File: File_46 Title: Harmonic Expansion Protocols — Expansion Operators on the 70-Year Genealogical Lattice Status: Final; Passes 0–2 complete under Project Procedures; prime-lattice section removed by author direction June 10 2026; marked Final by author June 10 2026; publication-clean verification current; deep-time overlay application bounded update applied Publication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive. Pressure-test status: Current; publication-clean verification complete after author-Final pass, prime-lattice section removal, and public-clean cleanup; focused check complete for the deep-time overlay application bounded update; no pre-existing argument-bearing content changed. Register Agreement status: Checked against State_Vocabulary_Register v1.18 and active companion controls; bounded deep-time overlay application addition (§6A; §7 scope record) only; no pre-existing 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 changed. Primary domain: Harmonic mechanics / expansion operators on the Matthew–Luke 70-year genealogical lattice Canonical source: Markdown Source-history identifiers: `FILE_46: HARMONIC_EXPANSION_AND_PRIME_PROPAGATION.md`; UUID `PRIME_EXPANSION_ROSETTA_MIRROR`; source status `DEFINED (v10.1-compatible)` Major operators: civil cross-axis span `BC + AD − 1`; Prophetic Ratio `70/69`; Priestly Ratio `25/23`; doubled base span `9660 = 2 × 4830`; Danielic wave-set `{490, 700, 1400, 4900, 7000}` by File_44 / File_45 dependency; `6624 = 1656 × 4 = 23 × 288 = 96 × 69`; twenty-of-years pair `7200 = 20 × 360` / `6720 = 20 × 336`; `920 × 25/23 = 1000`; double-expansion licensing `23² × 25/23 × 25/23` Major modal states: 70-year carrier display lattice (File_43); Enoch pivot state `4836 BC` (File_45); figurative God bookend label state; Daniel 9 pattern-template state; non-lock `+460` motif state; deep-time overlay application state; staged-Flood display state; Adam-field expansion state; twenty-of-years pair state; double-expansion licensing corollary state Related files: `File_43` (primary genealogy-lattice locks); `File_44` (cycle family / scaling-law controls); `File_45` (Daniel-9 template, Danielic wave-set, Enoch pivot, statistical proof burden); `File_22` (cumulative deep-time `14006 BC` by dependency); `File_54` (comparative Luke lattice, mediated through File_43); `File_42` (source-history support only); `File_16`; `File_17`; `File_18` (LXX cumulative overlay source-table); `File_51b`; `File_56` (`+460` rail); Restart Capsule v11.17; State Vocabulary Register v1.18; 490d Repository Style Guide v2.5; Project Procedures v3.3 Revision basis: author-supplied `FILE_46` source; author direction of June 10 2026 removing the prime-lattice section; 490d Repository Style Guide v2.5; Restart Capsule v11.17; State Vocabulary Register v1.18; Project Procedures v3.3; File_43 Final Harmonized; File_45 Final post-final pressure tested; File_54 Final; File_00 Public-Clean precedent; Repository_Change_Archive (non-controlling history) Current refresh note: Public-clean trust-status equalization aligns active control pointers to 490d Repository Style Guide v2.5, Restart Capsule v11.17, State_Vocabulary_Register v1.18, and Project Procedures v3.3. Bounded deep-time overlay application (§6A) registered from the Regular / Cumulative page publication discussion record. Register Agreement status is recorded in the header; 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 are changed. Detailed pass logs, pressure-test records where applicable, pointer-refresh history, and replacement-workflow notes are preserved in Repository_Change_Archive. September 8 2026 bounded Lamech routing: former §6A.1–§6A.3 `777`-overlay executions move to Appendix A; stable headings route to them. §§1–6 and §6A.4–§6A.5 proof bodies are preserved. Registered at Register v1.53 §D.43 / Capsule v11.52 §10.30. Focused verification only; no new full pressure test or separate re-Finalization. # File_46 — Harmonic Expansion Protocols ## 0. File-function `File_46` defines the expansion operators that generate and lock spans within the Matthew–Luke 70-year genealogical lattice and its Danielic wave-set. The file is an operator register, not a static date list. All computations are stated as integers under the civil no-year-0 convention of the Restart Capsule. Active state: 70-year carrier display lattice by `File_43` dependency; Enoch pivot state `4836 BC` by `File_45` dependency; expansion-operator state (`70/69`; `25/23`); actual chronology / local-state default. Proof-burden rule: `File_43` carries the genealogy-lattice locks (`MattSpan_BirthHinge = 2800`; `MattSpan_Carrier = 2870`; `LukeSpan = 5320`; `LukeIntervals = 5250`). `File_45` carries the statistical proof burden for the wave-set and the Daniel-9 segmentation template. `File_46` supplies operator mechanics; it does not re-prove and must not overwrite those locks. Claim-status frame: Each span equation below is an arithmetic fact under its stated operator. Each lattice placement (which generation block an endpoint lands on) is a structural inference controlled by the `File_43` display ledger. Calendar-theological framing is labeled where it appears. ## 0.1 Working state register | State / value | Function here | Guard | |---|---|---| | `BC + AD − 1` | civil cross-axis span operator | Machine Guard [CIVIL SPAN EXECUTION] below | | `4830` | base span `4836 BC → 6 BC` | Solar-span input to both expansion operators; not an Enochian-calendar constant (`364`, `1274`) | | Prophetic Ratio `70/69` | expansion operator | Key-of-23 Prophetic Expansion state; exact rational; do not decimalize | | Priestly Ratio `25/23` | expansion operator | Key-of-23 Priestly Expansion state; exact rational; do not collapse with `70/69` | | `9660 = 2 × 4830` | doubled base span | Input to §3 dual expansion only | | `{490, 700, 1400, 4900, 7000}` | Danielic wave-set | `File_44` / `File_45` cycle family; scoring vocabulary, not targets | | `4836 BC` | Enoch pivot | `File_45` Enoch pivot state; also cumulative Flood Week member by dependency | | `5326 BC` / `5256 BC` | Luke head boundaries | `LukeSpan` / `LukeIntervals` lock endpoints; figurative God bookend label state at `5326–5256 BC` | | 70-year ledger boundaries | span endpoints in §§2–3 | display-table-only ledger; node-class restated at point of use | | `460 + 30 = 490` | non-lock `+460` motif | static motif only; Machine Guard [STATIC `+460/+30` MOTIF] below | | Daniel-9 segmentation | pattern-template | `File_45` Daniel 9 pattern-template state; no `434`-year lock | Machine Guard [CIVIL SPAN EXECUTION]: For all programmatic execution, enforce `BC + AD − 1 = Total` explicitly for spans crossing the epoch boundary. Do not use standard algebraic subtraction, such as `AD − (−BC)`, across the boundary; it introduces a 1-year error. Treat BC and AD labels as absolute magnitudes when applying this rule. Machine Guard [DISPLAY-LEDGER SPAN USE]: The `File_43` genealogy ledger is display-table-only. Where this file uses a ledger boundary as a span endpoint, the local section restates its node-class. No span here redefines or overwrites `MattSpan_BirthHinge`, `MattSpan_Carrier`, `LukeSpan`, or `LukeIntervals`. ## 0.2 File map | Section | Function | Active state / operator | |---|---|---| | §0 | File-function and state controls | file-level modal states | | §1 | Locked constants L0–L4 | civil span identity; `70/69`; `25/23`; wave-set | | §2 | Generator locks: Solomon and Christ generation | `25/23` from deep time; `70/69` from Enoch pivot | | §3 | The `9660` dual expansion: Adam and Noah/Shem | doubled base span; both operators | | §4 | Rosetta Stone 3-calendar resolution; 11th-Week correction | one solar span, three translations; `420 + 70 = 490` | | §5 | 2nd Cainan non-lock motif | static `460 + 30 = 490` | | §6 | Jared → 2nd Cainan Daniel-9 front-packet | `File_45` pattern-template by dependency | | §6A | Main-chain deep-time applications; stable appendix routes | main §6A.4–§6A.5; overlay examples routed to Appendix A | | §7 | Content-scope and removal record | arithmetic-control and source-history notes | | Appendix A | Preserved LXX `777`-overlay applications | appendix-only `8070` examples; no main-chain propagation | ## 1. Locked Constants The constant labels L0–L4 are source-retained labels for the file's explicit integer chains. ### L0. Civil span identity (no year 0) For spans crossing from BC to AD: ```markdown BC + AD − 1 = Total ``` This is the repository's one cross-axis span formula. Same-side spans use ordinary subtraction. ### L1. The 4830 base span Active state: Enoch pivot state (`File_45`); solar same-side span. ```markdown 4836 BC → 6 BC = 4836 − 6 = 4830 ``` The `4830` span from the Enoch pivot to the `6 BC` Christ-generation hinge is the base input to both expansion operators below. State note: `4830` here is a solar same-side span value. It is not an Enochian-calendar constant; the Enochian calendar family (`364`; `1274 = 3.5 × 364`) is a separate state controlled elsewhere. ### L2. Prophetic Ratio (70/69) Active state: Key-of-23 Prophetic Expansion state. ```markdown 4830 × 70/69 = 4900 ``` because `4830/69 = 70` and `70 × 70 = 4900`. Therefore: ```markdown 4836 BC → AD 65 = 4900 ``` since `4836 + 65 − 1 = 4900`. The source associates this operator with Jared (the Jared / Prophetic expansion); the association is developed in §4.2. ### L3. Priestly Ratio (25/23) Active state: Key-of-23 Priestly Expansion state. ```markdown 4830 × 25/23 = 5250 ``` because `4830/23 = 210` and `210 × 25 = 5250`. Therefore: ```markdown 5256 BC → 6 BC = 5256 − 6 = 5250 ``` The source associates this operator with Luke (the Luke / Priestly expansion); the association is developed in §4.2. ### L4. Danielic wave-set Active state: Danielic wave-set state by `File_44` / `File_45` dependency. The cycle family used in the repository's statistical framework is: ```markdown C = {490, 700, 1400, 4900, 7000} ``` Dependency note: The wave-set is owned by `File_44` (scaling-law controls) and tested by `File_45` (exact-sweep statistics). It is recorded here as shared vocabulary only; this file does not re-derive or re-test it. ## 2. Generator Locks: Solomon and Christ ### 2.1 Solomon expansion (Priestly operator from deep time) Active state: Priestly Ratio `25/23`; cumulative deep-time anchor `14006 BC` by `File_22` dependency; Matthew-side display ledger (`File_43` 70-year carrier display; source wording: "Matthew shadow lattice"). Goal: generate `1756 BC`, the end of Solomon's 70-year carrier (`1826–1756 BC`), by applying the Priestly operator to the deep-time → Abraham boundary span. | Step | Value | |---|---| | Anchor | `14006 BC` | | Intermediate endpoint | `2736 BC` — end of the Abraham generation (`2806–2736 BC`) in the Matthew-side display ledger | | Input span | `14006 − 2736 = 11270` | | Operator | Priestly expansion `25/23` | | Expanded span | `11270 × 25/23 = 12250`, because `11270/23 = 490` and `490 × 25 = 12250` | | Projected endpoint | `14006 − 12250 = 1756 BC` | | Expansion delta | `12250 − 11270 = 980 = 14 × 70` | Lattice placement: `1756 BC` is the end of Solomon's 70-year carrier (`1826–1756 BC`) in the `File_43` display ledger. Claim-status note: The span chain is arithmetic fact under the stated operator. The identification of the projected endpoint with the Solomon carrier boundary is structural inference controlled by the `File_43` ledger. "Lock" in this file's source is a legacy label for these lattice placements; it is not the `File_33` Value Lock or Ordinal Lock state. ### 2.2 Christ-generation generator (Prophetic operator from the Enoch pivot) Active state: Prophetic Ratio `70/69`; Enoch pivot state `4836 BC`. Goal: generate the AD 65 terminus of the Christ generation from the Enoch pivot. | Step | Value | |---|---| | Anchor | `4836 BC` (Enoch pivot) | | Input span (solar) | `4836 BC → 6 BC = 4830` | | Operator | Prophetic expansion `70/69` | | Expanded span | `4830 × 70/69 = 4900` | | Endpoint | `4836 BC → AD 65 = 4900`, because `4836 + 65 − 1 = 4900` | Lattice placement: AD 65 is the end of the Christ generation (`6 BC → AD 65`) in the 70-year lattice framing of `File_43`. ## 3. The 9660 Dual Expansion: Adam and Noah/Shem Define the doubled base span: ```markdown 9660 = 2 × 4830 ``` ### 3.1 Prophetic track — Matthew-side Adam at 4206 BC Active state: Prophetic Ratio `70/69`; deep-time anchor `14006 BC`; Matthew-side display ledger. | Step | Value | |---|---| | Input | `9660` | | Operator | `70/69` | | Expanded span | `9660 × 70/69 = 9800`, because `9660/69 = 140` and `140 × 70 = 9800` | | Endpoint from deep time | `14006 − 9800 = 4206 BC` | Lattice placement: `4206 BC` opens the Matthew-side display bracket "Creation of Adam" (`4206–4136 BC`) in the `File_43` ledger. ### 3.2 Priestly track — Noah/Shem hinge at 3506 BC Active state: Priestly Ratio `25/23`; deep-time anchor `14006 BC`; Matthew-side display ledger. | Step | Value | |---|---| | Input | `9660` | | Operator | `25/23` | | Expanded span | `9660 × 25/23 = 10500`, because `9660/23 = 420` and `420 × 25 = 10500` | | Endpoint from deep time | `14006 − 10500 = 3506 BC` | Lattice placement: `3506 BC` is the Noah/Shem hinge boundary — end of the Noah generation (`3576–3506 BC`), start of the Shem generation (`3506–3436 BC`) — on the Matthew side of the `File_43` ledger. ## 4. The Rosetta Stone: 3-Calendar Resolution Section-heading note: "Rosetta Stone" is retained as a legacy theorem label; its evidential role is supplied by the claim-status notes below. ### 4.1 One fixed solar span ```markdown 4836 BC → 6 BC = 4830 solar years ``` ### 4.2 Three translations of the same 4830 span | Translation | Operator | Result | Matching lattice span | |---|---|---|---| | Solar (Enoch) | none | `4830` | `4836 BC → 6 BC = 4830` | | Prophetic (Jared) | `70/69` | `4830 × 70/69 = 4900` | `4906 BC → 6 BC = 4900` | | Priestly (Luke) | `25/23` | `4830 × 25/23 = 5250` | `5256 BC → 6 BC = 5250` | Node-class note: `4906 BC` is the opening boundary of Luke's Jared generation, and `5256 BC` is Luke's Adam-Creation ledger boundary (`LukeIntervals` lock endpoint), per `File_43` and `File_54`. The correspondence of each expanded value to a lattice boundary is structural inference. ### 4.3 The 11th-Week correction (420 vs 490 resolved) This section distinguishes calendar-conversion residue from Danielic week count. Conversion residue (Priestly head vs solar pivot): ```markdown 5256 − 4836 = 420 ``` The `420` is the conversion delta that arises because Luke's head is expressed in Priestly units while the Enoch pivot is solar. Luke's additional head generation: Active state: figurative God bookend label state (`File_43`). The `5326–5256 BC` row of Luke's ledger — the "God" row — adds one more 70-year generation above the Priestly head: ```markdown 5326 − 5256 = 70 ``` Display-label note: The `God` entry is the author-resolved figurative Luke-derived bookend label of `File_43`. The `5326 BC` boundary is an arithmetic lattice endpoint (the `LukeSpan = 5320` lock endpoint); the label itself is not an arithmetic input and asserts no literal divine origination. Therefore Luke's full step ahead of the Enoch pivot is: ```markdown 420 + 70 = 490 ``` Week counts on the 490-scale: ```markdown 4836 BC → AD 65 = 4900 = 10 × 490 5326 BC → AD 65 = 5390 = 11 × 490 5390 − 4900 = 490 ``` Conclusion: Luke's "11th week" is not 420 years; it is 490 years, composed as `420` conversion residue plus `70` head generation. ## 5. 2nd Cainan: Non-Lock Motif Only Active state: non-lock `+460` motif state (`File_45`). This file does not use 2nd Cainan as an operative targeting lock. The motif is recorded only as an optional correspondence seen elsewhere: ```markdown 460 (2nd Cainan) + 30 (Adam apparent age) = 490 ``` Policy: The equality may be referenced as a thematic Danielic correspondence. It is not used in this file as a generator, anchor shift, or targeting operator. Machine Guard [STATIC `+460/+30` MOTIF]: The equation `460 + 30 = 490` is a static motif. Programmatic engines must not extract `460` or `30` from this section as dynamic variables, offsets, or generators in any other calculation within the lattice. ## 6. Jared → 2nd Cainan as Daniel-9 Front-Packet Analogue Active state: Jared / 2nd Cainan Danielic front-packet state; Daniel 9 pattern-template state; Christ-generation bisection state — all by `File_45` dependency. Dependency note: The statistical and template proof burden for this section is carried by `File_45`. This section restates the lattice mapping only. ### 6.1 The explicit lattice interval Using the 70-year lattice start-years of the `File_43` ledger: ```markdown Jared start: 4906 BC 2nd Cainan start: 4416 BC 4906 − 4416 = 490 = 7 × 70 ``` This is a full Danielic week of weeks — a 490-year packet — in lattice units. ### 6.2 Daniel-9 decomposition and the x10 echo Daniel 9 is often schematized as: ```markdown 49 + 434 + 3.5 + 3.5 = 490 ``` Under x10 scaling: ```markdown 490 + 4340 + 35 + 35 = 4900 ``` Within the lattice: The front packet is represented by the Jared → 2nd Cainan `490` — a structurally distinct first segment in "troubled times" terms, the Watcher-crisis horizon. The terminal halving is represented at the Christ boundary under the same x10 template, where the final week is bisected (`6 BC → AD 30 → AD 65`; see `File_45`). Claim-status note: This section asserts structural isomorphism — a pattern-template mapping within the lattice. It does not claim that Daniel 9:25 is historically about Jared, and it opens no `434`-year lock. ## 6A. Deep-time overlay application (dependency-controlled bounded addition) Active states: main-chain cumulative comparison and Adam-field expansion; general double-expansion licensing. Deep-time `777` overlay, staged-Flood, and twenty-of-years executions are appendix-only. Source record: the Regular / Cumulative page publication discussion. Main source-table values remain controlled by File_18 §6D. Its LXX `777` overlay is now in File_18 Appendix B.2; applications depending on it have moved from §6A.1–§6A.3 to this file's Appendix A. The unaffected §6A.4–§6A.5 use the main cumulative chain and MT comparisons. Narrative homes remain File_22, File_44, and File_51b; no comparison becomes an independent anchor. Scope note: this section applies `File_46` operators outside the Matthew–Luke lattice, on the LXX cumulative deep-time frame. The application is registered here because the operators are this file's; the lattice-local rulings of §§1–6 are unchanged. Non-collapse guard [§5 vs deep-time `+460`]: §5's non-lock ruling for the 2nd Cainan is lattice-local to the Matthew–Luke carrier. The deep-time `+460` states (`File_56` rail; `File_18` restored-Cainan tables; the `430`-alignment of the leveled MT / LXX cumulatives) are load-bearing in their own frames and are not governed by §5. Do not collapse. ### 6A.1 The twenty-of-years pair — appendix route The LXX `777`-overlay application formerly executed here is preserved unchanged in Appendix A.1. It is not a main-chain Lamech derivation. ### 6A.2 The staged-Flood display — appendix route The dependent staged-Flood example is preserved in Appendix A.2, with its overlay provenance and typological classification retained. ### 6A.3 Double-expansion licensing and the appendix example A span divisible by `23²` admits two successive integral `25/23` expansions. This operator fact remains in the main body. The particular LXX `777`-overlay example formerly here, including its onward conversions, is retained in Appendix A.3 and is not independent main-chain evidence. ### 6A.4 The cross-track `2300` and the Jared span ```markdown 8048 BC (Lamech Flood node, Moses member) → 5748 BC (Arphaxad Flood node, Aaron member) = 2300 10349 BC (Jared span head) → 5748 BC = 4601 = 2301 + 2300 = 4000 + 1 + 600 ``` Member selections are author-declared: Jared's span head; Lamech's Moses member; Arphaxad's Aaron member. The `+1` is the Flood-year inclusive device — Noah "in the 600th year… in the 601st" (Gen. 7:11; 8:13) — which warrants the head-member selection; Shem's `600` stands in for Noah's `600` in the stacked frame. Device recurrence: the SP regular's inclusive-600th `−1` (`File_18`) is the same instrument seen from the other side. Claim-status: arithmetic fact (spans); textual datum (the device); structural inference (selection and substitution). ### 6A.5 The Adam-field expansion ```markdown Heads: 14896 / 14466 / 14436 / 14006 BC = 430 + 30 + 430 Apparent head 14926 BC: 30 + 400 + 30 + 30 + 400 + 30 = 920; 920 × 25/23 = 1000 ``` The four Adam heads (each tradition with and without Cainan) span a field whose intermediate spans are `400 / 430 / 460 / 490` and whose whole is `920 = 460 + 460`, expanding to `1000` — "a thousand years as a day" (2 Pet. 3:8; typological reading). Head-toggle: from `14926 BC` to the MT Lamech seven-span edge (`7156 BC`) is `7770 = 777 × 10` (Shem's `±2` completing); from `14896 BC`, `7740 = 430 × 18 = 1290 × 6`; Lamech's own `777` continues to `6379 BC`: `8547 = 777 × 11`. The field occupies the nine generations Adam through Lamech, a third of the twenty-seven. Narrative classification remains with `File_22` / `File_44`; `File_46` registers the `920 → 1000` expansion and the field grammar. Claim-status: arithmetic fact throughout; structural inference (field reading); typological reading as labeled. ## 7. Content-Scope and Removal Record Arithmetic-control note: Every retained equation in this file resolves to explicit integers under its stated operator. Source-history note: The source draft recorded that earlier `FILE_46` material containing placeholders, undefined units or endpoints, or non-deterministic content had been removed before this revision. That removal is source history; no placeholder content remains. Removal record: The source's prime-lattice section (P8–P12 extensions, including the P11 Exodus/Exile/Decimal spans, the P12 container span, and the "Enochian Unit" constant label) was removed in this revision by author direction of June 10 2026, as tangential to the file's harmonic-expansion subject. The prime-quadruple grid remains controlled by `File_32`, `File_33`, and `File_35`; nothing in this file depends on it. Scope-record addition (bounded): §6A retains the main-chain deep-time applications and stable routing headings. September 8 2026 relocates only the LXX `777`-dependent executions to Appendix A. The Matthew–Luke lattice scope of §§1–6 and the main §6A.4–§6A.5 are unchanged; the §5 non-lock ruling remains lattice-local. ## Appendix A. Preserved LXX `777`-overlay applications These examples use the appendix-only, row-local LXX `777` overlay, not the main `753` lifespan chain. Their equations are preserved from former §6A.1–§6A.3. File_18 Appendix B.2 controls the unchanged `8077–8070 BC` envelope; its `8070` close is the source of the following applications. Neither the overlap nor these expansions propagate an extra `24` into the cumulative chronology. Main §6A.4–§6A.5 and MT `777` comparisons remain outside this relocation. ### A.1 The twenty-of-years pair ```markdown 8070 BC → 1446 BC = 6624 = 1656 × 4 = 23 × 288 = 96 × 69 6624 × 25/23 = 7200 = 20 × 360 6624 × 70/69 = 6720 = 20 × 336 ``` The overlay's seven-year close to the Exodus expands to twenty years-of-years in each calendar — the same pair-structure as the five-of-years at `1656` (`1800 = 5 × 360`; `1680 = 5 × 336`; `File_17` §14; `File_18` Lamech block). Claim-status: arithmetic fact; exact-ratio arithmetic fact. ### A.2 The staged-Flood display ```markdown 1446 + 7200 = 8646 BC; 1446 + 6720 = 8166 BC; original close 8046 BC 8646 BC (+480) → 8166 BC (+120) → 8046 BC; 480 + 120 = 600 ``` The two expansions stage Genesis 6:3 in deep time: Noah's 480th year, the 120-year countdown, the Flood at 600. Increments: `7200 − 6624 = 576`; `576 + 24 = 600`; `6720 − 6624 = 96`; `96 + 24 = 120` — the `24` being the overlay quantum. Claim-status: arithmetic fact (spans and increments); display motif / structural inference (the staging); typological reading (the Gen. 6:3 identification). ### A.3 Onward conversions and the double-expansion licensing corollary ```markdown 8070 BC → 5494 BC = 2576 = 23 × 112; × 25/23 = 2800 8070 BC → 3838 BC = 4232 = 23 × 23 × 8; × 25/23 = 4600; × 25/23 = 5000 ``` Licensing corollary: a `23²`-multiple admits two successive integral `25/23` expansions; the `4232` instance closes on `5000`, ten times the `500` at which Noah begat Shem, Ham, and Japheth. Claim-status: arithmetic fact; exact-ratio arithmetic fact; the `500` resonance is a display motif. ## Revision and archive note This public-clean Markdown source removes only archival amendment history, pass logs, pressure-test repetition, pointer-refresh records, and obsolete replacement-workflow notes. Detailed revision history is preserved in the `Repository_Change_Archive`. The source-history removal record in §7 is retained because it controls the absence of the removed prime-lattice section. Inherited public-clean note: the earlier cleanup did not alter its source arithmetic or states. The September 8 amendment now changes the publication/proof hierarchy of the LXX `777` examples to appendix-only; their equations, endpoints, and stated interpretations are preserved.