
| Abijam | 3 | 913 | 911 | — |
| Asa | 41 | 911 | 870 | — |
| Jehoshaphat | 25 | 870 | 848 | — |
| Jehoram | 8 | 848 | 841 | — |
| Ahaziah | 1 | 841 | 841 | — |
| Athaliah | 6 | 841 | 835 | Usurper queen. |
| Joash | 40 | 835 | 796 | — |
| Amaziah | 29 | 796 | 767 | — |
| Uzziah | 52 | 767 | 740 | Azariah. |
| Jotham | 16 | 740 | 732 | — |
| Ahaz | 16 | 732 | 716 | Northern Kingdom falls, 722/721. |
| Hezekiah | 29 | 715 | 687 | Year 14 = 701 BC, Sennacherib. |
| Manasseh | 55 | 687 | 643 | — |
| Amon | 2 | 643 | 641 | — |
| Josiah | 31 | 640 | 609 | — |
| Jehoahaz | 0.25 | 609 | 609 | 3 months. |
| Jehoiakim | 11 | 609 | 598 | 1st Exile, 606; 2nd, 597. |
| Jehoiachin | 0.25 | 598 | 597 | 3 months. |
| Zedekiah | 11 | 597 | 586 | Fall of Jerusalem. |

#### 2.5.4 Arithmetic verification of the Temple states

```text
Literal cardinal state: 1446n−966n=480
Literal ordinal state: 1446n−967n=479 completed years; foundation in the following 480th year
Rounded Moses lock:     1526n−966n=560=14×40
Rounded Aaron lock:     1531n−971n=560=14×40.
```

`966n BC` is a shared label under different operators. `967n BC` remains the ordinal `480th-year` state; `966n BC` remains the cardinal elapsed-`480` state and the Rounded `560`-year Moses landing.

#### 2.5.5 Arithmetic verification of the `+50` Offset

```text
Schematic link, File_16: 1446 BC−430 years=1016 BC
Historical link, File_18: 1446 BC−480 years=966 BC
Offset: 1016−966=50 years.
```

The `50`-year offset allows the Triple-`430` harmonic, `1876→1446→1016→586`, to coexist with the literal `480`-year Temple count. It is a third ledger and must not be confused with the one-year Rounded monarchy offset.


## 3. SP Regular Baseline

Active state:
SP Normal / G2, native Sojourn `215`, Terah `+60` OFF, second Cainan OFF.

Anchors:
Exodus `1446 BC`; Entry into Egypt `1661 BC`; preferred Creation / genealogical chain head `4199 BC`; Lamech birth `3545 BC`; Flood start `2893 BC`; Flood close `2892 BC`; fixed Arphaxad `2891 BC`.

Frame conversion:
Add `215` to the affected regular dates for the reports’ full-430 comparison: Creation `4414`, Lamech `3760`, Flood `3108→3107`, Arphaxad `3106`. Appendix A distinguishes this current website setting from the older `+275` setting.

Counting convention:
Qualify each interval as ordinary completed-year subtraction or inclusive endpoint counting. The legacy name `SP Normal / Toggle ON` does not impose one convention on every interval or create a global one-year operator. The legacy SP Ideal / Exclusive `4200` comparison is one above the preferred head `4199`; this numerical relation does not generate the SP-local Noah/Shem companion rail or change upstream birth nodes.

The preferred SP head remains exactly `300` years earlier than MT Minimum-Regular: `4199−3899=300`. Creation-week, Adam-Day, and genealogical node classes remain distinct. The superseded `4415 Adam → 4414 Creation` repair is not restored in the preferred chain.

### 3.1 Creation to Flood: SP Normal / G2

The table uses the native SP frame. Jared, Methuselah, and Lamech retain their lifespan numbers under the inclusive Flood-cap convention. Their selected deaths lie at Flood start; ordinary subtraction to Flood close is the equivalent capacity calculation, not an alternative physical-death assignment.

| Patriarch / event | Birth BC | Death BC | Lifespan / count | Begetting age / binding |
|---|---:|---:|---|---|
| Creation Week | 4206 | 4199 | 7 | — |
| Adam / preferred chain head | 4199 | 3269 | 930 | 130 |
| Seth | 4069 | 3157 | 912 | 105 |
| Enosh | 3964 | 3059 | 905 | 90 |
| Kenan | 3874 | 2964 | 910 | 70 |
| Mahalalel | 3804 | 2909 | 895 | 65 |
| Jared | 3739 | 2893 | 847 inclusive | 62 |
| Enoch | 3677 | 3312 | 365 | 65 |
| Methuselah | 3612 | 2893 | 720 inclusive | 67 |
| Lamech | 3545 | 2893 | 653 inclusive | 53rd year to primary Noah; full 53 to companion |
| Noah — G2 primary | 3493 | 2543 | 950 | 500 to G2 primary Shem; other bindings in §3.2.1 |
| Noah — G2 companion | 3492 | 2542 | 950 | 500 to G2 companion Shem; other bindings in §3.2.1 |
| Flood — start / close | 2893 | 2892 | 1 event-year | — |

For the Flood row, the two coordinate columns mean start and close. The remaining uncapped lifespan rows retain their ordinary subtraction conventions; inclusive cap counting does not impose an extra year on every lifespan.

Arithmetic verification:

| Row / path | Verification |
|---|---|
| Adam | `4199−130=4069`, Seth. |
| Seth | `4069−105=3964`, Enosh. |
| Enosh | `3964−90=3874`, Kenan. |
| Kenan | `3874−70=3804`, Mahalalel. |
| Mahalalel | `3804−65=3739`, Jared. |
| Jared | `3739−62=3677`, Enoch. |
| Enoch | `3677−65=3612`, Methuselah. |
| Methuselah | `3612−67=3545`, Lamech. |
| Lamech → primary Noah | `3545−52=3493`: 53rd year at the declared annual station. |
| Lamech → companion Noah | `3545−53=3492`: 53 full units. |
| Primary Noah → Flood start | `3493−600=2893`. |
| Companion Noah → Flood start | `3492−599=2893`: ordinal 600th-year boundary, `599+`. |
| Companion Noah → Flood close | `3492−600=2892`; close independently belongs to `2893→2892`. |

The three admitted local paths use the one-year counting distinction once:

| Path | Lamech→Noah | Noah birth | Noah→Shem | Shem birth | Shem→Flood start | Flood start |
|---|---|---:|---|---:|---|---:|
| Primary Noah / primary Shem | 53rd year: 52 | 3493 | 500 full | 2993 | 100 full | 2893 |
| Companion Noah / primary Shem | 53 full | 3492 | 500th year: 499 | 2993 | 100 full | 2893 |
| Companion Noah / companion Shem | 53 full | 3492 | 500 full | 2992 | 100th year: 99 | 2893 |

`52+500+100 = 53+499+100 = 53+500+99 = 652`. The Flood therefore lies in Lamech’s `653rd` counted year. The annual coordinates do not supply an otherwise unstated birthday or fractional-year phase. Genesis 7:6 supplies the cardinal age expression; Genesis 7:11 supplies the ordinal 600th-year expression. Their coordination in this SP field is the study’s reconstruction.

#### 3.1.1 Methodological note: BJ / Jubilees corroboration

Claim-status: derivative/corroborating witness and structural inference in the project model. SP supplies the underlying architecture; the arithmetic alone does not prove the historical direction of literary dependence.

BJ / Jubilees places Shem’s birth at `2650 BC`, Ham’s at `2648 BC`, and Japheth’s at `2645 BC`. It places Ark preparation at `2550`, Flood start at `2549`, the earth-dry / closing boundary at `2548`, and Arphaxad at `2547`.

The retained conditional calculation reads the 601st-year closing boundary after `600` completed units: `2548+600=3148`, yielding a derived BJ Noah station. It gives `3148−2648=500` to Ham and `3148−2549=599` to Flood start. This illustrates interval-specific ordinal/completed reckoning; it does not generate SP’s upstream birth dates or a Flood companion rail.

BJ event coordinates translate by `+344` into the native SP frame and by `+559` into the equalized SP frame: `2550/2549/2548/2547 + 344 = 2894/2893/2892/2891`, or `+559 = 3109/3108/3107/3106`. The SP Ark-preparation interval remains conjectural, supported by the BJ parallel. The native SP `2894` / equalized `3109` is independently also the G3 Flood close; sharing a coordinate does not identify these event classes.

#### 3.1.2 Methodological note: 100-year harmonic preservation

Claim-status: derivative/corroborating structural comparison. BJ retains the following intervals while giving Shem the firstborn chronological position:

| Son | Birth BC | Event | Event BC | Interval |
|---|---:|---|---:|---|
| Shem, 1st | 2650 | Ark construction begins | 2550 | 100 years |
| Ham, 2nd | 2648 | Earth dry | 2548 | 100 years |
| Japheth, 3rd | 2645 | Arphaxad born | 2547 | 98 years, 2 Jubilees |

Keep birth-position correspondence separate from event correspondence. BJ births plus `345` reach native SP `2995/2993/2990`, selecting G3 primary / G2 primary / G1 companion from the Shem field. In the equalized frame the same birth-position translation is `+560`, reaching `3210/3208/3205`. It preserves BJ’s `2+3` spacing. The ordinary SP upper son-order reconstruction remains Japheth `3210` → Shem `3208` → Ham `3206`, with `2+2` spacing. Birth-order position, named person, and representative status are distinct; Report V and its companion supply the fuller interpretation.

#### 3.1.3 SP Flood cap and patriarchal deaths

For the nine pre-Noah rows Adam through Lamech, native G2 inclusive capacity is `birth−2893+1`, equivalently `birth−2892`. Noah is outside this cap domain.

| Row | Native G2 birth | Inclusive capacity to Flood start |
|---|---:|---:|
| Adam / preferred chain head | 4199 | 1307 |
| Seth | 4069 | 1177 |
| Enosh | 3964 | 1072 |
| Kenan | 3874 | 982 |
| Mahalalel | 3804 | 912 |
| Jared | 3739 | 847 |
| Enoch | 3677 | 785 |
| Methuselah | 3612 | 720 |
| Lamech | 3545 | 653 |

Capacities are not nine asserted lifespans. The retained SP lifespans of Jared, Methuselah, and Lamech meet their capacities and place their selected deaths at the G2 Flood start:

| Patriarch | Selected death BC | Inclusive verification | Equivalent capacity to Flood close |
|---|---:|---|---|
| Jared | 2893 | `3739−2893+1=847` | `3739−2892=847` |
| Methuselah | 2893 | `3612−2893+1=720` | `3612−2892=720` |
| Lamech | 2893 | `3545−2893+1=653` | `3545−2892=653` |

The equivalent closing-boundary calculation does not move their selected deaths to `2892`. The inclusive `+1` counts the endpoint year; it does not give Adam through Lamech a Noah/Shem companion birth rail.

For coherent Gear displacement `δ = −2, 0, +2`, transport each selected birth and Flood start together. The capacity stays `(birth+δ)−(2893+δ)+1 = birth−2893+1`; close is independently `2892+δ`. A cap takes the minimum of the current lifespan count and this qualified capacity. Gear carries the current capped lifespan unchanged and does not restore discarded information. This is guarded/source-qualified commutation, with no wider state-count claim.

#### 3.1.4 Ordinary Flood Gears, fixed Arphaxad, and the SP midpoint

This table uses the full-430 comparison frame, Terah `+60` OFF, MT/SP second Cainan OFF, and LXX native second Cainan ON. The LXX G2 Creation head is `5494`, consistent with `5494−3238=2256`; Cainan-OFF `5364` must not be paired with native-ON Flood `3238`.

| Tradition | G3 Flood start→close | G2 Flood start→close | G1 Flood start→close | Fixed Arphaxad |
|---|---|---|---|---:|
| MT | 2460→2459 | 2458→2457 | 2456→2455 | 2456 |
| LXX — native Cainan ON | 3240→3239 | 3238→3237 | 3236→3235 | 3236 |
| SP | 3110→3109 | 3108→3107 | 3106→3105 | 3106 |

Every row has the ladder `G3 start → G2 start → G1 start → G1 close = 2+2+1 = 5`. At this layer LXX is MT `+780`, including Arphaxad. Each Flood close arises from that Gear’s one-year event span, independently of SP Noah/Shem primary→companion. At held Sojourn, Terah, and Cainan settings, regular Arphaxad onward through Moses does not move with Gear; the separately scoped variant mechanisms retain their own permissions.

Subtract `215` from this table for the corresponding minimum/native frames. The native SP starts G3/G2/G1 are `2895/2893/2891`, with closes `2894/2892/2890`; fixed Arphaxad is `2891`.

The coherent SP Lamech biographies are:

| Gear | Native SP Lamech | Equalized SP Lamech | Lifespan count |
|---|---|---|---|
| G1 | 3543→2891 | 3758→3106 | 653 inclusive |
| G2 | 3545→2893 | 3760→3108 | 653 inclusive |
| G3 | 3547→2895 | 3762→3110 | 653 inclusive |

Preserve two separate observations:

1. G2 midpoint to fixed Arphaxad: `4414→3760→3106 = 654+654`, equivalently native `4199→3545→2891`. Lamech’s G2 birth is the midpoint; this is not a Flood midpoint.
2. G1 convergence: Lamech death / Flood start / fixed Arphaxad birth share `3106`, equivalently native `2891`, as three distinct node classes. No midpoint language belongs to this convergence.

### 3.2 Post-Flood to Patriarchs: SP Minimum / Arphaxad-bound suffix

At the held native settings, G2 Flood start `2893` is two ordinary years before fixed Arphaxad `2891`. Flood close `2892` is the intervening boundary. No SP companion operator acts on Arphaxad or the subsequent regular rows.

#### 3.2.1 SP Noah/Shem field and named bindings

Each slash-pair below is ordered primary / lower companion. The companion is one year farther forward in time. The rows display ordinary Gear combined with SP-local person-station adjacency; they are not six independently attested source states or a new unrestricted execution generator.

| Gear | Noah birth | Noah death | Shem birth | Shem death |
|---|---|---|---|---|
| G1 | 3491/3490 | 2541/2540 | 2991/2990 | 2391/2390 |
| G2 | 3493/3492 | 2543/2542 | 2993/2992 | 2393/2392 |
| G3 | 3495/3494 | 2545/2544 | 2995/2994 | 2395/2394 |

Add `215` for the reports’ equalized dates. Noah’s primary death column carries the inclusive/harmonic qualification and the lower column the ordinary-companion qualification. Matched birth/death endpoints preserve Noah `950` and Shem `600`; matched Noah/Shem births preserve `500`. The mixed G2 companion-Noah / primary-Shem path is `3492−2993=499`, the ordinal 500th-year alternative.

The native G2 post-Flood spans are `2893−2543=350` and `2892−2542=350`. The second uses Flood close and Noah’s companion death; it does not type the Flood close as a companion. The cross-pair `2893−2542=351` is not an unqualified `350`.

The following bindings preserve the prior usable stations while making their Gears explicit:

| Shem station / binding | Birth BC | Death BC | Qualified relation |
|---|---:|---:|---|
| G2 primary, Noah/Flood comparison | 2993 | 2393 | G2 primary Noah `3493−500=2993`; `2993−100=2893`, Flood start. |
| G2 companion, Noah/Flood comparison | 2992 | 2392 | G2 companion Noah `3492−500=2992`; ordinal `2992−99=2893`, Flood start. |
| G1 primary, Arphaxad-bound | 2991 | 2391 | `2991−100=2891`, fixed Arphaxad; also `3493−502=2991` from G2 primary Noah. |
| G1 companion, Noah-bound comparison | 2990 | 2390 | `3492−502=2990` from G2 companion Noah; it does not replace the full-100 Arphaxad-bound row. |

G2 primary Shem `2993` is `102` from fixed Arphaxad `2891`. These comparisons retain their endpoint roles and bindings. Noah/Shem alone have the full qualified cross-Gear endpoint-comparison permission in this domain; other patriarchs retain coherent-Gear biographies. Qualified Noah↔Flood comparisons are allowed, while the Flood remains an event start/close structure.

The post-Flood begetting table selects the G1 primary / Arphaxad-bound Shem row:

| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |
|---|---:|---:|---:|---:|
| Shem — Arphaxad-bound | 2991 | 2391 | 600 | 100 |
| Arphaxad | 2891 | 2453 | 438 | 135 |
| Shelah | 2756 | 2323 | 433 | 130 |
| Eber | 2626 | 2222 | 404 | 134 |
| Peleg | 2492 | 2253 | 239 | 130 |
| Reu | 2362 | 2123 | 239 | 132 |
| Serug | 2230 | 2000 | 230 | 130 |
| Nahor | 2100 | 1952 | 148 | 79 |
| Terah | 2021 | 1876 | 145, or 205 ideal | 70 |
| Abraham | 1951 | 1776 | 175 | — |

Arithmetic verification, Arphaxad-bound standard intervals:

| Row | Verification |
|---|---|
| Shem | `2991−100=2891`, Arphaxad. |
| Arphaxad | `2891−135=2756`, Shelah. |
| Shelah | `2756−130=2626`, Eber. |
| Eber | `2626−134=2492`, Peleg. |
| Peleg | `2492−130=2362`, Reu. |
| Reu | `2362−132=2230`, Serug. |
| Serug | `2230−130=2100`, Nahor. |
| Nahor | `2100−79=2021`, Terah. |
| Terah | `2021−70=1951`, Abraham. |

Convergence note:
SP Abraham, `1951 BC`, matches MT Minimum-Regular Abraham, `1951 BC`.

#### 3.2.2 Terah Dual-Lock: `145` versus `205`

In the SP post-Flood timeline, Terah functions as a dual-harmonic pivot.

| State | Lifespan | Target |
|---|---:|---|
| Textual / Normal | 145 years | Death at `1876 BC`. |
| Architectural / Ideal | 205 years | Mirrors MT and enables the 1000-year harmonic from Arphaxad's birth to Abraham's birth, `100 + 1000 + 100`. |

Both values target Abraham's birth at `1951 BC` and Terah's death at `1876 BC`. The SP text officially contracts Terah's lifespan, `205 → 145`, to land his death on Abram's call at age `75`. Architecturally, however, the `205` state remains visible: the SP has not eliminated the Terah problem so much as shifted it from begetting-age tension to lifespan tension. Therefore the SP `+60 Terah` possibility remains state-valid where opened, while SP cumulative tables retain the official `145` span.

#### 3.2.3 External alignment: BJ / Jubilees

The SP Creation, `4199 BC` Normal, is separated from the BJ / Jubilees Creation, `3856 BC`, by 343 years.

Repository perspective:

```markdown
343 years = 7 Jubilees
```

BJ / Jubilees consistently employs inclusive reckoning by source argument.

Claim-status: structural inference and shared-tradition evidence.
The 343-year gap, 7 Jubilees, fits the architectural requirement of the SP baseline while preserving the theological interval native to the Jubilees tradition.

### 3.3 Patriarchal period: SP Minimum

State note:
Same as MT Minimum-Regular in the Abraham → Levi / Joseph minimum state. Abraham has two birth states, `1951 BC` and `2166 BC`, by the `±215` Sojourn fork. This field is not affected by `+60 Terah` until the Terah boundary.

| Patriarch / event | Birth BC | Death BC | Lifespan | Key events |
|---|---:|---:|---:|---|
| Abraham | 1951 | 1776 | 175 | Call `1876 BC`. |
| Sarah | 1941 | 1814 | 127 | — |
| Isaac | 1851 | 1671 | 180 | — |
| Jacob | 1791 | 1644 | 147 | Entry `1661 BC`; `+215 → 1876`. |
| Levi | 1704 | 1567 | 137 | — |

### 3.4 Fixed epoch: SP; same as MT

Identical to MT §2.4. The timeline is unified from Abraham forward.

| Event / person | Date BC | Notes |
|---|---:|---|
| Aaron birth | 1529 | — |
| Moses birth | 1526 | — |
| Exodus | 1446 | Fixed anchor. |
| Conquest | 1406 | — |

## 4. LXX Regular Baseline

Active state:
LXX Regular-Minimum.

Anchor:
Exodus `1446 BC`; Entry into Egypt `1661 BC`.

Website adjustment:
Subtract `275` from Adam through Levi.

Note:
LXX Regular-Minimum = MT Minimum-Regular + `1380` years.

### 4.1 Creation to Flood: LXX Regular-Minimum

| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |
|---|---:|---:|---:|---:|
| Creation Week | 5286 | 5279 | 7 | — |
| Adam | 5279 | 4349 | 930 | 230 |
| Seth | 5049 | 4137 | 912 | 205 |
| Enosh | 4844 | 3939 | 905 | 190 |
| Kenan | 4654 | 3744 | 910 | 170 |
| Mahalalel | 4484 | 3589 | 895 | 165 |
| Jared | 4319 | 3357 | 962 | 162 |
| Enoch | 4157 | 3792 | 365 | 165 |
| Methuselah | 3992 | 3023 | 969 | 187 |
| Lamech | 3805 | 3052 | 753 | 182 |
| Noah | 3623 | 2673 | 950 | 500 |
| Flood | 3023 | 3022 | 1 | — |

Source note:
The main LXX reconstruction pairs restored begetting `182` with attested LXX lifespan `753` in both Regular and Cumulative execution. The remainder `571` is calculated. The lack of an identified surviving joint `182/753` attestation concerns the combination, not `753` itself; §4A.1 explains its retention as the author-preferred original LXX lifespan. Methuselah still dies in the Flood year (`3023 BC`); Lamech dies `29` years before (`3052 BC`). See §4A for the source distinction and qualified Key-of-23 explanation, and Appendix B for the MT-derived LXX `777` overlay and retained external references. No other row in this birth chain changes.

### 4.2 Post-Flood to Patriarchs: LXX Regular-Minimum

| Patriarch / event | Birth BC | Death BC | Lifespan | Begetting age |
|---|---:|---:|---:|---:|
| Shem | 3121 | 2521 | 600 | 100 |
| Arphaxad | 3021 | 2556 | 465 | 135 |
| 2nd Cainan | 2886 | 2426 | 460 | 130, LXX native |
| Shelah | 2756 | 2296 | 460 | 130 |
| Eber | 2626 | 2122 | 504 | 134 |
| Peleg | 2492 | 2153 | 339 | 130 |
| Reu | 2362 | 2023 | 339 | 132 |
| Serug | 2230 | 1900 | 330 | 130 |
| Nahor | 2100 | 1892 | 208 | 79 |
| Terah | 2021 | 1816 | 205 | 70/130 state-dependent |

Note:
The Terah / Abraham relation is resolved by the author-clarified four-position field. The displayed LXX Regular-Minimum Terah row, `2021–1816 BC`, is the no-`+60 Terah`, no-`+215 Sojourn` minimum row. In that state, Terah begets Abraham at `70`, producing Abraham `1951 BC`. When `+60 Terah` is active, Terah shifts to `2081–1876 BC`; the `130` begetting-state then also produces Abraham `1951 BC`. With the `+215 Sojourn` state active, the corresponding pair is `2236–2031 BC` with begetting-state `70`, producing Abraham `2166 BC`, and `2296–2091 BC` with begetting-state `130`, also producing Abraham `2166 BC`.

Therefore Abraham has two birth states, `1951 BC` and `2166 BC`, while Terah has four birth/death states.

Author-confirmed LXX table correction (September 2026): the former §4.2 Peleg/Reu/Serug lifespan cells `239/239/230` were copy errors, not manuscript variants. The controlling LXX Regular-Minimum values are `339/339/330`; births remain `2492/2362/2230 BC`, so the corrected deaths are `2153/2023/1900 BC`. Begetting ages remain `130/132/130`. This correction is independent of the Lamech `182/753` source hierarchy.

See MT §2.2.1 for `±2` anomaly details at tradition-specific dates.

### 4.3 Patriarchal period: LXX Regular-Minimum

Same as MT Minimum-Regular in the Abraham → Levi / Joseph minimum state. Abraham has two birth states, `1951 BC` and `2166 BC`, by the `±215` Sojourn fork. This field is not affected by `+60 Terah` until the Terah boundary.

### 4.4 Fixed epoch: LXX

Identical to MT §2.4.

## 4A. Lamech: common `182/753` reconstruction and the Key-of-23 crossover hypothesis

Active state: author-adopted LXX main reconstruction, September 8 2026. `182` is the restored regular begetting input; `753` is the retained attested LXX lifespan in both Regular and Cumulative execution. This supersedes the former regular-`777` / cumulative-`753` dual-locality ruling. Unless specified otherwise, the displays below use the website `+215 Sojourn`, no-`+60 Terah`, native-LXX-Cainan frame. Appendix A retains the minimum-frame conversion. Appendix B preserves the MT-derived LXX `777` overlay, overlap geometry, and lesser corroborations outside the main chronology.

### 4A.1 Source hierarchy and the component-wise reconstruction

The standard transmitted LXX record is `188 + 565 = 753`. **`753` itself is the attested/transmitted LXX lifespan in Genesis 5:31, not a reconstructed number.** This study retains it as the **preferred original LXX lifespan**, an author-adopted textual/structural conclusion supported especially by §4A.3. Its attestation is a textual fact; the judgment that it preserves the original LXX lifespan is distinct from that fact and does not establish the earliest Hebrew reading or a complete scribal transmission history.

The component-wise reconstruction pairs this retained `753` with the restored operative begetting age `182`, supported by the repository's MT/external-witness argument and source-selected birth chain. It gives `182 + 571 = 753`, with `571` calculated. No surviving manuscript witness jointly attesting `182/753`, or independently reading `571`, has been identified in the sources reviewed here. That qualification concerns the combined biography, not the attestation of `753`, and is not a claim that such a joint text could never have existed.

Smith is an external reconstruction witness, not an endorsement of this combined selection. His different full-biography restoration and its source qualifications are retained in Appendix B.1/B.7. MT-like ancestry is the author's working transmission hypothesis, not a historical priority established by the numerical comparisons.

Claim-status: attested LXX lifespan `753`; author-adopted judgment that it preserves the original LXX lifespan; restored begetting `182`; component-wise `182/753` reconstruction; calculated remainder `571`. Structural analysis supports retention of the attested lifespan but does not create joint manuscript attestation.

### 4A.2 What changes, and what stays fixed

| Frame / method | Main Lamech input or biography | Consequence |
|---|---|---|
| LXX Regular-Minimum | `3805 → 3052 BC`; begetting `182`; lifespan `753` | Noah remains `3623 BC`; Flood remains `3023 BC`. |
| LXX regular `+215` | `4020 → 3267 BC`; begetting `182`; lifespan `753` | Noah remains `3838 BC`; Flood remains `3238 BC`. |
| LXX cumulative | `753` chain value; Nisan member `8048 BC`; envelope `8053–8046 BC` | Existing cumulative coordinates and totals remain unchanged. |

```text
3805 − 3052 = 4020 − 3267 = 753
3805 − 3623 = 4020 − 3838 = 182
3052 − 3023 = 3267 − 3238 = 29
```

Lamech now dies `29` years before the regular LXX Flood. The selected Methuselah `187` / Lamech `182` birth chain still puts Methuselah's death at the Flood: `187 + 182 + 600 = 969`. No regular birth date, Creation endpoint, Noah biography, Flood anchor, or Cainan/Terah/Sojourn operator is changed by the lifespan decision.

The six LXX centenary begetting changes remain lifespan-preserving at their own rows. The whole regular LXX lifespan vector is no longer identical to MT: Lamech contributes a separate difference of `−24`. A Flood-cap rule does not generate the attested LXX `753`; that lifespan enters as LXX source data, not as a fitted numerical exception. Failure to derive it from an unmodified MT lifespan vector limits that proposed generator, not the LXX datum or its adopted source hierarchy.

### 4A.3 Primary structural rationale: the `69 | 529 = 598` family

The author ranks this family first among the structural reasons for retaining `753`; it is not ranked as independent manuscript evidence.

The LXX main Lamech death supplies an internal divider between declared Shem endpoints:

```text
3336 − 3267 = 69 = 3 × 23
3267 − 2738 = 529 = 23 × 23
3336 − 2738 = 598 = 69 + 529 = 2 × 299
598 × 300/299 = 600
69 × 70/69 = 70
69 × 25/23 = 75
529 × 25/23 = 575
```

Endpoint register: `3336 BC` is the Shem birth on the `3336–2736 BC` biography; `2738 BC` is the death on the alternate `3338–2738 BC` biography. Each matched biography retains `600`. The selected `3336 → 2738` span is therefore a cross-Gear `598` comparison, not Shem's ordinary lifespan. `3267 BC` is the main Lamech death (`4020 − 753`) and is not shifted to manufacture the partition.

The MT supplies the corresponding Key ingredients under its own controlled states:

```text
3127 − 3058 = 69
3056 − 2458 = 598
598 = 69 + 529
598 × 300/299 = 600
```

Here `3127 → 3058` is Enoch's ascension/end-of-life to Noah's standard birth; `3056 → 2458` is the alternate Noah birth to the standard Flood. File_02 §6.2–6.3 controls the latter `598 → 600` configuration. These are two separately located MT intervals; the scalar decomposition of `598` must not invent an intervening MT event or be represented as the same continuous three-node sequence as the LXX display.

The proposed crossover is that a Key grammar already visible in MT's Enoch–Noah/Flood field is concentrated in the LXX Lamech–Shem comparison. Shared inherited grammar, partial scribal awareness, or providential synchronization are possible interpretations. Exact arithmetic alone does not decide between them or establish a direction of transmission.

### 4A.4 Supporting lifespan relations: `24` and the SP century

```text
4114 − 2458 = 1656
1656 × 70/69 = 1680 = 5 × 336
1680 − 1656 = 24
777 − 753 = 24
753 − 653 = 100
454 − 24 = 430
```

The `777` in this main-body comparison is MT Lamech's unchanged lifespan; `753` is the adopted LXX lifespan and `653` is SP Lamech's lifespan. The `24` gain and the LXX–SP `100` difference give structural support to the choice of `753`. They do not imply that multiplying `753` by a Key yields `777`, or prove that SP was historically produced from the LXX. The cumulative `454 → 430` consequence remains controlled by §6D and uses the retained `753` input, rather than explaining that input independently of its selection.

### 4A.5 Supporting six-year anchored comparisons and their targets

An anchored expansion holds the later endpoint fixed. In positive BC labels, the earlier comparison endpoint is `a + (300/299)(b − a)`.

| Comparison | Earlier BC | Fixed later BC | Input span | Generated earlier BC |
|---|---:|---:|---:|---:|
| MT Lamech → Exodus | 3240 | 1446 | `1794 = 299 × 6` | 3246 |
| LXX Lamech, native Cainan / no `+60` → Terah firstborn in the `+60` state | 4020 | 2226 | `1794 = 299 × 6` | 4026 |
| LXX Lamech, Cainan OFF / `+60` ON → Sarah | 3950 | 2156 | `1794 = 299 × 6` | 3956 |

All three input spans expand to `1800 = 300 × 6`, gaining `6`. The first LXX route deliberately crosses Terah settings: `4020` belongs to no `+60`, whereas `2226 = 2296 − 70` is the firstborn threshold of the `+60` Terah state. The Sarah alternative uses `3950 = 4020 − 130 + 60`; Sarah remains `2156 BC`. Files 69 §5B.5 and 70 §2.3 control that firstborn/Sarah framework. These are translated realizations of one span mechanism, not automatically independent witnesses.

The paired promoted birth comparisons then expose the anchor consequences emphasized by the author:

```text
3246 − 1446 = 1800 = 5 × 360
4026 − 1446 = 2580 = 1290 + 1290 = 6 × 430
4026 − 1876 = 2150 = 5 × 430
1876 − 1446 = 430
4020 − 3240 = 4026 − 3246 = 780 = 390 + 390
4026 − 130 = 3896
3896 − 3246 = 650 = 5 × 130
3896 − 1446 = 2450 = 5 × 490 = 50 × 49
```

The exact `2450` belongs to the promoted Cainan-OFF comparison, not the unshifted `3890` member. `4026` and `3896` also occur as SOR labels elsewhere; those remain distinct node-classes controlled by File_20. These generated endpoints do not enter the main regular table or the Primary-anchor inventory.

### 4A.6 Possible origin of the transmitted `188`

The author's favored explanation is a cross-register gain-transfer: a six-year Key comparison around Lamech may have been preserved alongside the underlying begetting figure, then incorporated into transmission as though the adjusted value were the original. A marginal calculation, alternative comparison register, or subsequent conflation is a possible mechanism; no surviving sequence of scribal acts establishing one of these routes is supplied here.

```text
182 + 6 = 188
4020 − 182 = 4026 − 188 = 3838
```

These equations express equal Noah endpoints under different Lamech birth labels, not numerical synonymy of `182` and `188`. The nearby `69 → 75` supplies another possible six-year gain, but moving the whole Lamech biography six years earlier is a gain-transfer, not expansion of that same Shem interval. With Shem's birth fixed at `3336`, literal expansion of `69` to `75` would give death `3261`, not `3273`; the transferred `+6` biography is instead `4026 → 3273`, and its Shem gap is `63`.

The non-operative `188` comparison must also preserve path accounting. With Noah fixed, retaining all other begetting intervals moves the earlier chain by six years and changes the Creation-to-Noah total from `1656` to `1662`. With Methuselah's `187`, `187 + 188 + 600 = 975`, which places his `969`-year death six years **before**, not after, the Flood. The distinct `167/188` combination has `167 + 188 + 600 = 955` and a fourteen-year survival excess. Neither execution replaces the main `187/182` reconstruction.

Claim-status: exact arithmetic for the comparisons; author-favored but unproved transmission hypothesis for their entry into the text. The model does not establish historical MT priority, intentional ancient use of these exact anchors, or a probability of scribal causation.

### 4A.7 Main-chain / appendix hierarchy

Use `182/753` consistently in the actual regular and cumulative LXX reconstructions. Keep `571` explicitly calculated. Retain transmitted `188` as non-operative source data and as the object of the qualified hypothesis in §4A.6, not as a newly licensed toggle. LXX `777` biographies and cumulative extensions belong in Appendix B; their downstream operator examples belong in the relevant file's appendix. A short routing reference does not import those examples as main-chain evidence. The MT `777`, unrelated symbolic `777` structures, existing rounded protocols, and all main cumulative totals remain unchanged.

## 5. Source-numbering note

The supplied source has no Section 5. Public-clean handling preserves the jump from Section 4 to Section 6 because cross-file references already cite Section 6 for cumulative tables. This section is reserved only to document the source-numbering gap.

## 6. Cumulative Chronology Matrix

Active state:
Cumulative chronology.

Full tables source retained:
490d.com/mt-lxx-sp-lifespan-accumulative-long-chronology-table.

Methodology:
Lifespans are added end-to-end from Adam to Moses to generate deep-time scalars.

Joseph and half-clutch routing note:
The §6 tables remain the direct Adam–Moses/Aaron lifespan-stacking trunk and therefore do not add Joseph as a new patriarchal row. Corrected Final File_61 derives Joseph's original collateral double portion from the unchanged rows: backward from Kohath (`1906 → 1796` and `1909.5 → 1799.5 = 110`) and forward from Levi (`1933 → 1823` and `1936.5 → 1826.5 = 110`). Because these are fixed-offset `±110` constructions, File_61 and Final File_62 also derive the following downstream translations without changing the table source:

```text
Forward — Moses/Nisan:
original 1933 → 1823
H7       1926 → 1816
T14      1919 → 1809

Forward — Aaron/Tishri exact:
original 1936.5 → 1826.5
H7       1929.5 → 1819.5
T14      1922.5 → 1812.5

Backward — Moses/Nisan:
original 1906 → 1796
H7       1899 → 1789
T14      1892 → 1782

Backward — Aaron/Tishri exact:
original 1909.5 → 1799.5
H7       1902.5 → 1792.5
T14      1895.5 → 1785.5
```

Every portion remains `110`. These dates are downstream File_61/File_62 coordinates, not new File_18 rows; Joseph remains collateral rather than a direct trunk member.

| Cumulative element | Handling |
|---|---|
| Moses Line, Nisan / Spring | Primary trunk. |
| Aaron Line, Tishri / Fall | Secondary trunk, `+3.5` years. |
| The 3.5-year straddle | Aaron is born about 3/3.5 years before Moses and dies first (Av 1 in the repository’s 1407 BC terminal chronology); Moses dies later in the winter phase of 1406 BC. The `3.5` is a phase-track separation, not a lifespan change: Aaron remains `123`, Moses `120`. |
| Cumulative Shem `±2` anomaly | Propagates through the entire chain and creates a 7-year margin from lower bound to upper bound. |
| Adam Year 6 | `14006 BC` is treated as Year 6; Apparent Age is calculated from `14006 + 30 = 14036`. |

### 6A. MT Cumulative Chronology: the main trunk

Anchor:
Conquest / Death of Moses = `1406 BC`.

Scalar:
`12600` years = `10 × 1260` to Creation.

Column key:

| Column | Meaning |
|---|---|
| Moses Line, Nisan | Standard Spring reckoning. |
| Aaron Line, Tishri | Fall reckoning, `+3.5` years. |
| 7-year span | Harmonic window defined by Aaron Start – Moses End. |

| Patriarch / event | Lifespan | Moses Line, Nisan | Aaron Line, Tishri | 7-year span, start – end | Harmonic lock to 1406 BC |
|---|---:|---:|---:|---|---|
| Apparent Birth | — | 14036 BC | 14039.5 BC | 14041–14034 BC | Year 6 + 30 years |
| Adam, Year 6 | 930 | 14006 BC | 14009.5 BC | 14011–14004 BC | 12600 years = `10 × 1260` |
| Seth | 912 | 13076 BC | 13079.5 BC | 13081–13074 BC | — |
| Enosh | 905 | 12164 BC | 12167.5 BC | 12169–12162 BC | — |
| Kenan | 910 | 11259 BC | 11262.5 BC | 11264–11257 BC | — |
| Mahalalel | 895 | 10349 BC | 10352.5 BC | 10354–10347 BC | — |
| Jared | 962 | 9454 BC | 9457.5 BC | 9459–9452 BC | Watcher Era, 4600 to Flood |
| Enoch | 365 | 8492 BC | 8495.5 BC | 8497–8490 BC | — |
| Methuselah | 969 | 8127 BC | 8130.5 BC | 8132–8125 BC | — |
| Lamech | 777 | 7158 BC | 7161.5 BC | 7163–7156 BC | — |
| Noah | 950 | 6381 BC | 6384.5 BC | 6386–6379 BC | — |
| Shem | 600 | 5431 BC | 5434.5 BC | 5436–5429 BC | 480 + 120 structure |
| Ark Warning | 120 | 4951 BC | 4954.5 BC | 4956–4949 BC | Upper `4956` → Moses birth = 3430 |
| The Flood | — | 4831 BC | 4834.5 BC | 4836–4829 BC | Upper `4836` → Conquest = 3430 |
| Arphaxad | 438 | 4831 BC | 4834.5 BC | 4836–4829 BC | Born 2 years after Flood |
| Shelah | 433 | 4393 BC | 4396.5 BC | 4398–4391 BC | — |
| Eber | 464 | 3960 BC | 3963.5 BC | 3965–3958 BC | — |
| Peleg | 239 | 3496 BC | 3499.5 BC | 3501–3494 BC | Author-clarified: Nisan envelope `3501n–3494n BC`; parallel Tishri envelope `3502t–3495t BC`; `3495t → AD 1406t = 4900` by File_09 Mirror suffix inversion. |
| Reu | 239 | 3257 BC | 3260.5 BC | 3262–3255 BC | — |
| Serug | 230 | 3018 BC | 3021.5 BC | 3023–3016 BC | Lower `3016` → `7 × 230` |
| Nahor | 148 | 2788 BC | 2791.5 BC | 2793–2786 BC | Lower `2786` → `6 × 230` |
| Terah | 205 | 2640 BC | 2643.5 BC | 2645–2638 BC | — |
| Abraham | 175 | 2435 BC | 2438.5 BC | 2440–2433 BC | 989 to Exodus |
| Isaac | 180 | 2260 BC | 2263.5 BC | 2265–2258 BC | — |
| Jacob | 147 | 2080 BC | 2083.5 BC | 2085–2078 BC | — |
| Levi | 137 | 1933 BC | 1936.5 BC | 1938–1931 BC | Tribal Descent, `12 × 130` |
| Kohath | 133 | 1796 BC | 1799.5 BC | 1801–1794 BC | — |
| Amram | 137 | 1663 BC | 1666.5 BC | 1668–1661 BC | Lower `1661` = 215 Entry |
| Moses | 120 | 1526 BC | 1529.5 BC | 1531–1524 BC | — |
| Conquest | — | 1406 BC | 1406 BC | — | Target |

### 6B. MT Cumulative + 2nd Cainan

Active state:
Cumulative restored 2nd Cainan.

Logic:
Reinserts the 460-year lifespan of 2nd Cainan, LXX / Luke 3:36, into the MT Cumulative chain.

Effect:
Shifts all dates from Adam to Arphaxad earlier by 460 years.

Derived companion execution:

```markdown
14036 + 460 = 14496
14039.5 + 460 = 14499.5
14041–14034 + 460 = 14501–14494

14466 + 30 = 14496
14469.5 + 30 = 14499.5
14471–14464 + 30 = 14501–14494
```

The ordinary whole-year Aaron member is `14499 BC`; the exact phase-resolved member remains `14499.5 BC`. This companion is admitted only as an explicitly derived row.

| Patriarch | Lifespan | Standard, Moses | With Cainan, Moses Line | 7-year span with Cainan, start – end | Note |
|---|---:|---:|---:|---|---|
| Apparent Adam — derived companion | — | 14036 | 14496 | 14501–14494 | Aaron `14499` whole-year / `14499.5` exact; derived only, not a raw row |
| Adam, Year 6 | 930 | 14006 | 14466 | 14471–14464 | `14466` versus `1446`, Exodus |
| Seth | 912 | 13076 | 13536 | 13541–13534 | — |
| … | … | … | … | … | … |
| Jared | 962 | 9454 | 9914 | 9919–9912 | — |
| Flood | — | 4831 | 5291 | 5296–5289 | `5290` → Christ, Key of 23 |
| Arphaxad | 438 | 4831 | 5291 | 5296–5289 | — |
| Cainan | 460 | N/A | 4853 | 4858–4851 | Inserted variable |
| Shelah | 433 | 4393 | 4393 | 4398–4391 | Convergence point |
| … | … | … | … | … | Matches standard from here |

Cainan macro-vector note:
This table supplies the source field for the File_16 Cainan macro-vector. The active table-source values are Cainan `4858–4851 BC`, Shelah / convergence envelope `4398–4391 BC`, and selected member `4396 BC`. `File_18` supplies these values; `File_16` controls the `1876 BC` Nexus argument, Category B classification, and Bullseye Protocol use.

Comparative `60`-multiple note:
When the comparative SP and LXX cumulative Shelah envelopes are opened by dependency, MT, SP, and LXX all yield seven-year target windows by spans divisible by `60`: MT `60 × 42` to the Famine window, SP `60 × 40` to the Famine window, and LXX `60 × 49 = 6 × 490` to the preceding years of Plenty. This note is structural comparison only and does not alter the §6B table rows.

### 6C. SP Cumulative Chronology

Active state:
SP cumulative chronology.

Anchor:
Death of Joshua = `1296 BC`, SP tradition, 110 years.

Scalar:
`12100 = 110 × 110` years to Creation, lower bound.

Logic:
Uses SP lifespans, including Terah 145 and Lamech 653.

| Patriarch | Lifespan | Moses Line, Nisan | 7-year span, start – end | Harmonic lock |
|---|---:|---:|---|---|
| Adam | 930 | 13398 BC | 13403–13396 BC | Lower `13396` → Joshua = `110²` |
| Ark Warning | 120 | 4831 BC | 4836–4829 BC | Matches MT Flood |
| Flood | — | 4711 BC | 4716–4709 BC | 120 years after MT Flood |
| Peleg | 239 | 3436 BC | 3441–3434 BC | 70 Jubilees to Christ, 6 BC |
| Terah | 145 | 2580 BC | 2585–2578 BC | SP specific, 145 |
| Joshua | 110 | 1406 BC | 1411–1404 BC | Conquest |
| Death | — | 1296 BC | — | Target |

#### 6C.1 Day-4 phase-anchor display (File_56 dependency; routed July 2 2026, applied July 6 2026)

Active state:
SP Enochian Day-4 phase-anchor state, cumulative-only.

Under the `File_56` state, the SP cumulative decade reads:

| Decade node | Value | Label under File_56 |
|---|---:|---|
| Implied Day 1 | 13406 BC | decade opening; display label |
| Aaron / Adam member | 13401 BC | bears the sixth-day label |
| Day-10 terminus | 13396 BC | carries the `110²` Joshua lock |

This display coexists with the default Day-1 / Year-7 reading of the §6C table. Every numerical value is shared; only day-labels shift by `3`. `File_56` controls the phase-anchor state. SP regular chronology is unaffected.

### 6D. LXX Cumulative Chronology

Active state:
LXX cumulative chronology.

Anchor:
Conquest / Moses Death = `1406 BC`.

Logic:
Uses LXX lifespans, including Lamech's attested/transmitted `753`, retained as the author-preferred original LXX lifespan in agreement with Regular execution (§4A.1), and Nahor `208`. Includes 2nd Cainan. The former main-table overlay is preserved separately in Appendix B.2; all main-chain values remain unchanged.

| Patriarch | Lifespan | Moses Line, Nisan | 7-year span, start – end | Note |
|---|---:|---:|---|---|
| Adam | 930 | 14896 BC | 14901–14894 BC | — |
| Lamech, chain | 753 | 8048 BC | 8053–8046 BC | Flood chief marker: the death of Methuselah |
| Flood | — | 5745 BC | 5750–5743 BC | — |
| Cainan | 460 | 5280 BC | 5285–5278 BC | Includes 2nd Cainan |
| Peleg | 339 | 3856 BC | 3861–3854 BC | `3856 BC` = BJ / Jubilees Creation |
| Conquest | — | 1406 BC | — | Target |

Appendix routing:
The `777` cumulative overlay formerly printed here is preserved in Appendix B.2. It shares the Noah endpoint with the `753` chain and must not propagate upward. The LXX Flood's chief cumulative marker remains the death of Methuselah, matching the selected regular `187/182` alignment. The `14901 − 1446 = 13455 = 299 × 45` lock (File_56 dependency) and all main §6D coordinates remain unchanged.

`430`-alignment justification state (bounded addition):
Leveling the MT with the LXX by restoring Cainan (`+460`, §6B), the two cumulative chronologies differ by exactly `430` from Lamech back to Adam (`14896 − 14466`), but only with Lamech at `753`: the accumulated difference below him is `454`, and his `−24` trims it to Ezekiel's figure, carried unbroken to the head (`8048 − 7618 = 430` at Lamech). The four Adam heads — each tradition with and without Cainan: `14896 / 14466 / 14436 / 14006 BC` — read `430 + 30 + 430` (the Adam field; narrative at `File_22` / `File_46` §6A.5). Claim-status: arithmetic fact; the functional-choice reading is structural inference.

Flood-marker convention set (bounded addition):
MT cumulative — dual marking (death of Methuselah; birth of Arphaxad two years after; §6A). LXX cumulative — chief marker the death of Methuselah. SP cumulative — death-side marker unassigned, since Jared, Methuselah, and Lamech all die in the Flood year (§3); the Arphaxad marker stands universally. Claim-status: author-declared convention over textual data.

Cross-reference:
Entity logic: `File_02`, Shem `±2` anomaly, Regular and Cumulative distinctions. Axiom definition: `File_00`, localized baseline variants. Overlay locks and deep-time expansions: `File_46` §6A; `File_44` §6A; `File_51b` §7A.

## 7. Sumerian King List Integration

Active states:
Sumerian A / SKL Short; Sumerian B / SKL Long; 360:1 scale.

Source:
1260d.com / 490d.com merged chronology.

Scaling key:
360 Sumerian years = 1 Biblical year; source phrase: “A day is as a year.”

### 7.1 Primary anchors

State note:
The Primary Date column corresponds to Sumerian A / SKL Short where `17980` whole years are active. The Variant column corresponds to Sumerian B / SKL Long where the `+6480` relation and `24510` whole-year state are active.

| Event | Sumerian A / SKL Short | Sumerian B / SKL Long, `+6480` | Notes |
|---|---:|---:|---|
| Tower of Babel | 2906 BC | 2856 BC | Equally attested by source claim. |
| Flood | 20886 BC | 27366 BC | 360:1 from biblical Flood. |
| Pre-Creation | 452886 BC | 459366 BC | 432000 years to Flood. |

### 7.2 The `6480`-year variant

Active state:
Sumerian B / SKL Long and File_34-controlled precessional envelope.

An alternative text records “24510 years, 3 months and 3.5 days” instead of “17980 years” for the 23 post-Flood kings. The whole-year difference is `6530`. Under the File_21 / File_02 SKL Short / Long control, the exact shift relation is:

```markdown
24510 − 17980 = 6530
2906 − 2856 = 50
6530 − 50 = 6480
27366 − 20886 = 6480
```

This preserves the source-retained `24510` / `17980` whole-year totals while explaining why the active SKL Flood-anchor displacement is `6480` after the 50-year end-anchor gap is accounted for.

The primary anchor dates, `2906/2856 BC`, also carry their own `±2`, `±30`, and `+720` fine-tuning. Example:

```markdown
2906 + 720 = 3626 BC
```

With adjustments, the source gives:

```markdown
3658/3656/3608/3606 BC
```

Note:
`3606 BC = 6 × 360` years to the `1446 BC` Exodus. Full elaboration of anchor fine-tuning is beyond the scope of this baseline reference.

Source note:
Claim-status: dependency-controlled textual datum and structural inference.
The “3.5 days” is significant by source argument. The source relates it to the 3.5 days / years prophetic period in Revelation 11–13 and Daniel 7, 9, and 12.

#### 7.2.1 The Precessional Envelope: Berossus-SKL unification

Active state:
File_34-controlled SKL / Berossus dependency.

The `6480`-year variant gap functions as the key that unifies the Sumerian King List with Berossus chronology. Both systems use the same “3 months,” 90 days of precession, but interpret its vector differently.

| System | Interpretation | Vector | Flood anchor |
|---|---|---|---:|
| Berossus | `90 × 2` days Precession | Past | 34566 BC |
| SKL Upper | 90 days Precession | Past | 28086 BC |
| SKL Lower | 0, anchor | — | 21606 BC / 20886 BC |

Tier separation:
Each tier is exactly `6480` years from the next.

Alignment formula:

```markdown
Berossus_Flood = SKL_Lower_Flood + 12960
```

AI-processing rule:
Berossus and SKL are not independent chronologies in this source's integration state. They are the same system read with different precessional offsets.

Cross-reference:
Full derivation and manuscript tradition mapping: `File_34`, §5, The Precessional Envelope. Post-final `File_34` also controls Appendix B.5 for the SKL-to-Berossus `2370` corridor and `30 + 20 + 30` restoration corridor where those labels are referenced by SKL files.

### 7.3 The `+720` scale-state

Active state:
SKL `+720 scale-state`.

The `±2`-year anomaly at Shem scales to `720` years:

```markdown
2 × 360 = 720
```

This creates parallel date variants throughout.

Example, Adam / Alulim:

| Pair | Dates | Difference |
|---|---|---:|
| Primary pair | 262086 BC and 262806 BC | 720 years |

The `6480`-year gap can expand to `7200` years, `10 × 720`, for scaling purposes. Compare the MT-LXX gap range from `1380` to `1440`, `+60`, where `1440 = 1/5` of `7200`.

### 7.4 The `+2` and `+30` fine-tuning mechanism

Active states:
SKL `+2 local rail`; SKL `+30 Apparent Mode`; SKL `+720 scale-state`.

All SKL dates carry both the `±2` literal years and the `±30` literal years, paralleling Adam's apparent age in biblical chronology, applied throughout.

Example, Adam / Alulim full range:

| Rail | Dates |
|---|---|
| Base | 262086 / 262806 BC, 720 apart |
| With `±2` | 262088 / 262808 BC |
| With `+30` | 262116 / 262118 BC and 262836 / 262838 BC |

The same mechanism applies to `+6480` variant dates.

#### 7.4.1 Gap range

| State | Years | Explanation |
|---|---:|---|
| Minimum | 6450 | `6480 − 30`; 3 months of precession under Great Year 25800; `15 × 430`. |
| Standard | 6480 | Standard precessional display. |
| Maximum | 6510 | `7 × 930`, echoing Adam's lifespan. |
| Extended | 7200 | `10 × 720`, full scaling. |

#### 7.4.2 The “3 months” as unifying mechanism

Claim-status: dependency-controlled textual datum and structural inference.
The SKL phrase “24510 years, 3 months and 3.5 days” functions, by source argument, as evidence that the two variants form one system, just as MT, SP, and LXX are complementary witnesses. The `+3 months` links the chronologies through gear-switching.

| Scale | Display |
|---|---|
| Scale 1 | 1 day = 72 years, or 71.666; 3 months = 90 days = `6480/6450` years. |
| Scale 2 | 1 day = 360 years; 90 days from the active `+30 Apparent Mode` rails `2936/2886 BC` to Pillars `AD 29465/29515`. The Pillar dates are Projective Boundary / Temple-Time coordinate states by `File_21` dependency. |

File_21 cross-file control: the Jachin / Boaz Pillar coordinates are not derived solely from the SKL row. File_21 treats the SKL `90 × 360 = 32400` alignment as providential synchronization with the Temple-Time / Ezekiel temple measurement framework. Jachin extends to `AD 29515`, Boaz extends to `AD 29465`, and both converge at `AD 29395`. Source-context link: https://www.1260d.com/temple-time.pdf

#### 7.4.3 The “3.5 days” connection: MT-SKL Creation bridge

Claim-status: dependency-controlled textual datum and structural inference.
The “3.5 days” in the SKL phrase provides, by source argument, the key that links MT to SKL.

```markdown
3.5 days × 360 = 1260 years
```

```markdown
SKL 2886/2856 BC + 1260 = MT 4146/4116 BC
```

The full 7.5 days of Creation at 1:360 scale:

```markdown
7.5 × 360 = 2700 years
```

```markdown
LXX 5586/5556 BC → SKL 2886/2856 BC = 2700 years
```

#### 7.4.4 Breakdown of the 2700-year span

Active state:
Regular chronology comparison.

| Segment | Years | Days, divided by 360 | Creation day(s) |
|---|---:|---:|---|
| LXX → MT | 1440 | 4 | Days 1–4 |
| MT → 3606/3576 BC | 540 | 1.5 | Days 5–5.5 |
| 3606/3576 → 2886/2856 BC | 720 | 2 | Days 6–7 |
| Total | 2700 | 7.5 | Full Creation Week |

The terminal 720-year segment, Days 6–7, encodes:

- Day 6: Adam created.
- Day 7: God rested, Sabbath.

#### 7.4.5 Cumulative chronology alignment

| Position | Date BC | Years to SKL | Calculation | Creation day |
|---|---:|---:|---|---|
| Shem birth | 5436 | 2550/2580 | `7 × 360 + 30/60` | Day 1, exact |
| Flood | 4836 | 1980 | `5.5 × 360` | Day 2 |

Note:
The `2550/2580` difference reflects leap-month variants, 30/60 years, not imprecision. Both values place Shem exactly at Day 1. `2580 = 36` days of precession. The 360-calendar's 40-year cycle includes 7 leap months.

Typological note:
Day 1, Shem: “Let there be Light.” Shem, שֵׁם, “Name,” prefigures Christ as “Light of the World,” John 8:12, and “the Name above every name,” Phil 2:9, by source reading.

Typological note:
Day 2, Flood: God separated waters above from waters below, Gen 1:6–8. The Flood dissolved this separation temporarily, “windows of heaven opened,” Gen 7:11. The Cumulative Flood is positioned at Day 2 because it undoes Day 2's work.

SP integration:
SP offset from LXX = `1080` years = `3 × 360` = exactly 3 days. SP participates in the same Creation Week framework in both Regular and Cumulative states.

Multi-witness design argument, source-retained and classified:

| Witness field | Source reading | Claim-status |
|---|---|---|
| One tradition aligned with SKL | possible coincidence | limited structural observation |
| All three manuscript traditions, MT / LXX / SP, plus both modes, Regular / Cumulative | design | structural inference plus providential synchronization |

The source interprets the Creation Week as distributed across all witnesses, requiring their integration to see the complete picture. The theological claim that MT, LXX, and SP function as complementary witnesses to unified divine authorship is preserved as a theological note and providential synchronization. It does not by itself prove direct scribal intent.

Source-retained conclusion, classified:
The SKL anchor, `2886/2856 BC`, marks the cosmic end of the Creation Week: the point where God's rest is complete. The SKL text's “3.5 days” functions, by source argument, as a dependency-controlled bridge from MT Creation to SKL. The claim that the systems were designed as an integrated whole is preserved as providential synchronization and theological interpretation, while the local arithmetic burden remains with the stated `3.5 × 360`, `7.5 × 360`, and SKL rail calculations.

Function:
These fine-tuning mechanisms result from scaling the small biblical `±2` and `+30` states into Sumerian cosmic time. The gear analogy is retained as explanatory language; the argument remains structural inference unless the active rail and dependency are named.

### 7.5 Applying the variants

To apply the `+6480` variant, add `6480` years to all dates from Flood backward to Pre-Creation.

| Conversion | Source date | Variant date |
|---|---:|---:|
| Flood | 20886 BC | 27366 BC |
| Adam / Alulim | 262086 BC | 268566 BC |
| Pre-Creation | 452886 BC | 459366 BC |

### 7.6 Antediluvian kings as biblical patriarchs

| SKL king | Biblical parallel | Reign, SKL | Date BC, primary |
|---|---|---:|---:|
| Alulim | Adam | 28800 years | 262086 |
| Alalngar | Seth | 36000 years | 233286 |
| Enmenluana | Enosh | 43200 years | 197286 |
| Enmengalana | Kenan | 28800 years | 154086 |
| Tammuz | Mahalalel | 36000 years | 125286 or 107286 |
| Ensipadzidana | Jared | 28800 years | 89286 |
| Enmendurana | Enoch | 21000 years | 60486 |
| Ubara-Tutu | Noah | 18600 years | 39486 |

Source note:
An asterisk in the legacy table designated a new dynasty in SKL.

### 7.7 Post-Flood notable figures

| SKL figure | Reign / span | Date BC | Biblical parallel / notes |
|---|---:|---|---|
| Etana | 1500 years | 11696–10136 | “Shepherd who ascended to heaven.” Source-retained reign value; same-side span of displayed range is `1560`. Proof-bearing File_21 harmonic uses opening anchor: `11696 − 1406 = 10290 = 210 × 49`. |
| Balih | 400 years | 10136–9736 | Etana's miracle son; Isaac type. |
| 23 kings | 17980 years | Flood → 2906 | Total post-Flood to Babel. |

### 7.8 The Pillars of Time

File_21 cross-file control:
The Pillars are Projective Boundary / Temple-Time coordinate states, not ordinary historical chronology. File_21 standardizes the live repository spelling as `Jachin`, paired with Boaz. The inherited SKL chart / earlier File_21 source used `Jochin`; retain that form only as source-history spelling unless quoting the original chart.

| Pillar | AD date range | Scale |
|---|---:|---|
| Jachin | AD 29395–AD 29515 | 1 cubit = 720 years |
| Boaz | AD 29395–AD 29465 | 1 cubit = 490 years |

State note:
The shared inside-skin convergence coordinate is `AD 29395`; Boaz extends to `AD 29465`; Jachin extends to `AD 29515`. File_21 treats the SKL `3 months = 90 × 360 = 32400` relation as providential synchronization with the Temple-Time / Ezekiel temple measurement framework, not as the sole derivation. Source-context link: https://www.1260d.com/temple-time.pdf

### 7.9 Key harmonic connections

| Span | Years | Connection |
|---|---:|---|
| Tammuz → Enoch | `180 × 360` | 64800 years |
| Tammuz → Abraham | `360 × 360` | 129600 years |
| Etana → Conquest, 1406 BC | 210 Jubilees | 10290 years |
| Balih → Conquest, 1406 BC | 170 Jubilees | 8330 years |
| Total SKL span | 453600 years | `1260 × 360` |

## 8. Arithmetic Verification Table

Arithmetic-control scope:
These source-retained rows were checked during the Arithmetic Pass. Same-side BC spans use subtraction. Civil cross-axis spans use `BC + AD − 1` only where an AD target is explicitly opened. This pass is not a pressure test and does not resolve source-state contradictions reserved for later review.

| From | To | Span | Verification | Arithmetic-control result |
|---|---|---:|---|---|
| MT Minimum-Regular Adam | SP Normal / G2 Adam | 300 years | `4199 − 3899 = 300` | checks |
| MT Minimum-Regular Adam | LXX Regular-Minimum Adam | 1380 years | `5279 − 3899 = 1380` | checks |
| SP Normal / G2 Adam | LXX Regular-Minimum Adam | 1080 years | `5279 − 4199 = 1080` | checks |
| Entry, minimum | Entry, `+215` | 215 years | `1876 − 1661 = 215` | checks |
| MT Standard-Normal Adam | MT maximum Adam | 60 years | `4174 − 4114 = 60` | checks |
| MT Minimum-Regular Adam | MT Standard-Normal Adam | 215 years | `4114 − 3899 = 215` | checks |
| MT Minimum-Regular Adam | MT `+60 Terah` Adam | 60 years | `3959 − 3899 = 60` | checks |
| Entry, `1876 BC` | Exile, `586 BC` | 1290 years | `1876 − 586 = 1290` | checks |
| Entry, `1876 BC` | Exodus, `1446 BC` | 430 years | `1876 − 1446 = 430` | checks |
| Entry, `1661 BC` | Exodus, `1446 BC` | 215 years | `1661 − 1446 = 215` | checks |
| Cumulative Creation | Conquest | 12600 years | `14006 − 1406 = 12600` | checks |
| SKL Flood | Tower, primary | 17980 years | `20886 − 2906 = 17980` | checks |

### 8.1 Section-level arithmetic ledger

| Section | Arithmetic checked | Arithmetic-control result |
|---|---|---|
| §1.1 Variant matrix | `3899 + 60 = 3959`; `3899 + 215 = 4114`; `3899 + 275 = 4174`; `215 − 60 = 155` | checks |
| §1.2 Inter-tradition gaps | `4200 − 3899 = 301`; `5279 − 4200 = 1079`; `5279 − 3899 = 1380`; `301 + 1079 = 1380`; `4200 − 3901 = 299` | checks; residue line remains audit-controlled |
| §1.6 2nd Cainan | `460 − 130 = 330`; `504 − 134 = 370`; `3899 + 130 = 4029`; `4199 + 130 = 4329`; `5279 − 130 = 5149`; `14006 + 460 = 14466` | checks |
| §§2–4 Regular tables | Visible birth-to-death lifespans and begetting intervals | mostly check; SP Terah `145 (205)` and LXX Terah / Abraham are resolved as source-state displays within the Terah four-position field |
| §2.5 Kings ledger | `1446 − 480 = 966`; `1446 − 430 = 1016`; `1016 − 966 = 50` | checks |
| §3 SP / BJ relation | `4199 − 3856 = 343`; `2548 + 600 = 3148`; `3148 − 2648 = 500` | checks |
| §6A MT cumulative | Lifespan stacking from `14006 BC` to `1406 BC`; Aaron line `+3.5`; visible envelopes | checks; Peleg `3495t` is author-clarified as the Tishri terminal member of the parallel Peleg envelope and participates in the `4900` Mirror component check |
| §6B MT cumulative + Cainan | `14006 + 460 = 14466`; `4831 + 460 = 5291`; `5291 − 438 = 4853`; `4853 − 460 = 4393` | checks |
| §6C SP cumulative | `12100 = 110 × 110`; `13396 − 1296 = 12100`; `4831 − 4711 = 120`; `3436 − 6 = 3430`; `3430 = 70 × 49`; `1406 − 1296 = 110` | checks |
| §6D LXX cumulative | Visible LXX cumulative rows and envelopes | arithmetic display retained; Lamech / Nahor source-table values resolved by author clarification |
| §7 SKL primary anchors | `20886 − 2906 = 17980`; `27366 − 2856 = 24510`; `27366 − 20886 = 6480`; `452886 − 20886 = 432000`; `459366 − 27366 = 432000` | checks |
| §7 SKL scale states | `2 × 360 = 720`; `3.5 × 360 = 1260`; `7.5 × 360 = 2700`; `15 × 430 = 6450`; `7 × 930 = 6510`; `10 × 720 = 7200` | checks where active state is named |
| §7 SKL +6480 application | `20886 + 6480 = 27366`; `262086 + 6480 = 268566`; `452886 + 6480 = 459366` | checks |
| §7 SKL notable figures | Etana terminal to Conquest `11696 − 1406 = 10290 = 210 × 49`; Balih terminal to Conquest `9736 − 1406 = 8330 = 170 × 49` | checks when terminal member is active |

### 8.2 Audit-controlled arithmetic displays

| Display | Arithmetic-control finding | Handling |
|---|---|---|
| `(299 × 365.24) − (300 × 364) ≈ 7.5 days` | displayed form gives `6.76`; true-solar `365.2422` gives `7.4178`; File_11 physical residue gives `299/40 = 7.475` days | Author-clarified as conceptual residual-display / calibration language, not ordinary arithmetic from the abbreviated display. |
| Peleg Mirror note | `3495t + AD 1406t − 1 = 4900`; also `3502t + AD 1399t − 1 = 4900`, `3501n + AD 1400n − 1 = 4900`, and `3494n + AD 1407n − 1 = 4900` | Author-clarified. `3495t` is the Tishri terminal member, not an erroneous upper-member label. |
| SP Terah `145 (205)` | `2021 − 1876 = 145` checks; `205` from the same birth row would produce `1816 BC` | Author-clarified as textual `145` plus architectural `205` dual-lock; SP cumulative uses official `145`. |
| LXX Terah / Abraham four-position field | `2021 − 1816 = 205`; `2021 − 70 = 1951`; `2081 − 130 = 1951`; `2236 − 70 = 2166`; `2296 − 130 = 2166` | Resolved by author clarification. The displayed `70/130` begetting-state is state-dependent, not one executable value for the same Terah row. |
| Pillars 90-day relation | `2906 BC → AD 29465` and `2856 BC → AD 29515` produce `32370`, not `32400`; the relation checks if `+30 Apparent Mode` anchors `2936 BC` and `2886 BC` are active | Preserve; active `+30` rail should be named. File_21 classifies this as Projective Boundary / Temple-Time Pillar coordinate synchronization, not the sole derivation of the Pillars. |
| Cumulative Flood / SKL Day 2 | `4836 − 2856 = 1980 = 5.5 × 360`; `4836 − 2886 = 1950` | Preserve; row uses SKL Long target unless another dependency states otherwise. |
| Tammuz → Abraham `360 × 360 = 129600` | Not derivable from the visible Tammuz rows and standard Abraham anchors alone | Preserve as dependency-controlled SKL / Berossus display. |
| Total SKL span `453600 = 1260 × 360` | Checks when the SKL Short Pre-Creation `+720` rail `453606 BC` is active against `6 BC`; not directly from `452886 BC` base rail | Preserve; active `+720` rail should be named. |

## 9. Cross-Reference Index

### 9.1 Source-retained cross-reference index

| File | Section / topic | Data required from `File_18` |
|---|---|---|
| `File_00` | All axioms | Baseline dates for application. |
| `File_01` | Abraham entity | §2.3, MT; §3.3, SP; §4.3, LXX. |
| `File_02` | Flood entity | §§2.1–2.2; §6; §7. |
| `File_05` | Exodus entity | §§2.4–2.5. |
| `File_07` | Creation entity | §§2.1; 3.1; 4.1; 6. |
| `File_09` | Cumulative architecture | §6, all. |
| `File_10` | External validation | §7, Sumerian / SKL. |
| `File_16` | 1876 Nexus | §§2–5, convergence verification. |
| `File_17` | Time-span components | §8, arithmetic verification. |

### 9.2 Dependency-control additions

These additions are not presented as legacy source rows. They are dependency controls required by the current repository files.

| File | Dependency function |
|---|---|
| `File_04` | Jacob / LXX `33 + 397` and Entry-state controls where patriarchal rows are used. |
| `File_08` | Kings dual-ledger and `+50` offset control for §2.5. |
| `File_11` | Three-Gear, `299 → 300`, `300/299`, and Residue Protocol controls. |
| `File_12` | Calendrical physics and Enochian / residue controls for §1.2.1 and §7. |
| `File_14` | Biological-fractal and variant-gap terminology where `275`, `276`, `280`, and LXX Maximum material is opened. |
| `File_34` | Full SKL / Berossus derivation for §7. |
| `File_51a`; `File_54` | File map, state register, Machine Guard, and claim-status precedent. |

## Appendix A. Website Table Adjustments

Source-history function:
This appendix records how to convert website tables, 490d.com, to the minimum baseline used in `File_18`.

| Website table | Current setting | Adjustment to minimum |
|---|---|---|
| MT Regular | 430 in Egypt; no `+60 Terah` | Subtract 215. |
| SP Regular | `+60 Terah`; `+215 Sojourn` | Subtract 275 from Adam through Levi. |
| SP Regular, Noah / Shem | Local ordinal/cardinal counting field | Primary / lower companion at each Gear; lower = primary−1 for Noah/Shem only. |
| Flood in MT / LXX / SP | Ordinary G3/G2/G1 plus one event-year per Gear | Each close = start−1; independent of the SP person-station companion rail. |
| LXX Regular | `+60 Terah`; `+215 Sojourn` | Subtract 275. |
| SP-215 hybrid | `+60 Terah` applied | Subtract 60. |

Note on SP:
The ordinal `599+` and conventional cardinal `600` readings are reconciled through qualified SP Noah/Shem stations. They do not generate a one-year Flood uncertainty range or shift Adam through Lamech. §3 gives native G2 Flood start→close `2893→2892`, while Arphaxad stays `2891`; add `215` for `3108→3107` and `3106`. The Flood has ordinary three-Gear transport in MT, LXX, and SP. LXX remains native Cainan ON in the full-430 comparison, including Creation `5494`, Flood `3238→3237`, and Arphaxad `3236`.

July 2026 replacement pages (bounded addition):
The rewritten website pages supersede the settings above for the live site. Both pages present the three traditions level at the normative state: `+215 Sojourn`, no `+60 Terah`.

| Replacement page | Setting | Adjustment to minimum |
|---|---|---|
| Regular page, MT / LXX / SP tables | `+215`; no `+60`; LXX at the actual `5494` family; Lamech per §4A | Subtract 215. |
| Regular page, SP −215 landing values | no `+60`; native SP Sojourn | None (already minimum-frame). |
| Regular page, SOR section | MT sub-variant, `−220` from the MT `+215` state | `File_20` controls; not a File_18 table state. |
| Cumulative page, MT / LXX / SP | Full lifespan chains anchored at `1446 BC`; main §6 values; LXX `753` chain and separate Appendix B.2 `777` overlay | None (cumulative). |

## Appendix B. LXX Lamech `777` overlay, source comparison, and subsidiary corroborations

Status: appendix-only comparison and preservation layer, subordinate to the main `182/753` ruling in §4A. No row here replaces Lamech's main lifespan, adds a regular begetting interval, propagates an extra `24` through the cumulative chain, or proves a historical transmission sequence.

### B.1 The alternative full biography and the five-before-Flood comparison

The MT record and Smith's proposed LXX restoration are `182 + 595 = 777`. In this repository, applying MT `777` to the LXX is an appendix-only overlay, not the preferred original LXX lifespan. Smith's restoration is retained as an external reconstruction, not as a jointly attested original established here. The main LXX reconstruction retains attested `753` with restored `182` and does not claim Smith's support for that pair.

| Frame | LXX `777` comparison biography, BC | Flood BC | Death before Flood |
|---|---|---:|---:|
| Minimum | `3805 → 3028` | 3023 | 5 |
| `+215`, no `+60` | `4020 → 3243` | 3238 | 5 |

MT independently retains `3240 → 2463 BC`, with Flood `2458 BC`, and its own five-year pre-Flood margin. The former claim that the **main** MT and LXX biographies both end five years before their Floods is superseded: the LXX part is now confined to this `777` comparison, while main LXX `753` ends `29` years before.

### B.2 The cumulative overlay: shared endpoint, no propagation

| Cumulative LXX row | Lifespan | Nisan member | Seven-year start envelope, BC | Status |
|---|---:|---:|---|---|
| Lamech, main chain | 753 | 8048 | `8053–8046` | Main row retained in §6D. |
| Lamech, `777` overlay | 777 | 8072 | `8077–8070` | Appendix-only; row-local; non-propagating. |

Both starts lead to the same Noah envelope:

```text
8053 − 753 = 8077 − 777 = 7300
8048 − 753 = 8072 − 777 = 7295
8046 − 753 = 8070 − 777 = 7293
9022 − 969 = 8053
8077 − 8053 = 24
```

Thus the `777` overlay overlaps Methuselah's final `24` cumulative years rather than inserting new time before Noah. The unchanged `753` chain preserves `14901 − 1446 = 13455 = 299 × 45` (File_56 dependency) and the §6D `430` alignment. File_46 Appendix A now holds the preserved `8070` twenty-of-years, staged-Flood, and double-expansion examples; its §6A.1–§6A.3 remain routing points only where those overlay instances are concerned.

### B.3 Triad comparison and the two Key gains

```text
(182, 595, 777) + (6, −30, −24) = (188, 565, 753)
6 − 30 = −24
1794 × 300/299 − 1794 = 6
1656 × 70/69 − 1656 = 24
```

These exact differences compare the MT/Smith biography with the transmitted LXX triad. The signs and assignment of gains from different spans to one biographical record are the proposed crossover, not a single demonstrated textual operator. In particular, a `+24` span expansion does not automatically cause a `−24` lifespan change. The main chronology does not execute this triad as a reversible textual-history theorem.

### B.4 The two equal `782` arms and the `874` co-shift

```text
4020 − 3238 = 3238 − 2456 = 782 = 23 × 34
4020 − 2456 = 1564 = 23 × 68
2458 + 1680 = 4138
4138 − 3264 = 4114 − 3240 = 874 = 23 × 38
```

`4020` is LXX Lamech's main birth, `3238` the LXX Flood, and `2456` MT Arphaxad's birth/two-years-after-the-standard-Flood state. The `874` construction shifts Creation and Lamech's birth together by `24`, preserving their separation. This co-shift and the `777 − 753` duration difference are two uses of the same increment, not one mechanically causing the other. The earlier `874 = 23 × 34` wording was a slip; `23 × 34` is `782`.

### B.5 The `777` separation / overlap geometry

```text
4020 − 3243 = 777
3243 − 3240 = 3
3240 − 2463 = 777
```

The unshifted appendix LXX and MT biographies therefore form `777 | 3 | 777`.

If the entire MT biography, including its death, is translated six years earlier, it becomes `3246 → 2469 BC`. Against the unshifted LXX comparison this gives:

```text
4020 − 3246 = 774
3246 − 3243 = 3
3243 − 2469 = 774
```

The union now reads `774 | 3 | 774`. Translating the MT death with its birth is an additional declared whole-biography choice; the birth-to-Exodus expansion alone does not prescribe it. The longer sequence `774 + 3 + 3 + 771 + 6 = 1557`, from `4020` to `2463`, is arithmetically valid but is not itself a palindrome.

### B.6 Former Flood-Gear-from-above explanation: retained qualification

The previous §4A.6 used the LXX Flood Gears `3240 / 3238 / 3236 BC` (minimum `3025 / 3023 / 3021`) and the `3240 − 1446 = 1794` span, then spoke of advancing the Gear-2 Flood by six years. The exact anchored conversion applies to the `3240` Gear-3 endpoint; it gives `3246`. Applying its gain to Gear 2 is a further cross-Gear gain-transfer, not that same direct anchored expansion. This route is retained only as a qualified subsidiary comparison and is not needed for the main rule or the better-specified §4A.5 comparisons.

### B.7 Source register and evidential boundary

| Source | Use / limitation |
|---|---|
| File_18 §§2–4, §§6A–6D; File_02 §6.2–§6.3 | Repository chronology inputs, Shem/Noah bindings, cumulative envelopes, and `598 → 600`. |
| File_69 §5B.5; File_70 §2.3 | Terah firstborn `2226 BC` and Sarah `2156 BC`, with explicit Terah-state distinctions. |
| [Regular chronology page](https://490d.com/mt-lxx-sp-sp215-regular-short-chronology-table/) | Public page checked September 8 2026: main `182/753`, Lamech `4020–3267 BC`, and appendix-only LXX `777` are already displayed. The present package supplies a source-hierarchy wording replacement only; no new website edit is claimed deployed. |
| [Cumulative chronology page](https://490d.com/mt-lxx-sp-lifespan-accumulative-long-chronology-table/) | Public page checked September 8 2026: main `753` chain, `430` rationale, and row-local `777` overlay already separated in its Appendix A. The present wording clarification changes no chain coordinate and is not claimed deployed. |
| Smith Jr., H. B. (2018), “The case for the Septuagint's chronology in Genesis 5 and 11,” in J. H. Whitmore (ed.), *Proceedings of the Eighth International Conference on Creationism*, pp. 117–132; Tables 3–4 and Lamech discussion | External reconstruction witness. His proposed full restoration is not the selected `182/753` reconstruction. The September 8 discussion record reports his statement that `182` is absent from the surviving LXX witnesses he surveyed; support is drawn from MT and external witnesses, some themselves reconstructed. No fresh manuscript collation is claimed. |
| LAB 1:1–22; 5:8; Josephus, *Antiquities* 1:67, 82–87; Genesis 5:28–31 in NETS | Retained source references from the Lamech review. Direct readings and scholarly restorations must remain distinguished; no universal non-attestation theorem is inferred. |
| [Genesis 5:31, Brenton LXX](https://www.biblestudytools.com/lxx/genesis/5-31.html) | Direct published-text check, September 8 2026: lifespan `753`. This verifies the transmitted component, not a joint `182/753` manuscript or the historical-priority judgment. |
| Author discussion, September 8 2026 | Main `182/753` decision; retention of attested `753` as the preferred original LXX lifespan; preference for the `69 \| 529 = 598` family; supporting `+6/+24/100` comparisons; qualified crossover/transmission hypothesis. |

Historical inference ceiling: these patterns make the selected numbers structurally intelligible within the repository, but do not prove that a scribe used its BC anchors, that `188` was consciously encoded, that MT historically preceded every other witness, or that the lost joint `182/753` text existed. Providential interpretation remains the author's interpretive framework rather than an arithmetic parameter.


## Audit Notes

Audit note 1 — Section numbering:
The supplied source skips Section 5. Recommended handling: preserve Section 6 numbering and reserve §5 as a source-numbering note. Author decision required only if the author wants the legacy source renumbered.

Audit note 2 — Cainan cross-reference:
The source says §6B contains the full Cumulative + Cainan tables but later cross-references §6C as “Cumulative + Cainan tables.” Current source-control applies the high-probability correction: §6B is MT Cumulative + 2nd Cainan; §§6C–6D are SP / LXX cumulative comparison. Author decision required only if §6C was intended to carry a different local meaning.

Author clarification note 3 — 299 / 300 residue line:
The source-retained line `(299 × 365.24) − (300 × 364) ≈ 7.5 days` remains preserved, but Current source-state control classifies it as dependency-controlled conceptual residual-display / calibration language. `File_17` defines the exact `300/299` operator; `File_12` preserves legacy `299/300` wording only as source-history / inverse-caption language and gives the true-solar display `7.4178`; `File_11` distinguishes physical residue from conceptual residual-display and gives physical `300/299` residue as `299/40 = 7.475` days. `File_28` remains optional legacy provenance rather than a current blocker.

Audit note 5 — Lamech supersession record:
The September 8 2026 author ruling supersedes the July regular-`777` / cumulative-`753` split and the September prohibition on considering `188` as structural evidence for a qualified transmission hypothesis. Main execution is `182/753`; `188` remains non-operative; the LXX `777` layer is appendix-only. The earlier blanket claim that no historical stage ever paired `182/753` is replaced by the narrower reviewed-source non-attestation disclosure. Earlier editions are preserved in the revision package; the Repository Change Archive is not rewritten by this amendment.

Dependency note 4 — `File_28` dependency:
The source cites `File_28`, §1 for physics. Current repository status treats `File_28` as a retired placeholder / legacy provenance pointer, not an active proof file. Current source-state control no longer treats `File_28` as blocking the residue-control issue because the active project controls now assign the exact ratio to `File_17`, legacy wording / true-solar display to `File_12`, and physical-residue / conceptual residual-display to `File_11`. Use `File_28` for archive / provenance review only unless a future author decision reactivates its material through another controlling file.

Audit note 5 — SKL / Berossus compression:
§7 compresses SKL Short, SKL Long, Berossus, `+6480`, `+720`, `+30`, `+2`, and the appended `3 months and 3.5 days` datum. Visible arithmetic is checked only where locally executable. Full derivation remains dependency-controlled by `File_34`.

Audit note 6 — Theological design language:
Current claim-status control classifies source-retained design-proof language as structural inference, shared-tradition evidence, theological note, providential synchronization, or dependency-controlled claim as appropriate. The design language is preserved, but it does not carry the arithmetic burden by itself.

Audit note 7 — External LXX source-control:
Smith has been added once as an external LXX source-reconstruction witness because LXX Genesis chronology is materially active. The LAB / Josephus / Bible Archaeology material remains source-retained and may need source-control review if it becomes proof-bearing.

Author clarification note 8 — MT cumulative Peleg `3495t` member-label:
Resolved. MT cumulative Peleg spans `3501n–3494n BC`, with the parallel Tishri span `3502t–3495t BC`. The Conquest / land-rest span is `1406n–1399n BC`, with the parallel Tishri span `1407t–1400t BC`. Under File_09 Mirror suffix inversion, the AD-side display is `AD 1399t/1400n–1406t/1407n`. Component checks equal `4900 = 70 × 70 = 100` Jubilees. Therefore `3495t` is the Tishri terminal member participating in `3495t → AD 1406t = 4900`, not an erroneous upper-member label.

Author clarification note 9 — LXX Regular-Minimum versus LXX cumulative source-table state:
Resolved under the September 8 2026 ruling: both main LXX reconstructions select lifespan `753`, with begetting `182` in the regular chain and calculated remainder `571`. No joint attestation is claimed. Nahor's controlled `208` is unchanged. Appendix B preserves Smith's different full-biography reconstruction and the row-local `777` cumulative comparison without promoting either into main execution.

Author clarification note 10 — SP locality, ordinary Flood Gears, and ordinal/completed counting:
Superseded in scope by the September 18 2026 author ruling. The SP `−1` companion belongs only to Noah/Shem person-stations; the former upstream-ripple wording is withdrawn. Native G2 Noah `3493/3492` and Shem `2993/2992` give qualified paths to Flood start `2893`; Flood close `2892` comes independently from the event-year span. Lamech `3545→2893` is `653` inclusive. Ordinary Flood Gears apply across MT/LXX/SP, while regular Arphaxad `2891` stays fixed under Gear at held variant settings. G1 Shem `2991/2990` and deaths `2391/2390` remain under the named bindings in §3.2.1. The G2 `654+654` midpoint ends at fixed Arphaxad and remains distinct from the G1 triple coordinate convergence. BJ provides derivative/corroborating structural evidence in the project model; no SP companion operator transfers to MT or LXX.

Author clarification note 11 — SP Terah `145 (205)` dual-lock:
Resolved. `145` is the official SP textual lifespan and lands Terah's death at Abram's call. `205` is the architectural lifespan mirroring MT/LXX and showing that the Terah difficulty remains as a swapped lifespan / begetting-age issue rather than disappearing. The SP still permits a `+60 Terah` state where opened, while SP cumulative tables use the official `145` span.

Author clarification note 12 — Abraham / Terah four-position field:
Resolved. From Levi / Joseph back to Abraham, events have two possible date states because of the `215`-year Sojourn variant. Terah introduces `+60 Terah`, doubling the field to four: `2021–1816 BC`, `2081–1876 BC`, `2236–2031 BC`, and `2296–2091 BC`. Abraham's birth is therefore `1951 BC` or `2166 BC`, while Terah has four birth/death states. The File_18 LXX Regular-Minimum table now marks Terah's begetting age as `70/130 state-dependent` rather than forcing `130` onto the minimum `2021–1816 BC` row.

Author clarification note 12A — 2nd Cainan variant-boundary state:
Resolved. When restored 2nd Cainan is inserted into MT / SP regular chronology, 2nd Cainan himself has four possible date states, not eight. The four 2nd Cainan birth states are `2611/2551 BC` and `2396/2336 BC`, derived from Shelah birth states `2481/2421 BC` and `2266/2206 BC` by adding the `130` begetting-age hinge. The four 2nd Cainan death states are `2151/2091 BC` and `1936/1876 BC`, derived by subtracting the `460` lifespan. The eight-position propagation begins with Arphaxad / Flood and continues back to Adam only when restored 2nd Cainan is explicitly opened. The resulting generational variant-count ladder is `12–8–4–2–0`: Adam through Arphaxad / Flood have eight possible dates; 2nd Cainan through Terah have four; Abraham through Joseph / Levi have two; Kohath and Amram have zero direct regular pivot dates; Aaron / Moses onward remain fixed / unaffected.

Author clarification note 12B — Pentateuchal Funnel state:
Resolved. The `12–8–4–2–0` generational variant-count ladder is structurally important and should not be treated merely as boundary-line bookkeeping. When the Cainan hinge is active, it maps onto the Pentateuchal arcs as follows: Creation → Flood corresponds to Adam through Arphaxad / Flood, 12 generations with eight date states; Flood → Abraham corresponds to 2nd Cainan through Terah, 8 generations with four date states; Abraham → Entry into Egypt corresponds to Abraham, Isaac, Jacob, and Joseph / Levi, 4 patriarchal nodes with two date states; Egypt → Conquest / Moses death corresponds to Kohath and Amram as 2 floating no-direct-date generations, with Aaron / Moses fixed downstream. Claim-status: structural inference, with providential synchronization where the theological meaning is invoked.

Author clarification note 12C — multi-tradition scope of the Pentateuchal Funnel:
Resolved. The Pentateuchal Funnel is not local to MT. MT, SP, and LXX each encounter the same structural fork sequence at the same genealogical locations: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary. The tradition-specific status differs: MT / SP restore Cainan when that state is opened; LXX already includes Cainan in the active baseline and therefore uses the Cainan boundary as native source-table structure unless theoretical removal / reinsertion is explicitly opened. This clarification does not change the variant-count ladder, the `+130` regular Cainan value, the `+460` cumulative Cainan value, or any table anchor.

Author clarification note 12D — restored/native 2nd Cainan 27-generation completion and tebah / ark bridge:
Resolved and focused-pressure-tested. The Pentateuchal Funnel reaches `27 = 3 × 3 × 3` generations from Adam to Moses only when restored/native 2nd Cainan is active: Adam through Arphaxad / Flood = 12; 2nd Cainan through Terah = 8; Abraham through Joseph / Levi = 4; Kohath and Amram = 2 floating generations; Moses = 1 final deliverer generation. Without restored/native 2nd Cainan, the count is `26` and the post-Flood block is `7`, breaking the 8-generation block and the 27-generation completion. In MT / SP, restored 2nd Cainan is therefore required for this pattern. In LXX, 2nd Cainan is native and no additional `+130` is applied. The tebah / ark connection between Noah and Moses is retained as a typological / theological note explaining the meaning of the `8` and `1` endpoints, not as an arithmetic operator. This secondary generation-count pattern must not overshadow the primary `12–8–4–2–0` variant-count ladder or the 8-date / 4-date / 2-date / 0-date mechanics.

Audit note 13 — Pillars 90-day relation:
The §7.4.2 Pillars relation to AD `29465/29515` does not produce `32400` years from base `2906/2856 BC` by civil cross-axis arithmetic. It does check if the `+30 Apparent Mode` anchors `2936 BC` and `2886 BC` are active. File_21 resolves the argument role: this is a Projective Boundary / Temple-Time Pillar coordinate synchronization, not the sole derivation of the Pillars. Preserve the row and state that the `+30 Apparent Mode` rail is active before using the 90-day result.

Audit note 14 — Cumulative Flood / SKL Day-2 target:
The §7.4.5 line `Flood (4836 BC) → SKL = 1980 years = 5.5 × 360` checks against SKL Long `2856 BC`, because `4836 − 2856 = 1980`. It does not check against SKL Short `2886 BC`, where the span is `1950`. Recommended handling: preserve the row and name the active SKL Long target unless a later dependency opens another operator.

Audit note 15 — Tammuz → Abraham `129600`:
The §7.9 key-harmonic row `Tammuz → Abraham = 360 × 360 = 129600 years` is not derivable from the visible Tammuz rows and the standard Abraham anchors alone. Recommended handling: preserve as `File_34`-controlled SKL / Berossus material unless a later File_34 revision opens a more specific derivation.

Audit note 16 — Total SKL span `453600`:
The §7.9 row `Total SKL span = 453600 = 1260 × 360` checks when the SKL Short Pre-Creation `+720` rail `453606 BC` is active against `6 BC`, because `453606 − 6 = 453600`. It is not produced directly from the base rail `452886 BC`. Recommended handling: preserve and name the active `+720` rail.


## Unresolved Issues

No author-decision blocker remains. The following retained notes are dependency-boundary or source-history controls. They are not blockers to Final status if retained in the publication copy.

1. `File_28` remains a retired placeholder / legacy physics provenance pointer. It is not blocking the current residue-control issue after current source-state control, but it may still be useful for archive / provenance review if a future author decision routes any former material through an active controlling file.
2. Section 7's SKL / Berossus derivation remains dependency-controlled by `File_34`; Current source-state controls clarify rail labels but do not locally rederive SKL / Berossus.
3. The appendix website-adjustment table was reconstructed from malformed source text. The reconstructed rows remain visible for later review.
4. Tammuz → Abraham `129600` remains `File_34`-controlled because it is not derivable from the visible Tammuz rows and standard Abraham anchors alone.
5. The `2307` inclusive companion and the solar `7.5 × 365` comparison remain audit-controlled. They are not blockers because the executable File_18 update uses same-side arithmetic, the Enochian `2730 = 7.5 × 364` state, and File_16 dependency classification.

## Revision and archive note

This public-clean Markdown source retains the prior Final and full-pressure-tested baseline while applying the bounded July 24 2026 monarchy-state correction.

The amendment:

- assigns `1050t/n→1010t/n→970t/n→930t/n BC` to the literal/precise United Monarchy;
- assigns `1051n→1011n→971n→931n BC` to the File_51a Rounded Scaffold;
- records `1531n→971n=560` and `1526n→966n=560` as Rounded comparisons;
- preserves `967/966 BC` as ordinal/cardinal literal Temple states;
- preserves `1016 BC` as the separate Verbatim / Schematic `+50` pivot;
- leaves all unrelated regular, cumulative, Cainan, SKL, post-Solomon, Mirror, and theological material unchanged.

Detailed revision history belongs in the `Repository_Change_Archive`. The bounded amendment is independently focused-verified; no new full pressure test is claimed. The prior June 28 2026 full-pressure-test baseline remains retained for unaffected material.


## Revision Log — September 8 2026 bounded Lamech settlement

Author-directed correction: main LXX `182/753` in both methods; one regular death/lifespan row changed; cumulative overlay relocated to Appendix B; §4A replaced with source distinctions and qualified Key-of-23 hypothesis. Register v1.53 §D.43 / Capsule v11.52 §10.30 control this amendment. Focused arithmetic, diff, guard, dependency, and protected-region checks are recorded in the accompanying verification report. No new full-file pressure test, separate re-Finalization, website deployment, manifest update, or external archival capture is claimed.


## Bounded wording clarification — September 8 2026

Attested LXX `753` is now explicitly distinguished from restored `182`, calculated `571`, and the combined reconstruction at the source note, state row, existing Machine Guard, §4A.1, and §6D. The preferred-original judgment is retained as the author's textual/structural conclusion; MT-derived LXX `777` remains appendix-only. Register v1.54 §D.43 / Capsule v11.53 §10.30 route the clarification. No numeric table cell, equation, anchor, or operator changes; focused diff, guard-fidelity, and arithmetic checks only. The two live WordPress pages were reviewed; supplied wording replacements are not claimed deployed.


## Revision Log — September 18 2026 bounded SP / Flood-Gear correction

- Authority: author’s reviewed Report V / Canonical Register correction and explicit instruction to correct both reports and File_18; native LXX Cainan ON confirmed for both Creation and Flood.
- Scope: SP regular rows, named Noah/Shem bindings, relevant state/display/operator tables and Machine Guards, §2.2.1 comparison labels, §3, Appendix A, and clarification note 10. Unrelated table systems remain inherited.
- Numerical correction: native G2 Flood start/close `2892→2891` replaced by `2893→2892`; selected capped deaths of Jared/Methuselah/Lamech use `2893` with inclusive counts `847/720/653`. Noah `3493/3492` and deaths `2543/2542` are correctly ordered primary/companion. Creation `4199`, Lamech birth `3545`, and Arphaxad `2891` are retained.
- Mechanism correction: distinguish cross-tradition Flood Gears and event-year boundaries from the SP-only Noah/Shem `−1` companion. Withdraw whole-chain toggle/ripple language; retain interval-specific ordinal/completed readings and the qualified older Shem stations.
- LXX frame: normal native Cainan ON gives equalized G2 Creation `5494`, Flood `3238→3237`, and Arphaxad `3236`; no existing LXX main-table number changes.
- Verification: affected arithmetic and table comparisons, unchanged-region source diff, and Markdown structure checked. This is focused verification of an authorized amendment, not a new full-file pressure test or re-Finalization.
- Cross-file status: both companion reports corrected in the same task. Central State Vocabulary Register, Restart Capsule, earlier research checkpoints, publication records, and website deployment remain separate work; no update to those items is claimed.
- Unresolved author decisions within this correction: none. The conjectural SP Ark-preparation year retains its existing claim-status.