{"id": "d-7a3a2b42ad70a08f", "title": "14-file 70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-", "filename": "14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "role": "Source", "step": null, "sha256": "7a3a2b42ad70a08f9b44b087106b4f6517924c13a00817ecfadf1326da11b968", "bytes": 207515, "origins": ["Attached repository/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C0532_C0631/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C0632_C0731/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C0732_C0831/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C0832_C0931/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C0932_C1131/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "C480–C1634/Research_Cycles/C1132_C1431_Recovered/evidence/sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md"], "download": "/sources/7a3a2b42ad70a08f9b44b087106b4f6517924c13a00817ecfadf1326da11b968.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Rounded", "Inverse", "Calendar Keys", "Counts & NT"], "excerpt": "File: File_70_Supplement_A\nTitle: The Key-of-23 Fine Resolution of the 720/30 Rail\nSubtitle: The Four-Node Enochian–SKL Reconciliation, the 4346 BC MT Common-Parent, and the Cumulative–Danielic Completion\nStatus: Verification-complete bounded amendment working copy — September 6 2026; inherited Final source preserved; ", "content": "File: File_70_Supplement_A\nTitle: The Key-of-23 Fine Resolution of the `720/30` Rail\nSubtitle: The Four-Node Enochian–SKL Reconciliation, the `4346 BC` MT Common-Parent, and the Cumulative–Danielic Completion\nStatus: Verification-complete bounded amendment working copy — September 6 2026; inherited Final source preserved; Sothic module centrally registered at State Vocabulary Register v1.52 §D.42 / Restart Capsule v11.51 §10.29; new material not separately author-Finalized or full-file pressure tested.\nInherited Final status: Final; renewed author-invoked Finalization complete August 28 2026; Reopened Pass 0, Reopened Pass 1A, Reopened Pass 1B, the bounded LXX Terah-parallel / conjectural-leveling refinement, Independent Pass 2 Verification, and the combined pressure test complete; central registration of all `53/53` Machine Guards, affected-only no-change reciprocal review, and the expanded File_70 reciprocal route complete at State Vocabulary Register v1.51 Part D §D.41 / Restart Capsule v11.50 §10.28; frozen parents preserved; no source-level blocker remains\nCurrent canonical-filename note: The September 6 2026 publication/source filename is `file_70-supplement-a-key-of-23-fine-resolution-720-30-rail.md`. Earlier `File_70_Supplement_A...` names below are retained as historical frozen-parent, pass-source, or archive identifiers and are not current canonical URLs.\nAmendment trust scope: New sections, state rows, and guards are amendment-local pending separate author Finalization; central registration is complete at State Vocabulary Register v1.52 §D.42 / Restart Capsule v11.51 §10.29. All inherited Finalization, pressure-test, and publication assertions below refer to the frozen pre-amendment source unless expressly dated September 6 2026. No new full-file pressure test or live deployment is claimed.\nRisk level: High-risk Final reopened technical supplement; independently verified and pressure tested under the Reopened Pass-1A state, node-class, proof-weight, and claim-ceiling controls; the August 28 registration refresh changes trust-state and routing text only, preserves the frozen prior Final, and promotes no parent Primary anchor\nFrozen Final Supplement parent: `File_70_Supplement_A.Final_Pre_Dual_Reconciliation_Danielic_Reopening.md`; SHA-256 `8e7431c3cfbd76a06fa263a7278e8072659289c1847689816c8b7dc463e92cc8`\nFrozen reciprocal File_70 parent: `File_70.Final_Pre_Supplement_A_Dual_Reconciliation_Danielic_Reopening.md`; SHA-256 `08aa940bd061ed4102d0370d752ae03628258629f0f8c60472cc66931aaf665b`\nPre-registration Final source: `File_70_Supplement_A.Final_Pre_Central_Registration.md`; SHA-256 `3d2a7e540b9f60e0a4d8fb773f6f8097cb34712be5a21c1683a5b77bcbd11b75`\nImmediate pre-Finalization source: `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail_Reopened_Pass_2_Pressure_Tested.md`; SHA-256 `1760fff0f36005d479c309ce301aeba6207d9028d892a890d59d9a37565b4199`\nFinalization status: Complete August 28 2026 by explicit author instruction. Finalization changed no proof equation, arithmetic row, coordinate, operator, node class, dependency boundary, Machine Guard, evidence weight, claim ceiling, Primary-anchor tier, or principal conclusion. The subsequent central-registration refresh changes only status, control pointers, dependency/routing disposition, §0.9, §12.2, Appendix E.4, Appendix G.4, the Revision basis, and the Revision Log; the combined pre-Finalization pressure test remains the current proof trust basis\nFocused Finalization and registration verification status: Complete — all `446/446` canonical arithmetic rows, `53/53` Machine Guards, `27/27` dependency hashes, `14/14` mounted dependency assertions, the File_52e read-only assertion, proof-bearing equations, evidence weights, and publication-source structures remain intact; the `17` reopening guards and expanded File_70 reciprocal guard are reproduced verbatim at Register §D.41; no new full post-Finalization pressure test is claimed\nImmediate Pass-1A parent: `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail_Reopened_Pass_1A.md`; SHA-256 `be612e79f693f6ba016260df5dc0b56b475795ac5da9365b880af9a4b39757d5`\nImmediate pre-LXX Pass-1B parent: `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail_Reopened_Pass_1B.md`; SHA-256 `050e354ff7b1efbdf8a96dafd79c333311c3bbf2c117dfa52bf48fc26ff6cd7e`\nImmediate LXX-amendment parent: `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail_Reopened_Pass_1B_LXX_Amended.md`; SHA-256 `3a44e19b2116696a1a49493e21893d302854c22a98e4fbd9d041117592c1ac77`\nReopened Pass-0 controller: `File_70_Supplement_A.Reopened_Pass_0_Dual_Reconciliation_Danielic_Intake.md`\nReopened Pass-1A status: Retained — structure, terminology, modal states, node classes, proof hierarchy, dependencies, claim ceilings, appendix routing, and all `52` Pass-1A Machine Guards remain active and unchanged; the one bounded LXX guard is superseded in place by an expanded Terah-pair / conjectural-leveling guard, leaving `53` current guards\nReopened Pass-1B status: Complete with bounded LXX Terah-parallel / leveling refinement — the original `193`-row intake remains partitioned without overlap into `97` admitted canonical rows, `33` dependency-reference executions, `42` control-only executions, and `24` existing/reweight references; the LXX branch contains `20` Secondary and `5` Appendix rows, giving `122` newly admitted rows in the refined source; all execute exactly\nIndependent Pass-2 status: Complete — `446/446` canonical rows independently rebuilt and re-executed in Fraction and SymPy; `326/326` full-source parseable equality chains pass, including the conservative `269/269` body-equality ledger; source/manifest identity, inherited-row preservation, dependency hashes, guard bodies, and proof-region preservation pass\nCombined pressure-test status: Complete — `446/446` one-token arithmetic mutations rejected; `60/60` critical theorem and claim controls pass; `42/42` arithmetic wrong-state/operator/anchor attacks are rejected; `4/4` LXX claim-ceiling assertions, `27/27` dependency hashes, `14/14` mounted dependency assertions, and the File_52e read-only assertion pass; no arithmetic, state, node-class, dependency, proof-weight, or claim-ceiling defect identified\n\nProtected-region status: Existing §§1–7 and §§8.1–8.9 remain byte-exact against the frozen Final parent and Pass-1A parent; all `324` inherited equations, results, and IDs remain unchanged; seven inherited function-cell backticks are restored to frozen-parent wording; `22` inherited row weights remain promoted from Secondary to Primary without changing arithmetic\nArithmetic status: Independently verified — consolidated manifest `446/446 PASS` in rebuilt exact Fraction and SymPy engines; `324` inherited rows plus `122` newly admitted rows; `269/269` additional parseable body equalities pass; dependency and control executions remain outside the evidence count; no arithmetic correction required\nProof-weight status: Independently confirmed — consolidated manifest remains `176` Primary, `229` Secondary, and `41` Appendix; `22` inherited rows remain promoted without arithmetic change; the exact LXX family remains Principal corroboration, while the proposed `5846→5816` level-state interpretation remains Appendix-led conjecture\nMachine-Guard status: The inherited August 28 Final remains `53/53` registered guards across State Vocabulary Register §§D.40–D.41. The September 6 Sothic module adds six guards registered verbatim at v1.52 §D.42, yielding `59/59` current source guards; inherited guard bodies and evidence weights remain unchanged.\nRegister Agreement status: State Vocabulary Register v1.52 Part D §D.42 / Restart Capsule v11.51 §10.29 register and route the September 6 Sothic module in addition to the inherited §§D.40–D.41 Supplement state. Supplement A is centrally registered at `59/59`; File_70 remains `58/58` and unchanged. No inherited proof equation, evidence weight, generated coordinate, source chronology, or Primary-anchor inventory item changes.\nPublication-cleanup status: Public-clean Final canonical Markdown. Central registration, affected-only no-change reciprocal review, the expanded File_70 reciprocal full replacement, and trust-state source refresh are complete. WordPress, HTML, PDF, DOCX, manifest, archive, index, sitemap, deployment, and external archival capture remain separate\nCanonical source: Markdown\nCanonical filename: `file_70-supplement-a-key-of-23-fine-resolution-720-30-rail.md`\nCanonical raw-source URL: `https://490d.com/source/490d-unified-chronology/file_70-supplement-a-key-of-23-fine-resolution-720-30-rail.md`\nClassification: Technical Supplement / Harmonic Fine-Resolution Protocol / Four-Node Enochian–SKL Reconciliation / MT Common-Parent / LXX Terah-Parallel Corroboration / Danielic-Seam Synthesis\nUUID: PROTOCOL_KEY_OF_23_FINE_RESOLUTION_720_30_RAIL\nPrimary domain: Regular; Rounded; Cumulative; SKL; Enochic Genealogical; Calendar; Prophetic; Priestly; Enochian; Precessional; Comparative; Christological; Danielic; Theological by bounded interpretation\nTraditions: MT regular; MT Rounded Scaffold by explicit comparison; LXX actual and LXX Maximum Creation states; cumulative MT; Sumerian A / SKL Short; Sumerian B / SKL Long; Prophetic `360`; Priestly `336`; `361=19²` calendrical-body comparison; Enochian `364`; common solar `365`; Matthew/Luke genealogical schematics; Daniel 9 by pattern-template; NT Christological comparison\nPrimary textual corpus: Genesis 1:1–2:4; Genesis 5; Genesis 11:26–32; Exodus 12; Numbers 33; Joshua 1–5; 2 Kings 17–21 by schematic comparison; Matthew 1–4; Luke 2–4; Daniel 9–12 by calendar and pattern comparison; 1 Enoch 91–93 by File_68 dependency\nPrimary dependency-controlled anchors and states: Rounded MT `4106/4136/4296/4326 BC`; regular-MT endpoint/Year-6/apparent states `4114/4116/4144/4146 BC`, matched `+60 Terah` endpoint/Year-6 states `4174/4176 BC`, and expanded variant `4304 BC`; LXX actual endpoint/Year-6 `5494/5496 BC`; LXX Maximum endpoint/Year-6 `5554/5556 BC`; File_22/File_69 common `4346 BC` generated head; regular Creation phase envelope `4312t/4311n–4305t/4304n BC`; cumulative Creation `14006/14466 BC`; cumulative Flood/Enoch pivot `4836 BC`; SKL/MT comparison `3656/3606/3576 BC`; Short source total/anchors/Floods `17980`, `2936/2906`, `20916/20886 BC`; Long source total/anchors/Floods `24510`, `2886/2856`, `27396/27366 BC`; Enoch schematic `2947t/2946n–2877t/2876n BC`; Projective Pillars `AD 29465/29515`; File_68 schematic/co-registered `2216 BC`; Abraham/Sarah/Noah `2166/2156/2106 BC`; primary Exodus `1446 BC`; inherited `1476/1436/1407t/1406n BC`; Christ `7t/6n BC`, `AD 25/30/35/65/70`; scalar interface `12558/12600/12740`\nLocal or provisional supplement-generated coordinates: Long-corridor center `2872t/2871n BC`; Short-ladder center `2922t/2921n BC`; upper translated-bracket center `2952t/2951n BC`; Enoch-generation center `2912t/2911n BC`; phase brackets `2889t/2888n–2855t/2854n`, `2892t/2891n–2852t/2851n`, `2972t/2971n–2932t/2931n BC`; generated pure-`720` landing `2916 BC`; upstream reconciliation companion `2946 BC`; co-registered File_68 schematic / Supplement-generated Short endpoint `2216 BC`; five-year companions `4341/2871/1401 BC` and `AD 70`; upper-MT partition seams `2648/2666 BC` under distinct local states; generated outer heads `7286/14146/14846/15346 BC`; LXX generated `+30` companions `5584/5586 BC`, generated Priestly head `5846 BC`, and conjectural leveled companion `5816 BC`, independently co-registered as a Secondary preparatory node in File_52e; generated companions `3626/3608/2136/724/2196/2866/27356 BC`, `1409t/1408n`, `1405t/1404n`, `1402t/1401n BC`, `AD 720`, and scalar `24500`; none enters the repository Primary-anchor inventory\nPrimary and provisional values: `0.5`; `2`; `2.5`; `3`; `3.5`; `4.5`; `5`; `7`; `10`; `13`; `15`; `20`; `21`; `23`; `25`; `25.5`; `26`; `30`; `34`; `34.5`; `35`; `37.5`; `40`; `42`; `49`; `50`; `60`; `62`; `63`; `68`; `69`; `70`; `72`; `75`; `80`; `90`; `120`; `130`; `140`; `147`; `176`; `190`; `232`; `336`; `360`; `361`; `364`; `365`; `390`; `434`; `460`; `490`; `670`; `672`; `690`; `700`; `720`; `722`; `724.5`; `728`; `730`; `735`; `737.5`; `750`; `760`; `780`; `810`; `1242`; `1260`; `1380`; `1400`; `1410`; `1440`; `1470`; `1475`; `1500`; `1656`; `1680`; `17980`; `18000`; `24500`; `24510`; `24480`; `25200`; `2898`; `2900`; `2940`; `32400`; `33810`; `34300`; `36750`; `4048`; `4340`; `4400`; `4410`; `4830`; `4900`; `5816`; `5880`; `6480`; `6530`; `9660`; `9800`; `10120`; `10500`; `11000`; `12558`; `12600`; `12740`; `13440`; `241200`; `241920`; `259200`; `259920`; `365.25`; `458640`; `4586400`\nMajor operators: same-side BC subtraction; civil cross-axis `BC + AD − 1`; exact Priestly Key `25/23` and inverse `23/25`; exact Prophetic Key `70/69` and inverse `69/70`; exact Enochian completion `300/299`; anchored expansion and contraction about fixed `1446/1406 BC` targets; native coefficient completion `69u→70u/75u`; fixed-Pillar span execution with `AD 29465` unmoved; File_11 absolute `+0/+2/+4`; Shem-centered local `−2/0/+2`; SKL macro dilation `−720/0/+720`; optional nested local subrail; orthogonal applied-last `+30`; exact phase coordinate `coord(Xn)=X`, `coord(Xt)=X−0.5` for BC labels; provisional `PhaseNorm40`; midpoint by corresponding suffix; uniform translation `T_1470(x)=x−1470`; declared `×72` precessional and `×360` SKL day-year scalars; Danielic `×10/÷10` scale translation; `+50` source-gap/compensation state, not a ratio operator\nMajor modal states: subordinate File_70 supplement state; frozen-parent reopening state; coarse carrier; crossed-core fine resolution; Long-corridor center; Short-ladder center; Enoch-generation center; upper translated-bracket center; scalar half-field closure; phase-and-Gear coordinate envelope; PhaseNorm40; `70=35+35` generation state; `120=60+60=40+40+40` state; Key-completed `25|35|35|25` composition; SKL Short/Long source-state pair; pure-`720` reconciliation pair; bilateral complementary-Key state; Primary four-node Enochian–SKL reconciliation field; direct-Key-convergence versus field-completion state; MT standard/expanded/common-parent field `4114/4304/4346 BC`; anchored expansion/contraction duality; candidate pre-contraction Creation-head state; LXX Maximum/actual/apparent outer-register corroboration state; matched LXX–MT Terah-pair `1380=690+690` state; dual-Key-ready `1380→1400/1500` dependency state; generated LXX–Exodus Priestly head state; conjectural LXX `+30`-facing / leveled-companion state; File_52e Secondary `5816 BC` co-registration state; reconciliation-of-reconciliations ladder; first-arm `20+1` Enoch anatomy; carrier-close/five-year-companion ladders; native `69×140/69×490` coefficient state; Cumulative–Pillar co-registration; fixed-Pillar completion state; cumulative `35×360/35×364/40×336` comparison state; Danielic seam; `7|62|½|½` and refined `7|20|1|21|20|½|½` generation states; upper-MT raw/transformed Flood-seam state; generated-head non-promotion state; Christological quartet restraint; `90×72/90×360` scalar pair; `720/722/728/730` calendar-double spectrum; Projective Pillar state; appendix-only `361`/Baháʼí reception-history state; Enoch BC-fulcrum state; Christ full-axis fulcrum state; source `24510` / generated `24500` state\nMajor claim-status labels: source-retained chronology datum; dependency-controlled chronology datum; inherited verified arithmetic fact; Pass-1B verified arithmetic fact; generated companion; co-registered node; common operator-parent; candidate compositional archetype; structural inference; calendrical structural inference; fractal inference; Danielic pattern-template; shared-tradition evidence; principal corroboration; secondary structural support; reception-history note; providential synchronization; theological synthesis; appendix-only; audit note\nRevision basis: author discussion through August 28 2026; frozen Final Supplement A and reciprocal File_70 parents; Reopened Pass-0 through Pass-2 artifacts; bounded LXX Terah-parallel / conjectural-leveling refinement; author-invoked Finalization; central registration of the `17` reopening guards; affected-only no-change reciprocal review; expanded reciprocal File_70 full replacement; 490d Repository Style Guide v2.5; Project Procedures v3.5; Restart Capsule v11.50; State Vocabulary Register v1.51 Part D §D.41; frozen Files 00, 05, 06, 08, 09, 12, 13, 14, 18, 20, 21, 22, 43, 45, 46, 53, 68, and 69; File_52e by read-only File-Library assertion\n\n# File_70 Supplement A — The Key-of-23 Fine Resolution of the `720/30` Rail\n\n*The Four-Node Enochian–SKL Reconciliation, the `4346 BC` MT Common-Parent, and the Cumulative–Danielic Completion*\n## Related Repository Files\n\n| File / control | Function for `File_70 Supplement A` |\n|---|---|\n| `File_70` | Immediate conceptual parent and separate frozen reciprocal parent. Controls the Genesis *toledot* Atonement-Weave, heptadic scale recurrence, nested wheels, bounded SKL appendix, evidence-family restraint, and reciprocal routing. No Supplement proof body is embedded in File_70 during this reopening. |\n| `File_00` | Controls file-function framing, source-map discipline, center/node-class non-collapse, same-side versus civil cross-axis arithmetic, claim hierarchy, Primary-anchor restraint, and Machine-Guard form. |\n| `File_51a`; `File_54` | Control Rounded/Actual/Cumulative non-collapse, state-register form, comparative claim restraint, appendix routing, and evidence-accounting precedent. |\n| `File_21`; `File_34`; `File_18` | Control SKL Short/Long whole-year states, physical and `+30` anchors, Flood pairs, the source `+50`, `6480`, `360:1`, Projective Pillars, nested `±2/±720`, and raw table node classes. |\n| `File_50c`; `File_11` | Control the rigid SKL `±720` target bracket and the ordinary Three-Gear wheel; neither grants a new source coordinate or scan hit here. |\n| `File_22` | Controls the two regular-MT routes to `4346 BC`, the `4114/4304 BC` Creation states, and the inherited cumulative `12600/12740` theorem. The Supplement adds no replacement source chronology. |\n| `File_09` | Controls cumulative Creation, Flood, Cainan, and endpoint anatomy, including `14006/14466/4836 BC`. |\n| `File_68`; `File_69` | Control the Enoch `70/72` carriers, the `2946/2876 BC` schematic endpoints, the Enoch-centered genealogical architecture, and the `4346→2876→1406 BC→AD 65` ladder. The Supplement integrates but does not re-own those proof burdens. |\n| `File_43` | Controls existing genealogical uses of `2666 BC` and the Luke/Matthew bridge. The local transformed-seam use of `2666 BC` must remain distinct. |\n| `File_45` | Controls the Daniel 9 pattern-template `49+434+3.5+3.5=490`, its `10×` display, and the no-`434`-year-lock claim ceiling. |\n| `File_46` | Controls `4830`, `9660`, `70/69`, `25/23`, and `4900` operator mechanics. The Supplement supplies a new continuous coordinate assembly, not a replacement operator register. |\n| `File_52e` | File-Library source-history dependency for the Secondary LXX inverse/preparatory node `5816 BC` and its `5816→1406 BC=4410` relation. The Supplement imports only that co-registration; it does not import File_52e’s inverse proof spine or use it to prove the conjectural `5846→5816` rail assignment. |\n| `File_53` | Already contains the cumulative `4346/9660/9800/10120` family. Those relations remain dependency-controlled corroboration and cannot be counted as new independent Supplement witnesses. |\n| `File_20` | Controls the pre-existing BJ/Jubilees `2648 BC` Ham-birth label. The local generated upper-MT Flood seam at the same year-label remains a different node class. |\n| `File_05`; `File_06` | Control the primary `1446 BC` Exodus and historical `1406 BC` Conquest hierarchy. |\n| `File_13`; `File_14`; `File_08` | File_13 controls actual LXX `5494/5496/5526 BC` and Christological `AD 25/30/35/65` states; File_14 controls LXX Maximum `5554/5555/5556 BC` node classes; File_08 controls `AD 70` as the historical Second-Temple-destruction node. |\n| `File_12`; `File_17` | Control exact Key grammar, inverse/ratio restraint, `336/360/364` non-collapse, civil span execution, and Residue Protocol boundaries. |\n| `File_10`; `File_67`; `File_01`; `File_16`; `File_29` | Control the Precession Square/Pillar restraint, Hezekiah seam, Abraham/Sarah states, `+60/+130` variant vocabulary, and bounded Atonement/typological language. |\n| `File_36` / P19 | File-Library-only dependency for the `361×50` and Baháʼí reception-history display. It remains appendix-only and is not re-executed here. |\n| State Vocabulary Register v1.51 §§D.38–D.41 | Controls nested `±2/±720`, orthogonal `+30`, inherited File_70 firewalls, all `53/53` Supplement guards, and the current expanded File_70 reciprocal guard. |\n| Restart Capsule v11.50 | Governs repository-wide anchors, operators, modal states, the Primary-anchor inventory, and compact §10.28 routing for the expanded Supplement/File_70 state. |\n| 490d Repository Style Guide v2.5 | Governs canonical Markdown, exact states, phase suffixes, node-class language, claim labels, and source/publication separation. |\n| Project Procedures v3.5 | Governs the High-risk split. Pass 1A fixes structure, terminology, states, node classes, proof weight, and guards; Pass 1B executes arithmetic and argument. |\n\nDependency rule:\n\n`File_70 Supplement A` is locally controlling only for its fine-resolution synthesis, newly integrated terminology, state architecture, node classes, proof-weight hierarchy, common-parent interpretation, continuous coordinate assembly, and later locally executed arithmetic. It does not replace any parent chronology, source datum, calendar definition, Gear operator, SKL derivation, Enochic source-critical result, cumulative theorem, Danielic template, Christological date-state, Projective Pillar, or repository Primary anchor.\n## 0. File-function\n\n`File_70 Supplement A` is the technical fine-resolution companion to File_70. It preserves the inherited `720/30/690` proof and now integrates five additional exact structures under the Pass-1A state and Machine-Guard architecture:\n\n1. the full four-node Enochian–SKL reconciliation across `2946–2876 BC`;\n2. the regular-MT common operator-parent at `4346 BC`;\n3. the bounded LXX cross-tradition repetition of the `30\\|1410\\|30` and `±720` grammar;\n4. the Cumulative–Pillar co-registration around the same hinge;\n5. the continuous Danielic seam from cumulative Flood to the Christological carrier close.\n\nPass 1B executes the arithmetic and completes the argument. The theorem is not that one chronology replaces another, but that distinct source and generated states converge under declared operators while preserving their node classes.\n\nThe proof hierarchy is:\n\n1. **Primary inherited local spine:** Creation → Conquest → Christ under the inherited fine-resolution grammar.\n2. **Primary Enochian–SKL bridge:** the complete `2946|2916|2906|2876 BC` field, its `2911 BC` center, and its `−1470` biblical translation.\n3. **Primary MT common-parent theorem:** the two File_22 expansion routes meet at `4346 BC`; inverse execution confirms one exact operator-parent without proving composition order.\n4. **Primary reconciliation ladder:** `4346→2876→1406 BC→AD 65`, with the first arm resolved as `20+1` seventy-year units.\n5. **Principal Cumulative–Pillar corroboration:** native `69×140` and `69×490` spans admit the same `70/75` coefficient completions around the common hinge.\n6. **Principal LXX cross-tradition corroboration:** matched endpoint and Year-6 states with and without `+60 Terah` preserve `1380=690+690`; the outer registers repeat `30\\|1410\\|30`; `4836 BC` bisects the unshifted `5556/4116 BC` pair by `720|720`; the actual LXX endpoint generates a bounded Priestly route to the Short SKL field. A possible `5846→5816` leveling remains Appendix-led conjecture.\n7. **Primary Danielic capstone:** `4836→4346→6 BC→AD 30→AD 65` executes `490|4340|35|35=4900`, the `10×` form of the File_45 pattern-template.\n8. **Principal five-year companion:** `35|35|5`, with center status restricted to `2871 BC` and carrier status retained at `AD 65`.\n9. **Secondary and appendix continuations:** the upper-MT Flood partition, transformed seam, generated remote heads, and Cainan continuation.\n\nArithmetic fact, structural inference, candidate compositional hypothesis, typological reading, and theological synthesis remain separately labeled.\n\n### 0.1 Scope hierarchy and proof burden\n\n| Layer | Material | Weight | Reopened Pass-1A disposition |\n|---|---|---|---|\n| Primary inherited local proof | Native `30\\|690`; center/phase mechanics; Creation–Conquest–Christ corridor; cumulative `12558→12600/12740` | inherited principal spine | §§1–7 remain byte-exact |\n| Primary Enochian–SKL theorem | `2946\\|2916\\|2906\\|2876`; `30\\|10\\|30`; `10\\|50\\|10`; `35\\|35`; full lattice | Primary structural family | §8 promoted; §§8.1–8.9 equations remain byte-exact |\n| Primary MT theorem | `4114/4304/4346 BC`; anchored expansion/contraction; compensation identities | Primary common-parent family | new §9; exact execution complete in Pass 1B |\n| Primary integrative theorem | `4346→2876→1406 BC→AD 65`; first arm resolved through `2946 BC` | Primary reconciliation ladder | new §9; parent proof burdens preserved |\n| Primary Danielic synthesis | `4836→4346→6 BC→AD 30→AD 65`; `7\\|62\\|½\\|½`; refined middle body | Primary capstone | new §11; File_45 pattern-template remains controlling |\n| Principal corroboration | Native `69×140/69×490`; fixed-Pillar `70/75`; cumulative `35×360/35×364/40×336` | Principal Cumulative–Pillar co-registration | new §10; existing File_22/File_46/File_53 equations cited by dependency |\n| Principal corroboration / Appendix conjecture | matched LXX–MT `+60` and no-`+60` endpoint/Year-6 `1380` bodies; `30\\|1410\\|30`; `4836 BC` as `±720` midpoint; generated `5846→2906=2940`; conjectural leveling `5816→4346→2876` | exact cross-tradition corroboration plus quarantined level-state hypothesis | §9.9; Files 11/13/14/18 retain source-state control |\n| Principal corroboration | `35+35+5`; carrier-close and five-year companion ladders | Principal structural companion | §§9 and 12; no `75`-year carrier introduced |\n| Secondary structural support | `4304→2648→1406`; scalar conversion to `1680+1260`; transformed seam `2666 BC` | Secondary | end of §9 and Appendix C; collision guards mandatory |\n| Appendix-led | `7286/14146/14846/15346 BC`; Cainan `460→500`; further remote symmetries | Appendix / exploratory | Appendix C only; exact appendix execution complete in Pass 1B |\n| Reception-history | `361` body and Baháʼí Era display | appendix-only | inherited Appendix C routing retained |\n| Excluded | literal `434`-year lock; unqualified “original MT Creation date”; generated nodes as Primary anchors; prior excluded palindrome catalogues | outside scope | barred from re-entry |\n\n### 0.2 Working state register\n\n| State | Primary values / form | Node-class / function | Handling in Reopened Pass 1A |\n|---|---:|---|---|\n| Subordinate File_70 companion | separate Supplement A | technical companion | File_70 remains a separate frozen parent. |\n| Coarse carrier / orthogonal rail / crossed core | `720`; `30`; `690` | inherited carrier grammar | Existing proof retained. |\n| Long-corridor center | `2872t/2871n BC` | center of Long `1470/2940` and lower normalized `40` bracket | Never called the center of Enoch’s full generation. |\n| Short-ladder center | `2922t/2921n BC` | center of the parallel Short `1470` ladder | Audit/comparison state. |\n| Enoch-generation center | `2912t/2911n BC` | common center of phase-resolved `70` and generated `120` fields | Governing Enoch center; unsuffixed `2911 BC` is shorthand. |\n| Upper translated-bracket center | `2952t/2951n BC` | center of upper `40` bracket | Generated comparison center. |\n| Enoch schematic opening/close | `2947t/2946n`; `2877t/2876n BC` | dependency-controlled generation endpoints | Schematic, not literal historical biography. |\n| Primary four-node Enochian–SKL reconciliation field | `2946\\|2916\\|2906\\|2876 BC` | complete `70`-year field integrating direct convergences and `+30` companions | Primary theorem family. |\n| Direct-Key-convergence state | `2916/2876 BC` | reverse/forward complementary-Key convergence nodes | Distinct from field-completing `2946/2906 BC`. |\n| Full-lattice state | `2946/2936/2916/2906/2886/2876 BC` | nested source/generated Enoch field | One evidence family under non-overcount. |\n| Scalar half-field closure | `724.5→735`; `735+735=1470` | abstract scalar state | Does not identify the `2884/2858` coordinate execution. |\n| Coordinate-arm envelope | `13+724.5=737.5`; paired `1475` | phase-and-Gear coordinate state | Distinct endpoints and total from scalar closure. |\n| PhaseNorm40 state | `34.5→37.5`, residual `2.5`, generated corresponding-suffix `40` bracket | two-stage normalization | Not a fourth Key ratio. |\n| Enoch `70` state | `35+35`; `30+40`; `2947t/2946n–2877t/2876n` | phase-resolved generation | Shares center with, but is not identical to, the `120` state. |\n| Expanded `120` state | `60+60`; `40+40+40` | generated phase envelope | Additive composition; not one ratio output. |\n| SKL Short source state | `17980`; `2936/2906`; `20916/20886 BC` | source-controlled Short whole-year/base/+30/Flood state | Simultaneous with Long. |\n| SKL Long source state | `24510`; `2886/2856`; `27396/27366 BC` | source-controlled Long whole-year/base/+30/Flood state | Source `24510` remains controlling. |\n| Pure-`720` reconciliation state | `2916/2886 BC`; upstream `2946 BC` | generated/common landings with co-registration | Never replaces source anchors. |\n| Bilateral complementary-Key state | Short `750\\|700`; Long `700\\|750` by direction | directional Key exchange | Forward convergence `2876`; reverse convergence `2916`. |\n| MT standard Creation state | `4114 BC` | regular-MT Standard-Normal Creation endpoint | File_22/File_51a/File_69 dependency. |\n| MT expanded variant state | `4304 BC = 4114+60+130` under declared state | regular-MT `+60 Terah +130 Cainan` Creation state | Simultaneous variant; `−215` inactive. |\n| MT common operator-parent state | `4346 BC` | exact common anchored preimage / File_22–File_69 generated head | Strong structural classification; not transmitted chronology. |\n| Candidate pre-contraction Creation-head state | `4346 BC` | bounded compositional-archetype hypothesis | Arithmetic cannot establish historical priority. |\n| LXX–MT outer-register corroboration | endpoint `5584/5554/4174/4144/4114`; Year-6 `5586/5556/4176/4146/4116`; actual LXX `5494/5496`; midpoint `4836`; generated `5846 BC`; conjectural / File_52e-co-registered `5816 BC` | matched `1380=690+690`, dependency-owned `1380→1400/1500`, `30\\|1410\\|30`, `±720`, Priestly completion, and a quarantined level-state hypothesis | Exact relations are Principal corroboration; File_52e corroborates the `5816` coordinate only; the `5846→5816` rail assignment remains Appendix-led conjecture. |\n| Anchored expansion/contraction duality | `25/23↔23/25` about `1446`; `70/69↔69/70` about `1406` | reversible exact maps | Direction of calculation does not prove original order. |\n| Reconciliation-of-reconciliations ladder | `4346\\|2876\\|1406 BC\\|AD 65` | MT parent → SKL/Enoch close → Conquest → Christ close | Primary integrative theorem. |\n| First-arm Enoch anatomy | `4346→2946→2876 BC` | `20+1` seventy-year units inside first `1470` arm | Primary internal resolution. |\n| Carrier-close ladder | `4346\\|2876\\|1406 BC\\|AD 65` | repeated carrier-close field | Distinct from five-year companion. |\n| Five-year companion ladder | `4341\\|2871\\|1401 BC\\|AD 70` | generated/historical companion field | Principal corroboration; only `2871 BC` has independent center class. |\n| Native `69` coefficient state | `9660=69×140`; `33810=69×490` | Key-ready parent spans on opposite sides of `4346 BC` | Not Residue Protocol or lower-order remainder. |\n| Cumulative–Pillar co-registration | fixed `4346 BC` hinge; cumulative and Pillar sides | common-parent closure under both Keys | Principal corroboration. |\n| Fixed-Pillar state | `AD 29465` held fixed | BC endpoint moves by expansion gain | Projective Boundary, not historical chronology. |\n| Cumulative calendar-body comparison | `12600/12740/13440` | `35×360 / 35×364 / 40×336` completed spans | Coordinate executions remain state-specific. |\n| Cumulative Cainan continuation | `14466 BC`; `10120`; generated `11000` | File_53-controlled family plus bounded continuation | Appendix-led; no independent witness count. |\n| Danielic seam | `4836→4346→6 BC→AD 30→AD 65` | continuous cumulative-Flood-to-Christ coordinate assembly | Primary capstone. |\n| Danielic whole/segmentation state | `70×7=490`; `49+434+3.5+3.5=490` | multiplicative whole and additive pattern-template | Neither replaces the other. |\n| Refined seventy-generation anatomy | `7\\|20\\|1\\|21\\|20\\|½\\|½` | internal resolution of `7\\|62\\|½\\|½` | Structural synthesis; arithmetic executed in Pass 1B. |\n| Upper-MT raw Flood partition | `4304→2648→1406 BC` | generated partition using `1656\\|1242` | Secondary; `2648 BC` collides with BJ Ham label. |\n| Transformed Flood seam | `2666 BC` | generated coordinate after scalar conversion with `1406 BC` fixed | Not the raw `2648 BC` seam or any genealogical `2666 BC`. |\n| Generated outer-head state | `7286/14146/14846/15346 BC` | remote Key continuations | Appendix-only; Pass-1B arithmetic and Pass-2 node-class roles verified; no promotion. |\n| Christological quartet state | `6 BC\\|AD 25\\|AD 35\\|AD 65`; midpoint `AD 30` | translated `30\\|10\\|30` field and center | AD `25/35` comparison only; `AD 65` remains close. |\n| `90` carrier pair | `90×72=6480`; `90×360=32400` | precessional-quarter / SKL day-year-Pillar states | Units remain distinct. |\n| Calendar-double spectrum | `720/722/728/730` | `2×360`, `2×361`, `2×364`, `2×365` | No calendar definition is replaced. |\n| Projective-Pillar state | `AD 29465/29515`; center `AD 29490` | File_21/File_10 Projective Boundary | Not ordinary historical chronology. |\n| `361` reception-history state | `19²`; `AD 1844`; File_36/P19 | appendix-only corroboration | Not a complete solar year. |\n| Enoch BC-fulcrum state | Enoch-centered generation/variant architecture | BC-side structural fulcrum | Same-side BC architecture only. |\n| Christ full-axis fulcrum state | BC architecture carried through the epoch boundary | theological/civil-axis completion | Does not alter Christological date controls. |\n| Source/companion SKL close | `24510`; generated `24500` | source duration / Jubilee companion | Prior non-correction guard retained. |\n| Sothic Short-field symmetry, amendment-local | `x=−2921+15r+2g+p/4`; `5842`; twelve nodes | exact affine/paired-Mirror comparison | §13; generated center co-registration, not new Primary anchor. |\n| Sothic Mosaic–Joshua selection, amendment-local | `2936/2906/2886/2856`; `30/20/30`; `1380`; `50` | source-controlled packet reconstruction | One correlated family; not independent historical witnesses. |\n| Sothic Long/Christ/Moses comparison, amendment-local | `2920`; six-by-two Moses matrix; absent `4383` | fixed endpoints and negative-control state | §13.9; no unannounced adjacent-state completion. |\n\n### 0.3 Node-class register\n\n#### 0.3.1 Source-controlled and dependency-controlled nodes\n\n| Node / state | Controlled node-class | Controller | Promotion here? |\n|---:|---|---|---|\n| `17980`; `2936/2906`; `20916/20886 BC` | SKL Short whole-year, +30/base anchors, +30/base Floods | Files 21/34/18 | `No` |\n| `24510`; `2886/2856`; `27396/27366 BC` | SKL Long whole-year, +30/base anchors, +30/base Floods | Files 21/34/18 | `No` |\n| `4114 BC` | regular-MT Standard-Normal Creation endpoint | Files 22/51a/69 | `No` |\n| `4116/4144/4146 BC` | MT Standard-Normal Year-6 and endpoint/Year-6 apparent-age companions | Files 00/13/14 | `No` |\n| `4174/4176 BC` | MT Standard-Normal `+60 Terah` endpoint / Year-6 pair | Files 18/11/22 | `No` |\n| `5554/5556 BC` | LXX Maximum endpoint / Year-6 labels | Files 14/18 | `No` |\n| `5494/5496 BC` | actual LXX Creation endpoint / Year-6 pair after removal of the `+60 Terah` state | Files 13/68 | `No` |\n| `4304 BC` | regular-MT `+60 Terah +130 Cainan` Creation variant | Files 22/29/69 | `No` |\n| `4346 BC` | File_22 generated Super-Creation target / File_69 genealogical head; common anchored preimage in this synthesis | Files 22/69 | `No` |\n| `14006/14466 BC` | cumulative base/restored-Cainan Creation heads | Files 09/22/53 | `No` |\n| `4836 BC` | cumulative Flood/Enoch pivot | Files 09/22/45/46/54 | `No` |\n| `AD 29465/29515` | Boaz/Jachin Projective Pillars | Files 21/10 | `No` |\n| `2947t/2946n–2877t/2876n BC` | translated Enoch schematic generation | Files 68–69 | `No` |\n| `2876 BC` | Enoch schematic close / Jubilee pivot | Files 10/68/69 | `No` |\n| `3656/3606/3576 BC` | comparison nodes under declared SKL/Enoch/MT states | Files 18/21/34/50c/69 | `No` |\n| `2216 BC` | File_68 schematic label; co-registered with generated Short-ladder endpoint | File 68 plus Supplement arithmetic | `No` |\n| `2166/2156/2106 BC` | Abraham/Sarah/Noah field | Files 01/69 | `No` |\n| `1476/1446/1407t/1406n BC` | Joshua birth, Exodus, phase-resolved Conquest | Files 05/06/68 | `No` |\n| `696/726 BC` | Hezekiah seam / schematic Samaria | Files 67/08/16 | `No` |\n| `7t/6n BC`; `AD 25/30/35/65/70` | Christ birth, comparison midpoint/terminals, carrier close, Temple destruction | Files 13/08/43/54/68/69 | `No` |\n| `14004/14006 BC`; `12558/12600/12740` | cumulative endpoint/scalar interface | Files 09/22 | `No` |\n| `2648 BC` | BJ/Jubilees Ham-birth label | Files 20/18 | `No` |\n| `2666 BC` | existing genealogical/Enochic translated labels under several parent states | Files 43/68/69 | `No` |\n| `20166/262086/262116 BC` | Short-Flood Gear / Creation macro states | Files 18/21/50c | `No` |\n| `AD 1844` | Baháʼí Era reception-history endpoint | File_36/P19 dependency | `No` |\n\n#### 0.3.2 Supplement-generated, translated, co-registered, or provisional nodes\n\n| Node / value | Local node-class | Generation / co-registration | Handling |\n|---:|---|---|---|\n| `2872t/2871n BC` | Long-corridor center | midpoint of Long source pair and principal corridor | Generated center; not Enoch-generation center. |\n| `2922t/2921n BC` | Short-ladder center | midpoint of Short ladder/source pair | Comparison center only. |\n| `2912t/2911n BC` | Enoch-generation / `120` center | midpoint of Enoch generation and expanded field | Generated center; not `2916 BC`. |\n| `2952t/2951n BC` | upper translated-bracket center | lower bracket center translated by `80` | Generated. |\n| `2946 BC` | co-registered Enoch opening and field-completing `+30` companion | parent schematic label plus Supplement relation | Not a transmitted SKL terminal anchor. |\n| `2916 BC` | generated pure-`720` / reverse-Key convergence node | common Short/Long landing | Not a Short physical anchor. |\n| `2886 BC` | source Long +30 anchor plus generated physical pure-`720` landing | co-registered source/generated | Source class remains controlling. |\n| `2876 BC` | dependency-controlled Enoch close plus Supplement forward-Key convergence | co-registered parent/generated | Not a center. |\n| `3626/2216 BC` | Short-ladder generated endpoints | `2216` also carries File_68 schematic class | Secondary endpoint relations. |\n| `4341/2871/1401 BC`; `AD 70` | five-year companion ladder | generated BC companions plus historical AD endpoint | Principal corroboration; not carrier-close ladder. |\n| `2648 BC` | local generated upper-MT raw Flood seam | partition of the `4304→1406 BC` field | Shared label with BJ Ham; no event identity. |\n| `2666 BC` | local generated transformed seam | coordinate seam after expanded scalar components | Shared label with genealogical states; no identity. |\n| `5584/5586 BC` | generated LXX `+30` apparent-age companions | `5554/5556+30` under the opened comparison state | Principal corroboration only; not transmitted LXX labels. |\n| `5846 BC` | generated LXX–Exodus Priestly head | `5494→1446` span expanded by `25/23` with Exodus fixed | Row-level Secondary; candidate `+30`-facing role remains conjectural. |\n| `5816 BC` | conjectural leveled LXX Priestly companion / File_52e Secondary co-registration | proposed removal of a positional `+30` from generated `5846 BC`; independently retained in File_52e as a preparatory inverse node | Appendix-only structural hypothesis in this Supplement; File_52e corroborates the coordinate but not the rail assignment; not a Primary anchor. |\n| `7286/14146/14846/15346 BC` | provisional generated outer heads | fixed-Pillar or cumulative completion routes | Appendix-only until later verification. |\n| `AD 35` | generated Christological quartet comparison node | translation of `2906 BC` by the admitted double-`1470` field | Does not replace `AD 30` or `AD 65`. |\n| `33810/34300/36750` | Pillar-facing scalars | native/Prophetic/Priestly coefficient states | Scalar objects, not dates. |\n| `9660/9800/10500/10120/11000` | cumulative-facing scalars | native/completed/Cainan continuation states | File_46/File_53 dependency; no independent witness inflation. |\n| `12600/12740/13440` | completed cumulative spans | Prophetic/Enochian/Priestly calendar-body forms | Shared scalar does not merge coordinate executions. |\n| `4342t/4341n`; `1402t/1401n BC` | principal generated extremities | existing proof corridor | Never Primary anchors. |\n| `24500`; `2866/27356 BC` | generated Jubilee companion and endpoints | prior bounded SKL close | Source `24510` remains controlling. |\n\n### 0.4 Terminology and object-class register\n\n| Term | Controlled definition | Required distinction |\n|---|---|---|\n| **Four-node Enochian–SKL reconciliation field** | `2946\\|2916\\|2906\\|2876 BC`, completed by the direct Key convergences and their `+30` companions | whole Primary theorem; not four identical node classes |\n| **direct Key convergence** | `2916/2876 BC` as reverse/forward complementary-Key outputs | distinct from field-completing `2946/2906 BC` |\n| **full-field reconciliation** | the four-node and full-lattice coverage of Enoch’s `2946–2876 BC` generation | does not make every member a ratio output |\n| **common operator-parent** | `4346 BC` as the exact common anchored inverse preimage of `4114/4304 BC` | arithmetic/structural class; not transmitted chronology |\n| **candidate pre-contraction Creation head** | bounded hypothesis that `4346 BC` may preserve an archetypal parent state | composition order remains unknown |\n| **anchored expansion / anchored contraction** | exact Key map applied to the span from a fixed Exodus or Conquest anchor, then restored to that anchor | endpoint and anchor must be named |\n| **native `69`-coefficient state** | `69×unit` parent span that admits exact `70/75` completions | not Residue Protocol or lesser remainder |\n| **reconciliation-of-reconciliations ladder** | `4346\\|2876\\|1406 BC\\|AD 65` | joins MT, SKL/Enoch, Conquest, and Christ under preserved node classes |\n| **carrier-close ladder** | the repeated-`1470` ladder terminating at `AD 65` | not the five-year companion |\n| **five-year companion ladder** | `4341\\|2871\\|1401 BC\\|AD 70` | only `2871 BC` is independently a center |\n| **Cumulative–Pillar co-registration** | native `69×140` and `69×490` spans sharing the `4346 BC` hinge and complementary Keys | different units; one coordinated family |\n| **fixed-Pillar execution** | expansion changes the BC-side endpoint while the Projective Pillar remains fixed | never move the Pillar to preserve a preferred date |\n| **Danielic seam** | `4346 BC` as the boundary resolving `4830` into `490+4340` inside the cumulative Flood-to-Christ field | pattern-template, not direct Danielic referent |\n| **Danielic whole / additive segmentation** | `70×7=490` as whole; `49+434+3.5+3.5=490` as internal segmentation | neither replaces the other |\n| **raw Flood seam** | local `2648 BC` partition before Key conversion | not BJ Ham by identity and not transformed seam |\n| **transformed Flood seam** | local `2666 BC` coordinate after scalar conversion with terminal fixed | not the raw seam or genealogical `2666` |\n| **generated outer head** | remote BC endpoint created by a declared fixed-anchor completion | never a source date or Primary anchor without later control |\n| **Long-corridor center** | `2872t/2871n BC` | principal Long geometry, not Enoch-generation center |\n| **Enoch-generation center** | `2912t/2911n BC` | center of `70` and `120`; unsuffixed `2911` is shorthand |\n| **PhaseNorm40** | Priestly scalar completion followed by generated same-center phase bracket | not another Key ratio |\n| **BC fulcrum / full-axis fulcrum** | Enoch centers BC-side architecture; Christ completes the BC–AD axis | theological hierarchy without competition |\n\n### 0.5 Operator register\n\n| Operator / notation | Function | Scope control |\n|---|---|---|\n| same-side BC subtraction | elapsed span between BC labels | direction must be stated when translating dates |\n| `BC + AD − 1` | civil cross-axis span | mandatory; no year zero |\n| `25/23`; `70/69`; `300/299` | Priestly, Prophetic, Enochian exact-rational operators | no interchange or decimal approximation |\n| `23/25`; `69/70` | exact inverse contractions | use only against the corresponding fixed anchor |\n| `E_P(x)=1446+(x−1446)×25/23` | anchored Priestly expansion about the Exodus | executed dependency route; inverse checked as control |\n| `C_P(y)=1446+(y−1446)×23/25` | anchored Priestly contraction about the Exodus | exact inverse of `E_P` on admitted states |\n| `E_R(x)=1406+(x−1406)×70/69` | anchored Prophetic expansion about the Conquest | executed dependency route; inverse checked as control |\n| `C_R(y)=1406+(y−1406)×69/70` | anchored Prophetic contraction about the Conquest | exact inverse of `E_R` on admitted states |\n| `69u→70u` | Prophetic coefficient completion | unit `u` and endpoint state must be declared |\n| `69u→75u` | Priestly coefficient completion because `69×25/23=75` | unit `u` and endpoint state must be declared |\n| `S_P(B)=B+29465−1` | civil span from BC head `B` to the fixed `AD 29465` Pillar | Pillar remains fixed; result is a scalar span |\n| `coord(Xn)=X`; `coord(Xt)=X−0.5` | exact continuous coordinate for BC phase labels | used only for phase arithmetic |\n| midpoint by corresponding suffix | average of like-suffix coordinates | cross-suffix midpoints require explicit phase conversion |\n| provisional `PhaseNorm40` | maps the Key-completed scalar state into a generated same-center corresponding-suffix `40` bracket | two-stage construction; not a ratio |\n| `T_1470(x)=x−1470` | uniform same-side translation | output node class remains separate from input |\n| Danielic `×10/÷10` translation | moves between `49\\|434\\|3.5\\|3.5` and `490\\|4340\\|35\\|35` | scale translation, not event identity |\n| `×72`; `×360` | precessional-day and SKL day-year scalars | units cannot be interchanged |\n| `+50` | source-state gap/translation/compensation width | not a Key operator; local function must be named |\n| applied-last `+30` | state-dependent orthogonal rail | SKL, apparent-age, intercalation, and ministry uses remain distinct |\n| `−2/0/+2`; `−720/0/+720` | local and macro centered Gear wheels | units and active member must be declared |\n\n### 0.6 Claim-status and evidence-weight register\n\n| Claim-status / weight | Local use |\n|---|---|\n| Source-retained chronology datum | SKL `17980/24510`; source anchors/Floods; biblical and cumulative parent anchors |\n| Dependency-controlled chronology datum | Enoch generation, MT Creation states, `4346 BC`, Pillars, cumulative heads, Christological states |\n| Inherited verified arithmetic fact | one of the frozen parent’s `324` exact rows; prior Final trust retained |\n| Pass-1B verified arithmetic fact | admitted canonical row or exact non-counted dependency/control execution |\n| Generated companion / center | local coordinate produced by declared operation or midpoint |\n| Co-registered node | one label carrying parent and Supplement-generated classes without collapse |\n| Common operator-parent | exact common anchored preimage under the declared inverse maps |\n| Strong structural inference | common-parent architecture, reconciliation ladder, and Danielic seam inside the fixed model |\n| Candidate compositional archetype | possible pre-contraction priority of `4346 BC`; not demonstrated historical sequence |\n| Danielic pattern-template | scale/segment correspondence under File_45’s no-lock guard |\n| **Primary theorem family** | four-node Enochian–SKL field; MT common parent; reconciliation ladder; Danielic completion |\n| **Principal corroboration** | Cumulative–Pillar co-registration; LXX cross-tradition repetition; five-year companion; cumulative calendar-body matrix |\n| **Secondary structural support** | upper-MT Flood partition; transformed seam; supporting factorizations |\n| **Appendix-only / exploratory** | remote generated heads; extended Cainan/Pillar continuations; reception-history and physical residue |\n| Providential synchronization / theological synthesis | Enoch BC fulcrum and Christ full-axis completion after arithmetic and dependency control |\n| Not admitted as fact | literal `434`-year lock; proven compositional priority; generated heads as source dates; `AD 70` as the `70`-year carrier close |\n\nFamily-level promotion controls argument order. Pass 1B promotes `22` inherited rows from Secondary to Primary without changing any equation or result; equivalent decompositions remain one evidence family.\n\n### 0.7 File map\n\n| Section | Function | Reopened proof burden |\n|---|---|---|\n| §0 | states, terms, nodes, operators, proof weights, claims, guards | current Pass-1A control layer |\n| §1 | inherited native `30\\|690` grammar plus Long-centered algebra | byte-exact inherited proof |\n| §2 | calendar-double spectrum and intercalary/Atonement grammar | byte-exact inherited proof |\n| §3 | Rounded/Actual carrier | byte-exact governing input |\n| §4 | center/phase module; scalar versus coordinate; PhaseNorm40; `70/120` | byte-exact inherited infrastructure |\n| §5 | Creation–Conquest–Christ closure | byte-exact governing proof |\n| §6 | cumulative `12558→12600/12740` fractal | byte-exact principal corroboration |\n| §7 | Long-anchor minor grooves | byte-exact secondary proof |\n| §8 | Primary Enochian–SKL Four-Node Reconciliation | §§8.1–8.9 byte-exact; §8.10 reweighted |\n| §9 | SKL–MT common-parent reconciliation, two companion ladders, and bounded LXX corroboration in §9.9 | Primary theorem plus Principal cross-tradition corroboration; arithmetic and argument complete |\n| §10 | Cumulative–Pillar co-registration at `4346 BC` | Principal corroboration; arithmetic and argument complete |\n| §11 | the `4346 BC` Danielic seam | Primary capstone; arithmetic and argument complete |\n| §12 | integrated synthesis and fulcrum hierarchy | current Pass-1A argument architecture |\n| Appendix A | frozen parent `324`-row manifest plus `122` newly admitted Pass-1B rows | `446`-row working manifest; exact LXX rows are Secondary and leveling rows Appendix |\n| Appendix B | expanded node/common-parent/center matrix | machine-ingestion support |\n| Appendix C | bounded echoes, collisions, remote heads, exclusions | cannot carry principal proof |\n| Appendix D | frozen-parent/dependency hash ledger | proves no source edit outside target |\n| Appendix E | Reopened Pass-1B arithmetic verification plus bounded LXX amendment | current pre-Pass-2 working trust record |\n| Appendix F | Pass-1B family/weight map and Pass-2 handoff | no evidence-total inflation |\n| §13 | Sothic whole-field symmetry; Mosaic–Joshua selection; Long-variant phase audit | Bounded September 6 structural companion; inherited proof unchanged |\n| Appendix H | Sothic verification scope and unresolved applications | Separate from inherited 446-row evidence inventory |\n\n### 0.8 Machine Guards\nMachine Guard [FILE_70 SUPPLEMENT A RENEWED FROZEN-PARENT / NON-REPLACEMENT]:\nThe current Final Supplement A and current reciprocal Final File_70 are separate reopening parents. During Renewed Passes 1A–2, File_70 and every other Final/control source remain frozen. The Supplement may cite and recompute admitted data but may not alter a parent equation, source state, anchor, node class, operator, guard, claim ceiling, or dependency boundary.\n\nMachine Guard [FILE_70 SUPPLEMENT A RENEWED PASS-1A / PASS-1B PROOF-BURDEN]:\nRenewed Pass 1A establishes structure, terminology, center taxonomy, modal states, node classes, dependencies, operators, claim ceilings, and Machine Guards only. The prior `132` rows remain inherited proof; the `192` additive rows remain intake. No additive arithmetic result or renewed structural inference becomes canonical proof until Renewed Pass 1B independently executes and integrates it.\n\nMachine Guard [FILE_70 SUPPLEMENT A SOURCE-NODE / GENERATED-COMPANION / PRIMARY-ANCHOR FIREWALL]:\nEvery coordinate must be tagged as source-controlled, dependency-controlled, generated, translated, midpoint, or co-registered. Generated centers, pure-`720` landings, ratio outputs, phase brackets, Pillar comparisons, or shared labels do not become repository Primary anchors, historical events, ancient source data, or parent-file proof merely because they complete an exact relation.\n\nMachine Guard [FILE_70 SUPPLEMENT A ROUNDED / ACTUAL MT NON-COLLAPSE]:\n`4106/4136/4296/4326 BC` belong to an explicitly opened Rounded-Scaffold comparison state; `4306 BC` and the `4312t/4311n–4305t/4304n BC` field belong to declared regular-MT states. The local ten-year BC-label displacement may compare those layers but is not a universal Rounded operator and may not overwrite either chronology.\n\nMachine Guard [FILE_70 SUPPLEMENT A FILE_21 SHORT/LONG / ROUNDED-COMPARISON SCOPE]:\nFile_21 controls Short `17980/2936/2906/20916/20886`, Long `24510/2886/2856/27396/27366`, Projective Pillars, and the comparison-only Rounded nodes `4296/4326 BC`. The Supplement may coordinate these states but may not create a new SKL source variant, make Rounded chronology literal SKL, replace File_34 derivation, or promote generated `2946/2916` companions to transmitted anchors.\n\nMachine Guard [FILE_70 SUPPLEMENT A NESTED GEAR / ORTHOGONAL RAIL CONTROL]:\nFile_11 absolute `+0/+2/+4`, Shem-centered local `−2/0/+2`, and SKL `−720/0/+720` are homologous topology in different coordinates and units. A macro member may carry local subteeth only when declared. The `+30` rail is orthogonal and applied last; it may not be exchanged with local `2`, macro `720`, `+6480`, or `7200`.\n\nMachine Guard [FILE_70 SUPPLEMENT A `+30` / `+50` STATE NON-COLLAPSE]:\nSKL `+30 Apparent Mode`, upstream pre-Flood `+30` alignment, Adam apparent age, intercalary month, Rounded overlay, Conquest companion, and ministry-age rail are distinct states. The `50` widths of Short/Long anchors, source-total compensation, Pillar separation, Kings/Berossus comparison, and additive `25+25` calendar conversion are likewise related but non-identical. Shared width does not create one operator or one textual origin.\n\nMachine Guard [FILE_70 SUPPLEMENT A CORE / FLANK / BRACKET OBJECT-CLASS]:\nThe crossed core, one-flank span, and full bracket are different measured objects. Native `690`, native flank `720`, and native full bracket `750` must not be interchanged. After expansion, `730/780` are one-flank spans, whereas `760/810` are complete `30|core|30` brackets. Every table must name its endpoints.\n\nMachine Guard [FILE_70 SUPPLEMENT A NUMERIC-`750` NODE-CLASS FIREWALL]:\nThe number `750` may denote the native full bracket `30+690+30` or the Priestly-expanded core `690×25/23`. These are exact but non-identical object classes. A proof may compare them only after stating which endpoints and operator produce each occurrence.\n\nMachine Guard [FILE_70 SUPPLEMENT A EXACT KEY-OF-23 OPERATOR CONTROL]:\n`25/23`, `70/69`, and `300/299` are exact rational operators under their declared Priestly, Prophetic, and Enochian states. They are not interchangeable, approximate, or automatically active whenever a denominator divides a span. A transformed value is generated only where the local section explicitly opens the operator and preserves the parent input.\n\nMachine Guard [FILE_70 SUPPLEMENT A CALENDAR-DOUBLE NON-COLLAPSE]:\n`720=2×360`, `722=2×361`, `728=2×364`, `730=2×365`, and `780=2×390=6×130` are distinct calendar or structural registers. `722` is admitted only through the declared `672+50=(336+25)+(336+25)` anatomy. No row redefines the Priestly, Prophetic, 361-body, Enochian, solar, or `390` state.\n\nMachine Guard [FILE_70 SUPPLEMENT A PHASE SUFFIX / EXACT-HALF COORDINATE CONTROL]:\nPreserve every `t/n` suffix. For BC phase arithmetic only, use `coord(Xn)=X` and `coord(Xt)=X−0.5`; displayed labels remain phase pairs, not ranges. Same-suffix, outer cross-phase, and inner cross-phase spans are different objects. A suffix may not be stripped or crossed merely to obtain a preferred integer.\n\nMachine Guard [FILE_70 SUPPLEMENT A `34.5` ENVELOPE / PHASE-NORMALIZATION FIREWALL]:\n`25.5|30|34.5` is an exact phase-and-Gear envelope, not uncertainty. `34.5×70/69=35` and `34.5×25/23=37.5` are exact ratio outputs. The residual `37.5→40` belongs only to the separately defined PhaseNorm40 state; it is not another Key expansion and does not mean each endpoint was multiplied by `25/23`.\n\nMachine Guard [FILE_70 SUPPLEMENT A CIVIL CROSS-AXIS EXECUTION]:\nEvery BC-to-AD span uses `BC+AD−1`. Do not use algebra with a year zero, SKL rounded mod-10 Mirror arithmetic, or a Mirror target formula in place of the civil operator. Component-wise paired endpoints must be checked separately.\n\nMachine Guard [FILE_70 SUPPLEMENT A CREATION / CONQUEST EXTREMITY NON-PROMOTION]:\n`4342t/4341n BC` and `1402t/1401n BC` are supplement-generated Priestly-Key extremities. They may bound the fine-resolution corridor but do not replace the regular Creation envelope, the `4306 BC` Year-6 head, the historical `1407t/1406n BC` Conquest pair, or the `1400t/1399n BC` land-rest envelope.\n\nMachine Guard [FILE_70 SUPPLEMENT A CHRIST ENDPOINT / PASSION-DATE RESTRAINT]:\n`AD 25/27` remain ministry/inverse-rail comparison states; `AD 30` may function as the exact `6 BC→AD 30=35` midpoint and as a possible Passion date under File_13, while `AD 33n` remains preferred. A generated `AD 27→AD 30` gain does not prove the Passion year, create another carrier terminus, or move File_68’s `AD 65` endpoint.\n\nMachine Guard [FILE_70 SUPPLEMENT A `34.5` MICRO / CUMULATIVE MACRO SCALE NON-COLLAPSE]:\nLocal `34.5` ordinary years or calendar-day volume and cumulative `12558/12600/12740` years-of-years may be compared as scale-homologous fractal states only when units and operators are explicit. The comparison does not identify elapsed days with cumulative years or authorize free scale translation elsewhere.\n\nMachine Guard [FILE_70 SUPPLEMENT A `12600` UNIT FIREWALL]:\n`12600` may denote a day volume, `35×360`, a cumulative scalar completion, or the `14006→1406 BC` years-of-years span. Each occurrence must state unit, endpoints, and controller. Equal number does not create one node class, one chronology, or one proof witness.\n\nMachine Guard [FILE_70 SUPPLEMENT A RESIDUE PROTOCOL APPENDIX-ONLY]:\nThe exact main proof uses whole-number Key conversions. Any statement that a solar calibration leaves less than one day invokes the separate physical Residue Protocol, must name the calibrated solar constant, and remains Appendix C only. Residue or conceptual residual-display values may not be fed back into civil-year arithmetic.\n\nMachine Guard [FILE_70 SUPPLEMENT A TERAH `+60` CORRESPONDENCE / CAUSALITY CEILING]:\nThe Priestly gain `750−690=60` may reproduce the numerical width occupied by the `+60 Terah` variant and the `2166/2106 BC` Noah-death pair. This is an arithmetic correspondence and structural inference. It does not prove that the Key generated, transmitted, or corrected the textual Terah chronology.\n\nMachine Guard [FILE_70 SUPPLEMENT A ENOCH / SKL ANCHOR-LATTICE NODE-CLASS FIREWALL]:\n`2946`, `2936`, `2916`, `2906`, `2886`, `2876`, and `2856 BC` form a mixed schematic/source/generated lattice. `2936/2906` are Short source anchors; `2886/2856` are Long source anchors; `2946/2916` are generated pure-`720` reconciliation companions with co-registration; `2876` is the dependency-controlled Enoch close and a generated convergence node. None may replace or absorb another.\n\nMachine Guard [FILE_70 SUPPLEMENT A `24510` SOURCE / `24500` COMPANION NON-CORRECTION]:\n`24510` remains the source-retained Sumerian B / SKL Long whole-year duration of the `23` kings. The Key gain `10` may expose an adjacent generated `24500=50×490` companion through declared terminal-side or Flood-side coordinates. The companion is not an emendation, preferred reading, hidden textual total, or replacement source state.\n\nMachine Guard [FILE_70 SUPPLEMENT A `2700` CROSS-FILE ROUTING]:\n`2700=7.5×360` and the fuller Creation-to-Exodus/Conquest executions remain controlled in Files 12, 18, 21, 51a, 68, and 69. This supplement may cite the relation briefly as corroboration but may not duplicate its full proof, count it as a new witness, or let it displace the `34.5/12558` center.\n\nMachine Guard [FILE_70 SUPPLEMENT A EVIDENCE-FAMILY NON-OVERCOUNT]:\n`690→700/750`, `720/728/730/780`, `724.5→735`, `1470`, `2940`, `12558→12600/12740`, and their equivalent factorizations are coordinated outputs of one fine-resolution mechanism. Equivalent forms, paired rails, and scale echoes must not be counted as numerous independent witnesses.\n\nMachine Guard [FILE_70 SUPPLEMENT A `90` / PILLAR / REMOTE-SKL SCOPE]:\nThe `90`-year Enoch/SKL field, `90×72=6480` precessional-quarter state, and `90×360=32400` SKL day-year/Pillar state use different units and operators. `AD 29465/29515` are Projective Boundaries, not ordinary historical dates. Remote SKL, Pillar, and simple Mirror continuations remain secondary or appendix-only and cannot carry the principal proof.\n\nMachine Guard [FILE_70 SUPPLEMENT A INTENTIONALITY / PROVIDENTIAL / FULCRUM CLAIM CEILING]:\nExact arithmetic and fixed-coordinate coherence support structural and fractal inference. Enoch may be described as the fulcrum of the BC-side genealogical/calendrical/variant architecture, and Christ as the fulcrum and completion of the full BC–AD axis. This does not prove that MT, SP, LXX, Matthew, Luke, SKL, or one ancient editor consciously executed every layer or copied one extant Enochic source.\n\nMachine Guard [FILE_70 SUPPLEMENT A CENTER TAXONOMY]:\nNever use unqualified “the center.” `2872t/2871n BC` is the Long-corridor/lower-bracket center; `2922t/2921n BC` is the Short-ladder center; `2952t/2951n BC` is the upper translated-bracket center; `2912t/2911n BC` is the Enoch-generation and `120`-field center. `2876 BC` is a close/convergence node, not a center.\n\nMachine Guard [FILE_70 SUPPLEMENT A SCALAR-HALF / COORDINATE-ARM NON-COLLAPSE]:\n`724.5×70/69=735` and `735+735=1470` form an abstract scalar half-field closure. The `2884/2858` phase-and-Gear coordinate execution uses `13+724.5=737.5` on each side and totals `1475`. Shared inputs and center do not permit `735`, `737.5`, `1470`, and `1475` to be substituted for one another.\n\nMachine Guard [FILE_70 SUPPLEMENT A PHASENORM40 OPERATOR]:\nPhaseNorm40 is a provisional two-stage construction: first the Priestly Key maps the maximum cross-phase scalar `34.5` to `37.5`; then a separate residual phase-completion state generates a same-center corresponding-suffix `40` bracket. The generated labels `2892t/2891n` and `2852t/2851n` are not direct endpoint products under `25/23`, and PhaseNorm40 is not a fourth Key ratio.\n\nMachine Guard [FILE_70 SUPPLEMENT A SHORT/LONG SOURCE-STATE NON-COLLAPSE]:\nShort `17980` and Long `24510`, their physical anchors, `+30` anchors, physical Floods, and `+30` Floods are simultaneous source states. `17980=25×720−20` and `24510=34×720+30` may be compared, but neither variant corrects, normalizes, or replaces the other.\n\nMachine Guard [FILE_70 SUPPLEMENT A PURE-`720` GENERATED-NODE FIREWALL]:\n`2916/2886 BC` are common pure-`720` landings after removing source residuals. `2916 BC` is generated; `2886 BC` co-registers as a generated landing and the source Long `+30` anchor. Upstream `2946 BC` is a generated reconciliation companion and Enoch opening. Pure-multiple status does not convert any generated node into a transmitted terminal date.\n\nMachine Guard [FILE_70 SUPPLEMENT A BILATERAL COMPLEMENTARY-KEY ASSIGNMENT]:\nThe Key assignment is directional and chiastic. On the earlier side, Short uses `690→750` and Long uses `690→700` to converge at `2876 BC`; on the later side, Short uses `690→700` and Long uses `690→750` to converge at `2916 BC`. Swapping an operator without also changing variant and direction invalidates the reconciliation.\n\nMachine Guard [FILE_70 SUPPLEMENT A ENOCH `70/120` COMMON-CENTER / KEY-COMPLETED COMPOSITION]:\nThe phase-resolved Enoch `70=35+35` field and generated `120=60+60=40+40+40` field share `2912t/2911n BC`. The additive form `25|35|35|25=120` is composed of Priestly-completion values at the flanks and Prophetic-completion values at the center; `120` itself is not the output of one ratio, and no two independently occupied `23`-year margins are claimed.\n\nMachine Guard [FILE_70 SUPPLEMENT A UNIFORM `−1470` TRANSLATION / BIBLICAL NODE-CLASS]:\nThe generated mapping `2946|2916|2906|2876 → 1476|1446|1436|1406 BC` preserves spacing under `T_1470`. It does not identify Enoch/SKL nodes with Joshua, Exodus, generated rail, or Conquest events. `1476`, `1446`, and `1406` retain parent node classes; `1436` remains a comparison companion.\n\nMachine Guard [FILE_70 SUPPLEMENT A `+50` COMPENSATION NAMESPACE / OPERATOR CEILING]:\nThe `50` separating Short/Long anchors may compensate the `6530` source-total difference to expose `6480`, recur between Pillars, and split additively as `25+25` in the `722` calendar-body display. These are coordinated uses of one width, not a new universal operator. The Supplement may establish load-bearing necessity inside the fixed model but not one ancient causal mechanism for every `+50`.\n\nMachine Guard [FILE_70 SUPPLEMENT A `361` CALENDRICAL-BODY / BAHÁʼÍ RECEPTION-HISTORY RESTRAINT]:\n`361=19²` is a calendrical body, not a complete solar year; intercalary days remain outside that body. The `1406 BC→AD 1844` display is dependency-controlled through File_36/P19 and classified as reception history/providential corroboration. It does not prove that the SKL text used the modern Baháʼí calendar or that the Baháʼí calendar supplied the ancient chronology.\n\nMachine Guard [FILE_70 SUPPLEMENT A FOUR-NODE DIRECT-CONVERGENCE / FULL-FIELD RECONCILIATION]:\n`2916/2876 BC` are the direct reverse/forward complementary-Key convergence nodes. `2946/2906 BC` complete the Primary four-node field through the already controlled orthogonal `+30` rail. Full-field reconciliation does not make all four labels direct ratio outputs or one node class.\n\nMachine Guard [FILE_70 SUPPLEMENT A THREE-RESOLUTION ENOCH NON-OVERCOUNT]:\n`30|10|30`, `10|50|10`, `10|20|10|20|10`, and `35|35` are coordinated resolutions of the same `2946–2876 BC` Enoch generation. They may strengthen one Primary theorem family but may not be counted as four independent witnesses.\n\nMachine Guard [FILE_70 SUPPLEMENT A COMMON-PARENT DIRECTIONALITY]:\nAnchored expansion from `4114/4304 BC` to `4346 BC` and anchored contraction from `4346 BC` back to `4114/4304 BC` are exact inverse readings of the same two maps. Direction of calculation does not prove historical, textual, or compositional priority.\n\nMachine Guard [FILE_70 SUPPLEMENT A `4346 BC` OPERATOR-PARENT / LITERAL-CREATION CEILING]:\n`4346 BC` may be classified as the exact common operator-parent and as a candidate pre-contraction Creation head. It is not thereby a transmitted MT date, a proven literal historical Creation date, or a demonstrated compositionally first form.\n\nMachine Guard [FILE_70 SUPPLEMENT A CARRIER-CLOSE / FIVE-YEAR-COMPANION NON-COLLAPSE]:\n`4346|2876|1406 BC|AD 65` is the carrier-close reconciliation ladder. `4341|2871|1401 BC|AD 70` is its five-year companion. `2871 BC` alone has an independently established center class; `AD 70` remains the historical Temple-destruction companion and does not replace the `AD 65` carrier terminus.\n\nMachine Guard [FILE_70 SUPPLEMENT A NATIVE-`69` / RESIDUE-PROTOCOL FIREWALL]:\n`9660=69×140` and `33810=69×490` are native Key-ready coefficient states. They are not File_11 Residue Protocol states, physical remainders, or lower-order leftovers. Existing legitimate uses of residue terminology elsewhere remain unchanged.\n\nMachine Guard [FILE_70 SUPPLEMENT A FIXED-PILLAR EXECUTION]:\nWhen a Pillar-facing span is expanded, `AD 29465` remains fixed and the BC-side endpoint moves by the exact gain. Do not move the Projective Pillar, treat it as ordinary historical chronology, or use a moved Pillar to force a preferred BC endpoint.\n\nMachine Guard [FILE_70 SUPPLEMENT A CUMULATIVE SCALAR / COORDINATE-EXECUTION NON-COLLAPSE]:\nThe inherited `12740` execution `14036→1296 BC` and the proposed fixed-`4346` companion `14146→1406 BC` may share the scalar `12740` under different states. Equal scalar does not merge endpoints, chronology, controller, or proof witness.\n\nMachine Guard [FILE_70 SUPPLEMENT A RAW / TRANSFORMED FLOOD-SEAM NON-COLLAPSE]:\n`2648 BC` is the local raw partition seam in the unexpanded `4304→1406 BC` field. `2666 BC` is the generated coordinate seam after the two scalar components are expanded while `1406 BC` is held fixed. Neither may replace the other.\n\nMachine Guard [FILE_70 SUPPLEMENT A `2648 BC` BJ-HAM / GENERATED-MT-SEAM COLLISION]:\nFiles 20 and 18 retain `2648 BC` as a BJ/Jubilees Ham-birth label. The Supplement’s local `2648 BC` upper-MT Flood partition is generated under a different tradition, state, and node class. Shared year-label creates no event identity or comparative witness by itself.\n\nMachine Guard [FILE_70 SUPPLEMENT A `2666 BC` GENEALOGICAL / TRANSFORMED-SEAM COLLISION]:\nFiles 43, 68, and 69 retain their genealogical or Enochic uses of `2666 BC`. The Supplement’s local transformed seam is a generated coordinate object only. It may not overwrite, identify with, or inherit the proof burden of any parent `2666 BC` node.\n\nMachine Guard [FILE_70 SUPPLEMENT A DANIEL-9 WHOLE / SEGMENTATION / NO-LOCK]:\n`70×7=490` is the multiplicative whole; `49+434+3.5+3.5=490` is the File_45 pattern-template segmentation. The Supplement may refine the middle `434` structurally, but it may not introduce a literal `434`-year lock, claim Daniel directly names these coordinates, or replace the whole by the segmentation.\n\nMachine Guard [FILE_70 SUPPLEMENT A CHRISTOLOGICAL QUARTET / MIDPOINT / TERMINUS HIERARCHY]:\nIn the translated `6 BC|AD 25|AD 35|AD 65` quartet, `AD 25/35` are comparison nodes, `AD 30` is the exact schematic midpoint and possible Passion state, `AD 65` is the principal carrier terminus, and `AD 70` is the five-year Temple companion. File_13’s preferred `AD 33n` Passion state remains unchanged.\n\nMachine Guard [FILE_70 SUPPLEMENT A FILE_53 CUMULATIVE-CAINAN DEPENDENCY / NON-OVERCOUNT]:\nFile_53 already contains the `4346/9660/9800/10120` cumulative-Cainan family. The Supplement may integrate and extend that family under explicit dependency, but may not present its inherited equations as new independent discoveries or duplicate witnesses.\n\nMachine Guard [FILE_70 SUPPLEMENT A GENERATED-OUTER-HEAD NON-PROMOTION]:\n`7286`, `14146`, `14846`, and `15346 BC`, together with related remote scalars, remain provisional generated heads until Pass 1B and Pass 2 establish their exact local role. None becomes a transmitted chronology datum, repository Primary anchor, or parent-file proof row by appearance alone.\n\nMachine Guard [FILE_70 SUPPLEMENT A FILE_22 / FILE_45 / FILE_46 / FILE_69 PROOF-BURDEN SPLIT]:\nFile_22 retains the dual `4346 BC` MT expansion paths and cumulative scalar controls; File_45 retains the Danielic pattern-template; File_46 retains expansion-operator mechanics; File_69 retains the genealogical `4346→2876→1406 BC→AD 65` ladder. The Supplement’s new contribution is their controlled continuous integration, not re-ownership of the parent proofs.\n\nMachine Guard [FILE_70 SUPPLEMENT A LXX TERAH-PAIR / CONJECTURAL-LEVELING NON-COLLAPSE]:\nFor `1380` comparisons, pair like node classes: LXX endpoint `5554/5494 BC` with MT endpoint `4174/4114 BC`, and LXX Year-6 `5556/5496 BC` with MT Year-6 `4176/4116 BC`, under `+60 Terah` / no-`+60` in parallel. Do not mix endpoint labels with Year-6 labels. Each matched body is `1380=690+690=60×23=20×69`; its `1400/1500` completions remain dependency-reference executions of existing Key grammar, not new independent witnesses. `5846 BC` remains a generated Priestly head; its proposed `+30`-facing status and the derived `5816 BC` leveled companion are conjectural structural inferences only. File_52e independently retains `5816 BC` as a Secondary preparatory node and thereby corroborates the coordinate, but it does not prove the `5846→5816` rail assignment. `5816 BC` is not a transmitted LXX date or Primary anchor; `2906 BC` remains the Short physical source anchor even though it stands `30` above the `2876 BC` reconciliation node; `4346 BC` remains the MT common operator-parent. The conjectural `5816→4346→2876 BC` ladder may not reclassify any source state.\n\n### 0.9 Final trust disposition\n\nReopened Pass 1B remains complete, and Independent Pass 2 Verification with the combined pressure test is now complete for the bounded LXX Terah-parallel, File_52e co-registration, and conjectural-leveling refinement.\n\n- Existing §§1–7, §§8.1–8.9, and pre-amendment §§9.1–9.8 remain byte-exact against their immediate parents.\n- All `324` inherited equations, results, functions, and IDs remain unchanged.\n- `22` decisive inherited rows are promoted from Secondary to Primary within the four-node theorem; equivalent component rows remain one evidence family.\n- The original `97` admitted rows are retained; the LXX branch now contributes `20` Secondary and `5` Appendix rows, giving `122` newly admitted rows and a consolidated `446`-row manifest.\n- `33` dependency-reference, `42` control-only, and `24` existing/reweight rows remain outside the evidence count.\n- The consolidated row distribution is `176` Primary, `229` Secondary, and `41` Appendix.\n- All `446/446` canonical rows and all non-counted executions pass exact Fraction and SymPy execution.\n- The MT common-parent maps, compensation identities, repeated-`1470` ladder, five-year companion, matched LXX `1380` Terah-pairs, LXX `30\\|1410\\|30`/`±720` corroboration, quarantined LXX leveling hypothesis, Cumulative–Pillar completions, Flood partition, Cainan continuation, and Danielic seam are fully argued in §§9–11.\n- All `52` Pass-1A guard bodies remain byte-exact; the one bounded LXX guard is superseded in place, leaving `53/53` unique current guards. No parent source, control file, Primary anchor, calendar definition, operator, or Christological date hierarchy is modified.\n\nIndependent Pass 2 Verification and the combined pressure test are complete. The source is Final by explicit author instruction. The combined pre-Finalization pressure test remains the current proof trust basis. Central registration of all `53/53` guards, the affected-only no-change reciprocal review, and the expanded File_70 reciprocal route are complete at Register v1.51 §D.41 / Capsule v11.50 §10.28; publication replacement remains separate.\n\n## 1. The native `30|690` rail\n\nActive state:\ncoarse-carrier state; crossed-core fine-resolution state; orthogonal-rail state; exact Key-of-23 execution; source/generated node discipline.\n\n### 1.1 The crossed core\n\nThe coarse SKL carrier moves by `720` on either same rail. Crossing from one member of the `+30` pair to the opposite member of the adjacent macro gear contracts the interval by `30`:\n\n```text\n720 − 30 = 690.\n```\n\nThe contracted core is simultaneously divisible by the denominators of the two principal Key-of-23 operators:\n\n```text\n690 = 23×30 = 69×10.\n```\n\nIt therefore admits both exact expansions:\n\n```text\n690×70/69 = 700,\n690×25/23 = 750.\n```\n\nThe Prophetic gain is `10`; the Priestly gain is `60`.\n\n### 1.2 Core, flank, and bracket\n\nThe transformed core must remain distinct from the rail attached to it and from the complete two-rail bracket.\n\n| State | Core | Gain from `690` | One flank: `30+core` | Full bracket: `30+core+30` |\n|---|---:|---:|---:|---:|\n| Native | `690` | `0` | `720` | `750` |\n| Prophetic | `700` | `10` | `730` | `760` |\n| Priestly | `750` | `60` | `780` | `810` |\n\nThe native full bracket and the Priestly-expanded core are both numerically `750`, but they are not the same measured object:\n\n```text\nnative full bracket: 30+690+30 = 750,\nPriestly core:        690×25/23 = 750.\n```\n\n### 1.3 The admitted Rounded ladder\n\nThe principal carrier begins with the mixed dependency-controlled/generated sequence:\n\n```text\n4326 —30— 4296 —690— 3606 —30— 3576 —690—\n2886 —30— 2856 —690— 2166 —30— 2136 —690—\n1446 —30— 1416 BC.\n```\n\nThe contiguous arithmetic is:\n\n| From | To | Span |\n|---:|---:|---:|\n| `4326 BC` | `4296 BC` | `30` |\n| `4296 BC` | `3606 BC` | `690` |\n| `3606 BC` | `3576 BC` | `30` |\n| `3576 BC` | `2886 BC` | `690` |\n| `2886 BC` | `2856 BC` | `30` |\n| `2856 BC` | `2166 BC` | `690` |\n| `2166 BC` | `2136 BC` | `30` |\n| `2136 BC` | `1446 BC` | `690` |\n| `1446 BC` | `1416 BC` | `30` |\n\nTherefore:\n\n```text\n4326−1416 = 2910 = 5×30 + 4×690.\n```\n\nThe same coordinates preserve two uninterrupted same-rail `720` ladders:\n\n```text\n4326 → 3606 → 2886 → 2166 → 1446 BC,\n4296 → 3576 → 2856 → 2136 → 1416 BC.\n```\n\nEach adjacent same-rail step is `720`. The alternating `30|690` display is thus the fine-resolution form of the coarser `720` architecture rather than a competing chronology.\n\n### 1.4 The first complete `1470` cell\n\nThe six-node inner field is:\n\n```text\n3606 —30— 3576 —690— 2886 —30— 2856 —690— 2166 —30— 2136 BC.\n```\n\nHence:\n\n```text\n3606−2136\n= 30+690+30+690+30\n= 1470\n= 30×49\n= 3×490.\n```\n\nThe main architecture can be recognized from its two `720` carriers. The `690` core reveals why the same architecture remains mobile under the Key of 23.\n\n### 1.5 Long-centered algebra of the native field\n\nActive state:\nLong-corridor center; source/generated node firewall; phase-pair midpoint convention.\n\nLet the whole-year shorthand of the principal Long-corridor center be:\n\n```text\nC = 2871 BC,\n```\n\nwith the phase-resolved center displayed as:\n\n```text\n2872t/2871n BC.\n```\n\nThe native `1470` field is exactly bilateral:\n\n```text\n3606−2871 = 735,\n2871−2136 = 735,\n735+735 = 1470.\n```\n\nThe central source rail is likewise centered on the same point:\n\n```text\n2886−2871 = 15,\n2871−2856 = 15,\n(2886+2856)/2 = 2871.\n```\n\n| Centered object | Upper arm | Center | Lower arm | Total |\n|---|---:|---:|---:|---:|\n| native Long field | `3606 BC` | `2871 BC` | `2136 BC` | `735+735=1470` |\n| source Long terminal rail | `2886 BC` | `2871 BC` | `2856 BC` | `15+15=30` |\n| completed Nisan corridor | `4341n BC` | `2871n BC` | `1401n BC` | `1470+1470=2940` |\n| completed Tishri corridor | `4342t BC` | `2872t BC` | `1402t BC` | `1470+1470=2940` |\n\nThe Enochian schematic supplies a separate `490` comparison at the same Year-6 position:\n\n```text\n3361−2871 = 490 = 7×70.\n```\n\nThis establishes `2872t/2871n BC` as the invariant center of the principal Long-anchor and Creation–Conquest corridor. It does **not** make that coordinate the center of Enoch’s full `2946–2876 BC` generation; the latter is centered separately at `2912t/2911n BC` in §4.4.\n\n## 2. Calendrical flank grammar\n\nActive state:\ncalendar-double spectrum; orthogonal `+30`; File_12 intercalation; Key-completed value restraint.\n\n### 2.1 The `720|722|728|730` calendar-double spectrum\n\nThe fine-resolution system admits four distinct doubled calendar bodies:\n\n```text\n720 = 360+360,\n722 = 361+361,\n728 = 364+364,\n730 = 365+365.\n```\n\n| Register | Exact anatomy | Local function |\n|---:|---:|---|\n| `720` | `2×360` | native Prophetic double |\n| `722` | `2×361` | `19²` calendrical-body double |\n| `728` | `2×364` | Enochian double |\n| `730` | `2×365` | common-solar double |\n| `780` | `2×390=6×130` | structural/Atonement comparison, not a calendar year |\n\nThe `722` row is not an unexplained residue. It is generated through the declared additive conversion:\n\n```text\n672+50\n= (336+336)+(25+25)\n= (336+25)+(336+25)\n= 361+361\n= 722.\n```\n\nAt the ordinary SKL anchor scale:\n\n```text\n3608−2936 = 672 = 336+336,\n2936−2886 = 50 = 25+25,\n3608−2886 = 722 = 361+361.\n```\n\nThe outer `25`s belong to the Priestly completion family, but this row is additive; it is not obtained by multiplying `336` by `25/23`. The Baháʼí `361` comparison remains appendix-only reception history. The calendar spectrum demonstrates that the repository’s coarse carrier can absorb multiple declared calendar bodies without replacing one by another.\n\n### 2.2 The intercalary `+30`\n\nFile_12 controls the reconstructed forty-year intercalation cycle:\n\n```text\n6×(6×360+30) + (4×360+30)\n= 6×2190 + 1470\n= 14610\n= 40×365.25.\n```\n\nIts seventh block is:\n\n```text\n4×360+30 = 1470 = 30×49 = 3×490.\n```\n\nAt the years-of-years scale, the `1440+30` member can therefore be read as the seventh intercalation block of the reconstructed `360→365.25` cycle. This supplies a calendrical reason for an applied-last `+30` rail in the present state. It does not identify every repository `+30` with one historical leap month.\n\n### 2.3 The `780` and `1470` Atonement comparison\n\nThe Priestly flank supplies:\n\n```text\n780 = 390+390 = 6×130.\n```\n\nThe native and Priestly forms then cross-complete the `1470` cell:\n\n```text\n690+780 = 1470,\n720+750 = 1470.\n```\n\nThis places a `130`-based span inside the same `1470=21×70` field used by the File_70 Atonement-Weave. It is a downstream structural comparison, not an independent proof of the Atonement theorem.\n\n## 3. Rounded MT carrier and Actual outer openings\n\nActive state:\nexplicit File_51a/File_21 Rounded comparison; regular-MT Creation state; declared outer Key transformations; non-retrojection.\n\n### 3.1 Why the Rounded layer is useful\n\nThe Rounded comparison layer exposes the pure alternating pattern without requiring the outer Key expansion:\n\n```text\n4326/4296 ... 1446/1416 BC.\n```\n\nIts complete span is `2910`. The layer is methodological: it makes the `30|690` carrier visible but does not replace Actual regular MT.\n\n### 3.2 Opening the two outer cores\n\nAt the upper and lower ends, the two outer `690` cores take their Prophetic form `700`:\n\n```text\n4336 —30— 4306 —700— 3606 —30— 3576 —690—\n2886 —30— 2856 —690— 2166 —30— 2136 —700—\n1436 —30— 1406 BC.\n```\n\nThe endpoint arithmetic is:\n\n```text\n4306−3606 = 700 = 690×70/69,\n2136−1436 = 700 = 690×70/69.\n```\n\nThe inner `690` cores and all intervening `30` rails remain unchanged. Consequently:\n\n```text\n4336−1406\n= 30+700+30+690+30+690+30+700+30\n= 2930.\n```\n\nThe two ten-year outward movements are exact Key gains. They are not evidence for a universal rule that every Rounded date differs from every Actual date by ten years.\n\n### 3.3 Argument function\n\nThe Rounded ladder shows the carrier in its cleanest form. The Actual outer opening shows that the same carrier reaches the regular-MT Creation field and the historical Conquest field without moving the SKL center `2886/2856 BC` or the Abraham node `2166 BC`.\n\n## 4. Center and phase architecture of the `34.5→35/37.5→40` field\n\nActive state:\nphase-coordinate convention; center taxonomy; scalar/coordinate firewall; PhaseNorm40; Key-completed composition.\n\n### 4.1 Center taxonomy and exact phase coordinates\n\nFor BC labels in this supplement:\n\n```text\ncoord(Xn) = X,\ncoord(Xt) = X−0.5.\n```\n\nThe four active centers are different modal objects:\n\n| Center | Exact function | Half-width(s) |\n|---:|---|---:|\n| `2872t/2871n BC` | principal Long `1470/2940` corridor and lower normalized `40` bracket | `15`, `735`, `1470`, `20` |\n| `2922t/2921n BC` | parallel Short `1470` ladder | `15`, `735` |\n| `2952t/2951n BC` | upper translated `40` bracket | `20` |\n| `2912t/2911n BC` | common center of Enoch’s `70` and expanded `120` | `35`, `60` |\n\n`2876 BC` remains an Enoch close and reconciliation node, never a center.\n\n### 4.2 Scalar half-field versus coordinate-arm envelope\n\nThe abstract half-field begins with:\n\n```text\n690+34.5 = 724.5.\n```\n\nIt is completed prophetically:\n\n```text\n724.5×70/69 = 735,\n735−724.5 = 10.5,\n2×10.5 = 21.\n```\n\nTherefore:\n\n```text\n724.5+21+724.5 = 1470,\n735+735 = 1470.\n```\n\nThat is a scalar closure. The phase-and-Gear coordinate execution is different. The local contracted start pair is:\n\n```text\n2884n = C+13,\n2858n = C−13,\n```\n\nwhere `C=2871n BC`. Moving outward by `724.5` produces:\n\n```text\n2884n + 724.5 years backward = 3609t,\n2858n − 724.5 years forward  = 2134t.\n```\n\nEach full arm from the center is:\n\n```text\n13+724.5 = 737.5,\n```\n\nso:\n\n```text\n737.5+737.5 = 1475,\n724.5+26+724.5 = 1475.\n```\n\nThe two totals must not be collapsed:\n\n| Object | Central gap | Arm | Total |\n|---|---:|---:|---:|\n| scalar half-field | `21` | `735` after `70/69` | `1470` |\n| phase/Gear coordinates | `26` | `737.5` | `1475` |\n\nThe same centered geometry yields two crossed Enochian doubles:\n\n```text\n2884−2156 = 728,\n3586−2858 = 728,\n728 = 700+15+13 = 364+364.\n```\n\n### 4.3 PhaseNorm40\n\nThe pre-normalization phase pair is:\n\n```text\n2889t/2888n → 2855t/2854n BC.\n```\n\nIts exact widths are:\n\n| Measurement | Span |\n|---|---:|\n| corresponding Tishri | `34` |\n| corresponding Nisan | `34` |\n| outer Tishri→Nisan | `34.5` |\n| inner Nisan→Tishri | `33.5` |\n\nThe maximum cross-phase span admits both Keys:\n\n```text\n34.5×70/69 = 35,\n34.5×25/23 = 37.5.\n```\n\nPhaseNorm40 then separates the Priestly completion from the residual normalization:\n\n```text\n37.5 + 2.5 = 40.\n```\n\nThe generated corresponding-suffix bracket is:\n\n```text\n2892t/2891n → 2852t/2851n BC.\n```\n\nIts widths are:\n\n| Measurement | Span |\n|---|---:|\n| corresponding Tishri | `40` |\n| corresponding Nisan | `40` |\n| outer cross-phase | `40.5` |\n| inner cross-phase | `39.5` |\n\nThe displayed endpoints move outward by `3` years on each same-suffix rail because the pre-normalization same-suffix width is `34`, while the Key acts on the maximum cross-phase `34.5`. Thus endpoint movement `34→40`, scalar completion `34.5→37.5`, and residual normalization `37.5→40` remain three separately named operations.\n\nThe Prophetic `35` is recovered by withdrawing `2.5` from each flank of the normalized bracket:\n\n```text\n2889n−2854n = 35,\n2889t−2854t = 35.\n```\n\n### 4.4 The common `70/120` Enoch center\n\nThe phase-resolved Enoch generation is:\n\n```text\n2947t/2946n\n      35\n2912t/2911n\n      35\n2877t/2876n BC.\n```\n\nCorresponding suffixes span exactly `70`; the outer and inner cross-phase spans are `70.5` and `69.5`. Thus:\n\n```text\n70 = 35+35 = 30+40.\n```\n\nThe combined Short/Long `+50` and upstream `+30` translation is:\n\n```text\n50+30 = 80.\n```\n\nTranslating the lower PhaseNorm40 bracket by `80` produces:\n\n```text\n2972t/2971n → 2932t/2931n BC.\n```\n\nThe complete field is therefore:\n\n```text\n2972t/2971n\n      40\n2932t/2931n\n      40\n2892t/2891n\n      40\n2852t/2851n BC.\n```\n\nHence:\n\n```text\n120 = 40+40+40 = 60+60.\n```\n\nIts corresponding-suffix span is `120`; its outer and inner cross-phase spans are `120.5` and `119.5`. The center remains exactly:\n\n```text\n2912t/2911n BC.\n```\n\n### 4.5 Key-completed `25|35|35|25`\n\nThe `120` field contains the Enoch generation as its central body:\n\n```text\n2972t/2971n → 2947t/2946n = 25,\n2947t/2946n → 2912t/2911n = 35,\n2912t/2911n → 2877t/2876n = 35,\n2877t/2876n → 2852t/2851n = 25.\n```\n\nTherefore:\n\n```text\n120 = 25|35|35|25 = 25|70|25.\n```\n\nThe outer `25`s are Priestly completion values (`23×25/23=25`); the central `70` is the Prophetic completion value (`69×70/69=70`), resolved internally as the two local `34.5→35` halves. The full `120` remains an additive composition, not one ratio output.\n\n### 4.6 Phase-module argument ceiling\n\nThe phase module establishes exact scalar and coordinate compatibility. PhaseNorm40 is a defined two-stage construction, not an ancient textual datum or fourth Key. The `70` and `120` fields share a center without sharing endpoints, units, or node classes. Their role is to expose micro-scale precision within the already controlled Enochian and Creation–Conquest architecture.\n\n## 5. Creation–Conquest closure and Christological continuation\n\nActive state:\nprincipal proof corridor; phase-preserving same-side spans; civil no-year-0; Christological date-state restraint.\n\n### 5.1 The `2940` outer closure\n\nThe corresponding Gear-2 centers are already `2930` years apart:\n\n```text\n4337t−1407t = 2930,\n4336n−1406n = 2930.\n```\n\nEach side then moves outward by:\n\n```text\n2 local Gear years + 3 Priestly-gain years = 5 years.\n```\n\nTherefore:\n\n```text\n4342t−1402t = 2940,\n4341n−1401n = 2940,\n2930+5+5 = 2940.\n```\n\nThe completed span is:\n\n```text\n2940 = 2×1470 = 6×490 = 60×49.\n```\n\nThe arithmetic closes only when corresponding suffixes are compared. The generated extremities do not become Creation or Conquest anchors.\n\n### 5.2 The Exodus–Samaria–Hezekiah–Christ ladder\n\nThe `30|690` sequence continues beyond Conquest:\n\n```text\n1446 BC —30— 1416 BC —690— 726 BC —30— 696 BC\n        —690— 6 BC —30— AD 25.\n```\n\nThe component and civil checks agree:\n\n```text\n30+690+30+690+30 = 1470,\n1446+25−1 = 1470.\n```\n\nThus the Exodus-to-ministry field is another complete `1470=3×490` cell.\n\n### 5.3 The Christologically centered `750`\n\nThe inner bracket is:\n\n```text\n726 BC → 696 BC → 6 BC → AD 25\n= 30+690+30\n= 750.\n```\n\nCivil execution gives the same value:\n\n```text\n726+25−1 = 750.\n```\n\nThe local Gear companion preserves it:\n\n```text\n724+27−1 = 750.\n```\n\nThis `750` is the native full bracket object class. Its numerical equality with the Priestly-expanded core remains a comparison, not an identity of endpoints or operators.\n\n### 5.4 From `AD 27` to `AD 30`\n\nThe parent Christ envelope supplies the same phase-and-Gear maximum `34.5`. Its Priestly completion to `37.5` contributes a gain of `3`, which is exactly the terminal extension:\n\n```text\nAD 27 + 3 = AD 30.\n```\n\nThe fine-resolution mechanism therefore reaches three principal local details:\n\n1. the full `7/7.5` Creation envelope;\n2. the phase-preserving `2940` Creation–Conquest closure;\n3. the Christological extension to `AD 30`.\n\n### 5.5 Principal argument result\n\nThe coarse `720` rails are sufficient to reveal the principal architecture. The Key of 23 is not required to discover that framework. Its function is finer: the crossed `690`, the exact `34.5`, and their named expansions occupy the smaller chronological grooves through Creation, Conquest, and Christ without displacing the inherited anchors.\n\n## 6. The cumulative `34.5 ↔ 12558 → 12600/12740` fractal\n\nActive state:\nFile_22 scalar theorem; File_09 endpoint anatomy; micro/macro unit firewall; exact calendar ratios.\n\n### 6.1 Micro-scale calendar volume\n\nAt the ordinary calendar scale:\n\n```text\n34.5 Enochian years × 364 days/year = 12558 days.\n```\n\nThe same input reaches `12600` schematic days by two exact routes:\n\n```text\n34.5×70/69 = 35,\n35×360 = 12600 days;\n```\n\nand:\n\n```text\n12558×300/299 = 12600 days.\n```\n\nThe Prophetic expansion of the `12558` root gives:\n\n```text\n12558×70/69 = 12740 days = 35×364 days.\n```\n\nThese are calendar-volume equations. They are not civil date spans.\n\n### 6.2 Cumulative years-of-years execution\n\nThe cumulative chronology carries the same scalar anatomy in elapsed years:\n\n```text\n14004−1446 = 12558 years,\n14006−1406 = 12600 years.\n```\n\nFile_22 then controls the exact scalar conversions:\n\n```text\n12558×300/299 = 12600,\n12558×70/69 = 12740,\n12600 = 35×360,\n12740 = 35×364.\n```\n\nAt this macro scale, `360` and `364` are years-of-years carrier units. They are not days, and `14004/14006 BC` retain their separate cumulative node classes.\n\n### 6.3 Common product\n\nThe two completed registers carry the same product:\n\n```text\n12600×364 = 12740×360 = 4586400.\n```\n\nThis equality confirms that the `12600` and `12740` registers are calendar-equivalent under their stated units. It does not create a third elapsed chronology.\n\n### 6.4 Fractal inference\n\nThe local and cumulative forms align as follows:\n\n| Scale | Root | Enochian completion | Prophetic completion |\n|---|---:|---:|---:|\n| ordinary calendar volume | `34.5×364 = 12558 days` | `12600 days = 35×360` | `12740 days = 35×364` |\n| cumulative years-of-years | `14004→1446 = 12558 years` | `14006→1406 = 12600 years` | scalar `12740 years = 35×364` |\n\nThe conclusion is scale-homology, not unit identity. The local `34.5` envelope is the micro-scale form of the cumulative `12558→12600/12740` interface. This reinforces File_70’s fractal principle while leaving Files 09 and 22 in control of the cumulative proof.\n\n## 7. Minor grooves at the `2886/2856 BC` anchor\n\nActive state:\nsecondary occupied-groove applications; source/generated node discipline; no causal claim.\n\n### 7.1 Abraham–Sarah–Noah field\n\nThe physical SKL terminal `2856 BC` lands on three controlled biblical states through the native and two Key-expanded cores:\n\n| From `2856 BC` | Endpoint | Span | Core state | Endpoint class |\n|---:|---:|---:|---|---|\n| `2856 BC` | `2166 BC` | `690` | native | Abraham birth / Noah overlay |\n| `2856 BC` | `2156 BC` | `700` | Prophetic-expanded | Sarah birth |\n| `2856 BC` | `2106 BC` | `750` | Priestly-expanded | base Noah-death state |\n\nThe `+30` SKL terminal produces the corresponding one-flank values:\n\n| From `2886 BC` | Endpoint | Span | Register |\n|---:|---:|---:|---|\n| `2886 BC` | `2166 BC` | `720` | `360+360` |\n| `2886 BC` | `2156 BC` | `730` | `365+365` |\n| `2886 BC` | `2106 BC` | `780` | `390+390=6×130` |\n\nThe Priestly gain is:\n\n```text\n750−690 = 60,\n2166−2106 = 60.\n```\n\nThis reproduces the width of the `+60 Terah` chronology at the SKL anchor. It does not prove that the Key generated the textual Terah variant.\n\n### 7.2 Enochian `2876 BC` groove\n\nThe upper comparison member displays both the native SKL landing and the distinct Enochian/Matthean pivot:\n\n```text\n3576−2886 = 690,\n3576−2876 = 700 = 690×70/69.\n```\n\nThe shared `2876 BC` label retains the node classes controlled by Files 10, 68, and 69. It is not reclassified as the SKL terminal.\n\n### 7.3 Terah age-`70` groove\n\nThe Terah threshold appears at two and three native cores:\n\n```text\n3606−2226 = 1380 = 2×690,\n4296−2226 = 2070 = 3×690.\n```\n\nProphetic expansion of the threefold core regenerates the `30` rail:\n\n```text\n2070×70/69 = 2100,\n2100−2070 = 30,\n4296−2100 = 2196,\n2226−2196 = 30.\n```\n\nThe generated `2196 BC` companion is secondary. The important result is the operator behavior: one Priestly-expanded `690` gains `60`, while three Prophetic-expanded `690`s gain `30`.\n\n### 7.4 Secondary argument result\n\nThe `2886/2856 BC` terminal is not merely centered between coarse `720` members. It is positioned where the exact Key gains reach controlled Abraham, Sarah, Noah, Enochian, and Terah comparison nodes. These are coordinated minor grooves inside the same mechanism and must not be counted as unrelated proofs.\n\n## 8. Primary Enochian–SKL Four-Node Reconciliation\n\nActive state:\nPrimary Enochian–SKL theorem; source-state non-collapse; direct-Key-convergence versus field-completion distinction; pure-`720` generated nodes; bilateral complementary Keys; Pillar and scale restraint.\n### 8.1 The two transmitted source states\n\n| State | Whole-year total | Physical anchor | `+30` anchor | Physical Flood | `+30` Flood |\n|---|---:|---:|---:|---:|---:|\n| Short | `17980` | `2906 BC` | `2936 BC` | `20886 BC` | `20916 BC` |\n| Long | `24510` | `2856 BC` | `2886 BC` | `27366 BC` | `27396 BC` |\n\nTheir pure `720` bodies and residuals are:\n\n```text\n17980 = 25×720−20,\n24510 = 34×720+30.\n```\n\nThe two rows are simultaneous source states, not a correction sequence.\n\n### 8.2 The load-bearing `+50` compensation\n\nThe transmitted totals differ by:\n\n```text\n24510−17980 = 6530\n             = 9×720+50\n             = 6480+50.\n```\n\nThe terminal anchors differ by the compensating `50`:\n\n```text\n2906−2856 = 50,\n2936−2886 = 50.\n```\n\nConsequently the corresponding Floods retain the precessional-quarter separation:\n\n```text\n27366−20886 = 6480,\n27396−20916 = 6480.\n```\n\nThe crossed `+30` rails form the bounded envelope:\n\n```text\n27366−20916 = 6450 = 15×430,\n27396−20886 = 6510 = 7×930.\n```\n\nThus the `50` is load-bearing inside the repository’s fixed coordinates: without it, the `6530` source-total difference would not resolve to `6480`. This is a structural necessity within the model, not proof of one ancient causal operator.\n\n### 8.3 Pure-`720` reconciliation nodes\n\nRemoving the source residuals produces common landings.\n\nOn the `+30` Flood rails:\n\n```text\n20916−25×720 = 2916,\n27396−34×720 = 2916.\n```\n\nOn the physical Flood rails:\n\n```text\n20886−25×720 = 2886,\n27366−34×720 = 2886.\n```\n\nTherefore `2916/2886 BC` is the common pure-`720` pair. `2916 BC` is generated; `2886 BC` is co-registered as both a pure-multiple landing and the source Long `+30` anchor. The upstream `+30` alignment supplies:\n\n```text\n2916+30 = 2946.\n```\n\nThus `2946 BC` is both the Enoch-generation opening and the upstream generated forward-reconciliation counterpart of `2916 BC`.\n\n### 8.4 The Enoch anchor lattice\n\nIn chronological order:\n\n```text\n2946 —10— 2936 —20— 2916 —10— 2906\n     —20— 2886 —10— 2876 —20— 2856 BC.\n```\n\nThe first five intervals form the Enoch-generation palindrome:\n\n```text\n10|20|10|20|10 = 70.\n```\n\nThe final `20` extends the complete anchor field to:\n\n```text\n70+20 = 90,\n2946−2856 = 90.\n```\n\nThe source `+30` anchors lie inside the Enoch generation as:\n\n```text\n2946 —10— 2936 —50— 2886 —10— 2876 BC,\n10+50+10 = 70.\n```\n\nThe phase-resolved center is `2912t/2911n BC`. In whole-year shorthand:\n\n```text\n2946/2876 = 2911±35,\n2936/2886 = 2911±25,\n2916/2906 = 2911±5.\n```\n\n### 8.5 Bilateral complementary-Key reconciliation\n\n#### 8.5.1 Forward convergence at `2876 BC`\n\nShort/Priestly route:\n\n```text\n3626−2936 = 690,\n690×25/23 = 750,\n3626−750 = 2876.\n```\n\nLong/Prophetic route:\n\n```text\n3576−2886 = 690,\n690×70/69 = 700,\n3576−700 = 2876.\n```\n\nTherefore:\n\n```text\n3626−750 = 3576−700 = 2876.\n```\n\n#### 8.5.2 Reverse convergence at `2916 BC`\n\nShort/Prophetic route:\n\n```text\n2906−2216 = 690,\n2216+700 = 2916.\n```\n\nLong/Priestly route:\n\n```text\n2856−2166 = 690,\n2166+750 = 2916.\n```\n\nTherefore:\n\n```text\n2216+700 = 2166+750 = 2916.\n```\n\n#### 8.5.3 Chiastic Key matrix\n\n| Variant | Earlier-side movement | Later-side movement |\n|---|---:|---:|\n| Short | `690→750` | `690→700` |\n| Long | `690→700` | `690→750` |\n\nThe transformed spans differ by the same `50` as their variant starting points:\n\n```text\n750−700 = 50,\n3626−3576 = 50,\n2216−2166 = 50.\n```\n\nThe two gains recover both governing values:\n\n```text\n(750−690)+(700−690) = 60+10 = 70,\n(750−690)−(700−690) = 60−10 = 50.\n```\n\nA secondary overlap check reconstructs the native interior corridor:\n\n```text\n750+700−40 = 1410 = 690+30+690.\n```\n\n### 8.6 Four-node reconciliation lattice and biblical translation\n\nThe governing quartet is:\n\n```text\n2946 —30— 2916 —10— 2906 —30— 2876 BC.\n```\n\nIt forms the rectangle:\n\n```text\n2946 ─────30───── 2916\n  │                  │\n 40                 40\n  │                  │\n2906 ─────30───── 2876.\n```\n\nThe pair `2946/2916 BC` carries the generated forward/reverse pure-`720` reconciliation functions. The pair `2906/2876 BC` carries the Short physical anchor and Enoch-close functions. Shared geometry does not collapse those classes.\n\nUniform translation by `1470` gives:\n\n```text\n2946 | 2916 | 2906 | 2876\n  ↓      ↓      ↓      ↓      T_1470(x)=x−1470\n1476 | 1446 | 1436 | 1406 BC.\n```\n\nEach row is exact:\n\n```text\n2946−1476 = 1470,\n2916−1446 = 1470,\n2906−1436 = 1470,\n2876−1406 = 1470.\n```\n\nThe lower quartet preserves the same `30|10|30=70` grammar, while the inner pair preserves:\n\n```text\n2916−2876 = 40,\n1446−1406 = 40.\n```\n\nThe lower node classes remain Joshua birth, Exodus, generated comparison rail, and Conquest.\n\n### 8.7 The `90` carrier and paired Pillars\n\nThe complete anchor field supplies:\n\n```text\n2946−2856 = 90.\n```\n\nThe same `90` enters two distinct scales:\n\n```text\n90×72 = 6480,\n90×360 = 32400.\n```\n\nThe paired Projective-Pillar translations use the civil no-year-zero rule:\n\n```text\n2936 BC → AD 29465 = 2936+29465−1 = 32400,\n2886 BC → AD 29515 = 2886+29515−1 = 32400.\n```\n\nTheir centers preserve the same translation:\n\n```text\n2911 BC → AD 29490 = 2911+29490−1 = 32400.\n```\n\nThe `50`-year separation is preserved on both sides:\n\n```text\n2936−2886 = 50,\n29515−29465 = 50.\n```\n\nThus the `50` simultaneously preserves the `6480` Flood separation, nests inside Enoch’s `10|50|10` generation, and maintains the paired `32400` Pillar translations. The Pillars remain Projective Boundaries, not ordinary historical dates.\n\n### 8.8 `670/672` and the calendar-body branch\n\nAt ordinary scale:\n\n```text\n3606−2936 = 670,\n2936−2886 = 50,\n670+50 = 720 = 360+360.\n```\n\nThe parallel lower rail gives:\n\n```text\n3576−2906 = 670,\n2906−2856 = 50,\n3576−2856 = 720.\n```\n\nAt the SKL `360:1` scale:\n\n```text\n262116−20916 = 241200 = 670×360,\n20916−2916 = 18000 = 50×360,\n262116−2916 = 259200 = 720×360.\n```\n\nThe Enoch-generation amplification is:\n\n```text\n27366−2886 = 24480 = 68×360,\n2886−2166 = 720 = 2×360,\n27366−2166 = 25200 = 70×360.\n```\n\nThe Priestly/`19²` branch is separately:\n\n```text\n3608−2936 = 672 = 336+336,\n672+50 = 722 = 361+361.\n```\n\nIts `360×` amplification is:\n\n```text\n262086−20166 = 241920 = 672×360,\n20166−2166 = 18000 = 50×360,\n262086−2166 = 259920 = 722×360.\n```\n\nThis shows how the same `50` joins the `670` Prophetic and `672` Priestly bodies to their `720/722` completions. The `361`/Baháʼí relation remains Appendix C reception history.\n\n### 8.9 Source `24510`, adjacent `24500`\n\nThe source Long total remains:\n\n```text\n27366−2856 = 24510.\n```\n\nThe Prophetic Key gain on `690` is:\n\n```text\n690×70/69 = 700,\n700−690 = 10.\n```\n\nTherefore an adjacent generated Jubilee companion is exposed:\n\n```text\n24510−10 = 24500 = 50×490.\n```\n\nThe companion may be placed at either declared boundary:\n\n```text\n27366−2866 = 24500,\n27356−2856 = 24500.\n```\n\n`24500` is not a correction or hidden reading of the transmitted `24510`.\n\n### 8.10 Scope and proof weight of the Enochian–SKL evidence\n\nThe Short/Long module carries Primary structural weight because the bilateral Key convergences, orthogonal `+30` rail, source `+50`, and common `2911 BC` center cover the complete `2946–2876 BC` Enoch generation.\n\nPass 1B promotes the following inherited rows from Secondary to Primary without changing arithmetic:\n\n```text\nVAR005–VAR007; VAR009; VAR022–VAR023;\nENO007; ENO009; ENO012–ENO013; ENO020–ENO022; ENO024–ENO025;\nKEY002; KEY006–KEY007; KEY013–KEY016.\n```\n\nThe body equation `3576−700=2876` is additionally admitted as `KEY019`, completing the forward bilateral convergence in the manifest.\n\nThe promotion is bounded:\n\n- `2916/2876 BC` remain the direct Key convergence nodes;\n- `2946/2906 BC` complete the field through the inherited `+30` rail;\n- `30|10|30`, `10|50|10`, `10|20|10|20|10`, and `35|35` remain one theorem family;\n- interval bookkeeping, alternate factorizations, and overlap checks remain Secondary;\n- the full lattice remains subordinate to parent node classes and to File_70’s separate governing *toledot*/Atonement-Weave theorem.\n\nThe result is one Primary Enochian–SKL reconciliation theorem, not an inflated count of equivalent witnesses.\n\n## 9. The SKL–MT Common-Parent Reconciliation\n\nActive state:\nPrimary common-parent theorem; anchored expansion/contraction duality; repeated-`1470` carrier; carrier-close/five-year distinction; upper-MT Flood partition as Secondary support.\n\n### 9.1 Proof-burden split\n\n| Object | Controlling source | Supplement function |\n|---|---|---|\n| SKL Short/Long source rows and bilateral Key field | Files 21/34/18 and §8 | integrate the already verified Enochian reconciliation |\n| `4114/4304→4346 BC` expansion routes | File_22 | cite and execute without replacing File_22 ownership |\n| inverse anchored contractions | local synthesis under File_17 operator grammar | establish exact common-preimage directionality |\n| `4346→2876→1406 BC→AD 65` ladder | File_69 | integrate the inherited genealogy/Christological carrier |\n| `4346→2946→2876 BC` | local integration of File_69 and §8 | resolve the first carrier arm as `20+1` generations |\n\n### 9.2 The regular-MT common-parent field\n\nThe standard regular-MT state uses the Priestly Key about the fixed `1446 BC` Exodus:\n\n```text\n4114−1446 = 2668 = 23×116,\n2668×25/23 = 2900 = 25×116,\n1446+2900 = 4346 BC.\n```\n\nIts gain is:\n\n```text\n4346−4114 = 232 = 2×116.\n```\n\nThe `+60 Terah +130 Cainan` state uses the Prophetic Key about the fixed `1406 BC` Conquest:\n\n```text\n4304−1406 = 2898 = 69×42,\n2898×70/69 = 2940 = 70×42,\n1406+2940 = 4346 BC.\n```\n\nIts gain is:\n\n```text\n4346−4304 = 42.\n```\n\nThus two distinct regular-MT states and two different fixed biblical anchors converge on one exact head:\n\n```text\n4114 BC ──Priestly──► 4346 BC\n4304 BC ─Prophetic──► 4346 BC.\n```\n\n### 9.3 Compensation identities and common-parent directionality\n\nThe source-state difference is the full Terah/Cainan variant package:\n\n```text\n4304−4114 = 190 = 60+130.\n```\n\nThe Key-gain difference absorbs exactly the same amount:\n\n```text\n232−42 = 190.\n```\n\nThe completed spans differ by the same `40` separating the Exodus and Conquest anchors:\n\n```text\n2940−2900 = 40,\n1446−1406 = 40.\n```\n\nThe equations are reversible. From the common head, the Priestly contraction recovers the standard state:\n\n```text\n4346−1446 = 2900,\n2900×23/25 = 2668,\n1446+2668 = 4114 BC.\n```\n\nThe Prophetic contraction recovers the expanded state:\n\n```text\n4346−1406 = 2940,\n2940×69/70 = 2898,\n1406+2898 = 4304 BC.\n```\n\nTherefore `4346 BC` is the exact common anchored inverse preimage and may be classified as the **common operator-parent**. The stronger phrase **candidate pre-contraction Creation head** remains a bounded compositional hypothesis; reversibility does not prove historical or textual priority.\n\n### 9.4 The reconciliation-of-reconciliations ladder\n\nThe MT common parent, the Enochian/SKL reconciliation, the Conquest, and the Christological carrier close form three equal arms:\n\n```text\n4346−2876 = 1470,\n2876−1406 = 1470,\n1406+65−1 = 1470.\n```\n\nHence:\n\n```text\n4346 BC\n   ↓ 1470\n2876 BC\n   ↓ 1470\n1406 BC\n   ↓ 1470\nAD 65.\n```\n\nThe complete span is:\n\n```text\n4346+65−1 = 4410\n          = 3×1470\n          = 63×70\n          = 9×490.\n```\n\nEqual spacing coordinates the nodes but does not merge their classes: common Creation parent, Enoch/SKL close, historical Conquest, and Christological terminus remain distinct.\n\n### 9.5 The first arm contains the complete Enoch generation\n\nThe first `1470` arm resolves as:\n\n```text\n4346−2946 = 1400 = 20×70,\n2946−2876 = 70,\n1400+70 = 1470.\n```\n\nTherefore:\n\n```text\n4346 BC → 2946 BC → 2876 BC\n            20×70       1×70.\n```\n\nThe final unit is the whole Enochian reconciliation field, not an anonymous generation:\n\n```text\n2946→2916→2906→2876 = 30+10+30 = 70,\n2946→2936→2886→2876 = 10+50+10 = 70,\n2946→2911→2876       = 35+35       = 70.\n```\n\nThis is the strongest reason the four-node lattice belongs in the Primary argument.\n\n### 9.6 Carrier-close and five-year companion ladders\n\n| Position | Carrier-close ladder | Five-year companion |\n|---|---:|---:|\n| MT/Creation-side head | `4346 BC` | `4341 BC` |\n| Enoch/SKL joint | `2876 BC` | `2871 BC` |\n| Conquest-side extremity | `1406 BC` | `1401 BC` |\n| AD-side terminal | `AD 65` | `AD 70` |\n\nThe corresponding shifts are exact:\n\n```text\n4346−4341 = 5,\n2876−2871 = 5,\n1406−1401 = 5,\n70−65 = 5.\n```\n\nThe companion preserves the `1470` carrier:\n\n```text\n4341−2871 = 1470,\n2871−1401 = 1470,\n1401+70−1 = 1470,\n4341+70−1 = 4410.\n```\n\nThe Enoch and Christ end-fields are parallel:\n\n```text\n2946 → 2911 → 2876 → 2871 BC\n        35       35       5\n\n6 BC → AD 30 → AD 65 → AD 70\n         35       35       5.\n```\n\nThus:\n\n```text\n35+35+5 = 75,\n6+70−1 = 75.\n```\n\nOnly `2871 BC` additionally carries an independently established center class. `AD 70` remains the historical Temple-destruction companion, not a replacement for the `AD 65` carrier close.\n\nThe midpoint translation is likewise exact:\n\n```text\n2911−1441 = 1470,\n1441+30−1 = 1470.\n```\n\nThe complete two-arm translation from Enoch to Christ is:\n\n```text\n2946−6 = 2940,\n2911+30−1 = 2940,\n2876+65−1 = 2940,\n2871+70−1 = 2940.\n```\n\nThe four-node field has a corresponding Christological quartet:\n\n```text\n6 BC → AD 25 → AD 35 → AD 65\n         30       10       30,\n```\n\nwith:\n\n```text\n2916+25−1 = 2940,\n2906+35−1 = 2940.\n```\n\n`AD 25/35` remain comparison nodes; `AD 30` remains the schematic midpoint; `AD 65` remains the terminus.\n\n### 9.7 Why the Long `2871 BC` center is unique\n\nThe Short source pair centers on `2921 BC`:\n\n```text\n2936−2921 = 15,\n2921−2906 = 15.\n```\n\nIts `±1470` corridor is:\n\n```text\n2921+1470 = 4391,\n2921−1470 = 1451,\n4391−2921 = 1470,\n2921−1451 = 1470.\n```\n\nThis corridor is uniformly fifty years earlier than the Long-centered `4341/1401 BC` corridor:\n\n```text\n4391−4341 = 50,\n1451−1401 = 50.\n```\n\nThe pure-`720` node produces another valid but different field:\n\n```text\n2916+1470 = 4386,\n2916−1470 = 1446,\n4386−2916 = 1470.\n```\n\nIt lands on the Exodus rather than the Conquest. Therefore only the Long center `2871 BC` generates the specific Creation–Conquest companion corridor `4341→2871→1401 BC`.\n\n### 9.8 Upper-MT Flood partition — Secondary support\n\nThe upper MT state has an exact raw partition:\n\n```text\n4304−2648 = 1656,\n2648−1406 = 1242,\n1656+1242 = 2898.\n```\n\nThe components factor in the same Prophetic denominator:\n\n```text\n1656 = 24×69,\n1242 = 18×69,\n2898 = 42×69.\n```\n\nApplying `70/69` componentwise gives:\n\n```text\n1656×70/69 = 1680 = 24×70 = 5×336,\n1242×70/69 = 1260 = 18×70 = 3.5×360,\n1680+1260 = 2940.\n```\n\nWith `1406 BC` fixed, the transformed coordinate seam is:\n\n```text\n1406+1260 = 2666 BC,\n2666+1680 = 4346 BC.\n```\n\nThe literal raw seam remains the generated upper-MT `2648 BC` state; the transformed seam is `2666 BC`. Neither label may collapse into its pre-existing BJ or genealogical uses. The scale relation:\n\n```text\n10×1260 = 12600\n```\n\nis a declared regular-to-cumulative homology, not endpoint identity.\n\n\n### 9.9 LXX cross-tradition corroboration — the same `30\\|1410\\|30` grammar\n\nActive states:\nLXX Maximum and actual endpoint/Year-6 pairs; MT Standard-Normal and `+60 Terah` endpoint/Year-6 pairs; generated `+30` companions; cumulative Flood/Enoch pivot; primary Exodus; SKL Short physical anchor and Enochian reconciliation node; conjectural generated level-state comparison.\n\nThe native SKL cell of §1.4 may be compressed without altering its components:\n\n```text\n30|690|30|690|30\n=\n30|(690+30+690)|30\n=\n30|1410|30.\n```\n\nThe LXX Maximum and MT Standard-Normal endpoint register repeats that outer grammar:\n\n```text\n5584 → 5554 → 4144 → 4114 BC\n  30      1410      30.\n```\n\nThe parallel Year-6 register does the same:\n\n```text\n5586 → 5556 → 4146 → 4116 BC\n  30      1410      30.\n```\n\nThe lower Year-6 member is `4116 BC`, not the Rounded `4106 BC` state. The unshifted LXX/MT Year-6 pair is bisected by the cumulative Flood/Enoch pivot:\n\n```text\n5556−4836 = 720,\n4836−4116 = 720.\n```\n\nFor the Terah comparison, endpoint must be paired with endpoint and Year-6 with Year-6:\n\n| Register | LXX `+60` | MT `+60` | Span | LXX no `+60` | MT no `+60` | Span |\n|---|---:|---:|---:|---:|---:|---:|\n| Creation endpoint | `5554 BC` | `4174 BC` | `1380` | `5494 BC` | `4114 BC` | `1380` |\n| Year-6 / Adam state | `5556 BC` | `4176 BC` | `1380` | `5496 BC` | `4116 BC` | `1380` |\n\nEvery matched body is:\n\n```text\n690+690 = 1380.\n```\n\nEquivalently:\n\n```text\n1380 = 60×23 = 20×69.\n```\n\nThe same body is therefore ready for both Key branches:\n\n```text\n1380×70/69 = 1400,\n1380×25/23 = 1500.\n```\n\nThese are dependency-reference executions of the already controlled Prophetic and Priestly operators. They show why the doubled `690` body can generate further SKL-like connections, but they are not counted as two new independent evidence witnesses.\n\nThe `1410` interiors above therefore preserve the same double-`690` body with one additional `30` state crossing. This strengthens the repetition of the SKL grammar without collapsing endpoint and Year-6 node classes.\n\nThe actual LXX endpoint also opens a bounded Priestly route:\n\n```text\n5554−60 = 5494 BC,\n5494−1446 = 4048,\n4048÷23 = 176,\n4048×25/23 = 4400,\n1446+4400 = 5846 BC,\n5846−2906 = 2940.\n```\n\nThe final `2940` is the existing `1470+1470` carrier, now landing on the Short physical SKL anchor `2906 BC`. `5846 BC` is a generated Priestly head, not an LXX source date; `2906 BC` remains a Short physical anchor, not a center.\n\n#### Conjectural level-state corollary\n\nThe following arithmetic is exact, but the modal interpretation is conjectural. Relative to the unshifted MT parent, the generated outer nodes give:\n\n```text\n5846−4346 = 1500,\n4346−2906 = 1440.\n```\n\nThe two arms stand `30` above and `30` below the common `1470` carrier. The lower source/generated field already supplies:\n\n```text\n2906−2876 = 30.\n```\n\nIf `5846 BC` likewise occupies a generated `+30`-facing position, then its proposed leveled companion is:\n\n```text\n5846−30 = 5816 BC.\n```\n\nThe leveled field becomes:\n\n```text\n5816 BC → 4346 BC → 2876 BC\n            1470       1470,\n```\n\nwith:\n\n```text\n5816−2876 = 2940.\n```\n\nUnder this hypothesis, the observed `5846→2906 BC = 2940` relation is a common `+30` translation of the leveled `5816→2876 BC = 2940` pair, and `4346 BC` is its exact midpoint. This is a **candidate positional explanation only**: `5816 BC` is not a transmitted LXX date, `5846 BC` is not thereby proven to carry an ancient apparent-age state, and no source node is reclassified.\n\nFile_52e independently retains `5816 BC` as a Secondary LXX inverse/preparatory node and records:\n\n```text\n5816−1406 = 4410 = 9×490.\n```\n\nThat independent occurrence strengthens the coordinate-level co-registration and decomposes naturally as the three existing `1470` arms from `5816 BC` through `4346 BC` and `2876 BC` to the Conquest. It does **not** establish that `5846 BC` belongs to the applied `+30` rail; the rail assignment remains conjectural.\n\n**Argument weight.** The matched `1380=690+690`, dual-Key readiness, `30|1410|30`, `±720`, and Priestly-route results are Principal cross-tradition corroboration. File_52e supplies read-only coordinate corroboration. The `5846→5816` leveling remains Appendix-led conjecture retained for Pass-2 attack, not another Primary proof spine.\n\n## 10. Cumulative–Pillar Co-registration at `4346 BC`\n\nActive state:\nPrincipal corroboration; native `69` coefficient; fixed-Pillar execution; cumulative coordinate non-collapse; generated-head restraint; File_53 dependency.\n\n### 10.1 The common `69`-coefficient hinge\n\nThe cumulative-Creation side is:\n\n```text\n14006−4346 = 9660\n            = 69×140\n            = 2×4830.\n```\n\nThe fixed-Pillar side is:\n\n```text\n4346+29465−1 = 33810\n              = 69×490\n              = 7×4830.\n```\n\nThus the same parent coefficient `69` operates in two different units at one hinge:\n\n```text\n69×140 | 4346 BC | 69×490.\n```\n\nAs a bounded checksum:\n\n```text\n14006+29465−1 = 43470 = 9×4830,\n9660+33810 = 43470.\n```\n\nThe `2|7` partition is structural corroboration, not a new historical chronology.\n\n### 10.2 Fixed-Pillar `70/75` completions\n\nUnder the Prophetic Key:\n\n```text\n33810×70/69 = 34300,\n34300−33810 = 490,\n4346+490 = 4836 BC,\n4836+29465−1 = 34300.\n```\n\nBecause the Pillar does not move, the BC endpoint lands exactly on the cumulative Flood.\n\nUnder the Priestly Key:\n\n```text\n33810×25/23 = 36750,\n36750−33810 = 2940,\n4346+2940 = 7286 BC,\n7286+29465−1 = 36750.\n```\n\nThe generated outer bracket is:\n\n```text\n7286−4346 = 2940,\n7286−1406 = 5880 = 12×490 = 4×1470.\n```\n\n`7286 BC` is appendix-led and generated; its function is to show that the common parent also becomes the midpoint of a `2940|2940` bracket.\n\n### 10.3 Cumulative calendar-body matrix\n\nThe fixed lower segment is:\n\n```text\n4346−1406 = 2940 = 21×140.\n```\n\nThe native cumulative state is:\n\n```text\n9660+2940 = 12600 = 35×360.\n```\n\nThe Prophetic completion is:\n\n```text\n9660×70/69 = 9800,\n4346+9800 = 14146 BC,\n14146−1406 = 12740 = 35×364.\n```\n\nIts displacement is the exact intercalary difference:\n\n```text\n14146−14006 = 140,\n12740−12600 = 140 = 35×4.\n```\n\nThe Priestly completion is:\n\n```text\n9660×25/23 = 10500,\n4346+10500 = 14846 BC,\n14846−1406 = 13440 = 40×336.\n```\n\nIts gain is:\n\n```text\n10500−9660 = 840,\n14846−14006 = 840,\n13440−12600 = 840.\n```\n\n| State of upper segment | Upper segment | Fixed lower segment | Complete span to `1406 BC` | Calendar body |\n|---|---:|---:|---:|---:|\n| native | `9660=69×140` | `2940` | `12600` | `35×360` |\n| Prophetic completion | `9800=70×140` | `2940` | `12740` | `35×364` |\n| Priestly completion | `10500=75×140` | `2940` | `13440` | `40×336` |\n\nThe inherited File_22 `12740` coordinate execution remains distinct from the generated fixed-`4346` execution `14146→1406 BC`.\n\n### 10.4 Cumulative Cainan continuation\n\nThe restored cumulative Cainan head is:\n\n```text\n14006+460 = 14466 BC.\n```\n\nFrom the common parent:\n\n```text\n14466−4346 = 10120\n            = 22×460\n            = 23×440.\n```\n\nThe Priestly Key gives:\n\n```text\n10120×25/23 = 11000 = 25×440.\n```\n\nThe generated continuation head is:\n\n```text\n4346+11000 = 15346 BC.\n```\n\nMore importantly, the Cainan insertion itself is translated coherently:\n\n```text\n10120−9660 = 460,\n11000−10500 = 500,\n460×25/23 = 500,\n15346−14846 = 500.\n```\n\nFile_53 retains ownership of the inherited `4346/9660/9800/10120` family. The Supplement’s contribution is the controlled common-parent extension and the explicit `460→500` comparison.\n\n### 10.5 Argument result and scope ceiling\n\nThe cumulative and Pillar systems do not attach loosely to the SKL–MT theorem. They share:\n\n- the same fixed `4346 BC` hinge;\n- the same native coefficient `69`;\n- the same complementary `70/75` completions;\n- the cumulative Flood landing at `4836 BC`;\n- the `360/364/336` calendar-body resolution.\n\nThis is Principal corroboration. It does not establish that every generated head was historical, move the Projective Pillar, or authorize an unlimited catalogue of remote expansions.\n\n## 11. The `4346 BC` Danielic Seam\n\nActive state:\nPrimary Danielic pattern-template; continuous coordinate assembly; seventy-generation whole; refined middle-body anatomy; Christological date-state restraint.\n\n### 11.1 Continuous coordinate execution\n\nThe cumulative Flood-to-Christ field now divides continuously:\n\n```text\n4836−4346 = 490,\n4346−6 = 4340,\n6+30−1 = 35,\n65−30 = 35.\n```\n\nTherefore:\n\n```text\n4836 BC → 4346 BC → 6 BC → AD 30 → AD 65\n             490       4340      35       35\n```\n\nand:\n\n```text\n490+4340+35+35 = 4900,\n4836+65−1 = 4900.\n```\n\n### 11.2 The formerly undivided `4830`\n\nFile_46 controls the base span:\n\n```text\n4836−6 = 4830 = 69×70.\n```\n\nThe common-parent seam resolves it as:\n\n```text\n490+4340 = 4830,\n7×70 + 62×70 = 69×70.\n```\n\nThe Prophetic Key adds the final generation:\n\n```text\n4830×70/69 = 4900 = 70×70,\n4900−4830 = 70.\n```\n\nThat final `70` is the Christ generation, divided as `35+35`.\n\n### 11.3 Multiplicative whole and additive segmentation\n\nThe governing Danielic whole is:\n\n```text\n70×7 = 490.\n```\n\nIts additive pattern-template is:\n\n```text\n49+434+3.5+3.5 = 490.\n```\n\nAt `10×`:\n\n```text\n490+4340+35+35 = 4900.\n```\n\nThe continuous coordinate execution supplies the exact missing opening packet:\n\n```text\n4836→4346 BC = 490 = 10×49.\n```\n\nWithout `4346 BC`, the inherited field appears only as `4830+35+35`; with the seam, `4830` resolves as `490+4340`.\n\n### 11.4 Refined seventy-generation anatomy\n\nThe coarse generation anatomy is:\n\n```text\n7 | 62 | ½ | ½ = 70.\n```\n\nThe middle body first resolves through the two reconciliations and the Conquest-to-Christ span:\n\n```text\n1470+1470+1400 = 4340,\n21+21+20 = 62,\n147+147+140 = 434.\n```\n\nThe complete Enoch generation refines the first `21` as `20+1`:\n\n```text\n4346−2946 = 1400 = 20×70,\n2946−2876 = 70 = 1×70.\n```\n\nThe full coordinate execution is therefore:\n\n```text\n490+1400+70+1470+1400+35+35 = 4900.\n```\n\nIn generation units:\n\n```text\n7+20+1+21+20+0.5+0.5 = 70.\n```\n\nAt the Danielic scale:\n\n```text\n49+140+7+147+140+3.5+3.5 = 490,\n140+7+147+140 = 434.\n```\n\nThus the central `434` contains the MT-to-Enoch, Enoch-to-Conquest, and Conquest-to-Christ architecture rather than remaining an undifferentiated scalar.\n\n### 11.5 Why the seam matters\n\n`4346 BC` now performs four coordinated functions:\n\n1. common operator-parent of the two regular-MT Creation states;\n2. head of the repeated-`1470` reconciliation ladder;\n3. hinge between native cumulative and Pillar `69`-coefficient spans;\n4. boundary after the opening seven generations and before the sixty-two-generation Danielic body.\n\nThis makes `4346 BC` structurally indispensable inside the model. Arithmetic does not prove that it was compositionally prior, a transmitted MT date, or the literal referent of Daniel 9.\n\n### 11.6 Christological claim ceiling\n\n- `6 BC` remains the Christological birth hinge.\n- `AD 25/35` remain comparison nodes.\n- `AD 30` remains the exact schematic midpoint and a possible Passion state.\n- `AD 33n` remains the preferred Passion state by File_13.\n- `AD 65` remains the seventy-year carrier terminus.\n- `AD 70` remains the five-year historical Temple companion.\n\nThe Danielic pattern explains the architecture; it does not alter the parent Christological hierarchy.\n\n## 12. Integrated Fine-Resolution Synthesis\n\nPass 1B establishes the following ordered theorem:\n\n1. **Native carrier:** `720`, orthogonal `30`, and crossed `690` establish the fine-resolution grammar.\n2. **Enochian–SKL reconciliation:** the full `2946|2916|2906|2876 BC` field resolves Enoch’s complete `70` years through `30|10|30`, `10|50|10`, and `35|35`.\n3. **MT common parent:** `4114/4304 BC` contract from and expand to the exact common head `4346 BC` under the two anchored Keys.\n4. **Reconciliation ladder:** `4346→2876→1406 BC→AD 65` consists of three equal `1470` arms; the first is internally `20+1` generations.\n5. **Five-year companion:** `4341→2871→1401 BC→AD 70` preserves the carrier while retaining distinct node classes.\n6. **LXX cross-tradition corroboration:** matched `+60` and no-`+60` endpoint/Year-6 pairs preserve `1380=690+690=60×23=20×69`, with dependency-owned completions to `1400/1500`; the outer registers repeat `30\\|1410\\|30`; `5556→4836→4116 BC` is `720|720`; the actual LXX endpoint produces `5846→2906 BC=2940`. A possible common `−30` leveling to `5816→2876 BC`, centered on `4346 BC`, remains conjectural and Appendix-led; File_52e independently corroborates the `5816 BC` coordinate, not the rail assignment.\n7. **Cumulative–Pillar co-registration:** `9660=69×140` and `33810=69×490` meet at `4346 BC` and complete to `70/75` states.\n8. **Calendar-body completion:** the cumulative field resolves as `35×360`, `35×364`, and `40×336` under distinct coordinate executions.\n9. **Danielic seam:** `4836→4346→6 BC→AD 30→AD 65` executes `490|4340|35|35=4900`, the exact `10×` pattern of `49|434|3.5|3.5=490`.\n\n### 12.1 Enoch and Christ as distinct fulcrums\n\n> **BC-side fulcrum.** Enoch functions as the internal fulcrum of the same-side BC architecture. The Short/Long source states, bilateral Keys, centers, and first `1470` arm all pass through his complete schematic generation.\n>\n> **Full-axis fulcrum.** Christ functions as the completion of the combined BC–AD architecture. The cumulative Flood, common Creation parent, Enochian reconciliation, Conquest, and final generation converge in the `AD 65` close and bounded `AD 70` companion.\n\nEnoch’s centrality does not compete with Christ’s. Enoch resolves the BC mechanism; Christ receives and completes it across the civil epoch boundary.\n\n### 12.2 Final argument status\n\nThe arithmetic, argument, and independent verification are complete:\n\n- `446/446` canonical rows execute exactly in two exact engines;\n- `33/33` dependency-reference, `42/42` control-only, and `24/24` existing/reweight rows execute exactly outside the evidence count;\n- the inherited `324` equations/results/IDs remain unchanged;\n- `22` inherited rows are reweighted without changing arithmetic;\n- `122` rows are newly admitted—`96` original new relations, `KEY019`, `20` exact LXX corroboration rows, and `5` Appendix-level LXX leveling rows;\n- dependency ownership and node-class ceilings are preserved;\n- no generated node is promoted to the Primary-anchor inventory;\n- all `52` Pass-1A Machine Guard bodies remain unchanged and the one superseding LXX guard leaves `53/53` unique current guards.\n\nThe source is Final by explicit author instruction. The combined pre-Finalization pressure test remains the current proof trust basis. All `53/53` guards are centrally registered; the affected-only no-change review and expanded File_70 reciprocal route are complete; publication work remains separate.\n\n## 13. Sothic–Mosaic anchored symmetry of the SKL terminal field\n\n\n**Amendment state:** Bounded September 6 2026 working addition; exact finite-set, phase, and anchor relations verified, centrally registered at State Vocabulary Register v1.52 §D.42; not separately author-Finalized. This module imports File_12 §5A's locally opened Sothic companions and leaves the inherited 446-row manifest, 53 guards, evidence weights, and Enoch-centered proof unchanged. The new rows form one correlated structural family, not an additional external witness tally.\n\n### 13.1 Coordinate convention\n\nLet `x=0` denote January 1, AD 1. In the schematic quarter-year model:\n\n\\[\nx(Bn\\text{ BC})=-B+\\tfrac14,\\quad x(Bt\\text{ BC})=-B+\\tfrac34,\n\\]\n\n\\[\nx(\\text{AD }An)=A-1+\\tfrac14,\\quad x(\\text{AD }At)=A-1+\\tfrac34.\n\\]\n\nNisan and Tishri are represented by April 1 and October 1 for phase arithmetic. This is not a claim about reconstructed ancient lunar month dates. The paired Mirror is the set reflection `M(x)=−x`, rendered in chronological order as:\n\n\\[\nYt/(Y-1)n\\text{ BC}\\longmapsto\\text{AD }(Y-1)t/Y n.\n\\]\n\nSingle-date same-label Mirror and Rounded/mod-10 Mirror are different protocols and are not substituted here. [File_09 Appendix A; State Vocabulary Register]\n\n### 13.2 The complete set and its center\n\nThe source set consists of the six pairs:\n\n`2939t/2938n`, `2937t/2936n`, `2935t/2934n`, `2909t/2908n`, `2907t/2906n`, `2905t/2904n BC`.\n\nIts extrema differ by:\n\n\\[\n34.5=30+4+0.5=3\\times11.5.\n\\]\n\nThe midpoint is:\n\n\\[\n\\frac{-2938.25-2903.75}{2}=-2921,\n\\]\n\nthe close of December 31, 2922 BC / opening of January 1, 2921 BC. Supplement A's existing `2922t/2921n` pair brackets this instant; the pair is not the instant itself. [inherited Supplement center register]\n\nThe exact generator is:\n\n\\[\nX=\\{-2921+15r+2g+p/4\\}.\n\\]\n\nThe `±15` produces the two 30-separated rails, `g∈{−1,0,1}` produces the `−2/0/+2` local Gears, and `p∈{−1,1}` supplies the two phases. There are twelve distinct nodes.\n\n### 13.3 One uniform translation, one affine involution\n\n\\[\nT(x)=x+5842,\\qquad5842=4\\times1460.5.\n\\]\n\nThen:\n\n\\[\n\\boxed{T(X)=M(X).}\n\\]\n\nApplying the inverse Mirror after translation gives:\n\n\\[\n\\boxed{R(x)=-5842-x=2(-2921)-x,\\quad R(X)=X,\\quad R^2=\\mathrm{id}.}\n\\]\n\nIt is one affine involution permuting all twelve nodes by six transpositions. This whole-field result is stronger than selected-route coverage alone.\n\n| Source pair, BC | Uniform translated pair, AD | Inverse-Mirror pair, BC |\n|---|---|---|\n| `2939t/2938n` | `2904t/2905n` | `2905t/2904n` |\n| `2937t/2936n` | `2906t/2907n` | `2907t/2906n` |\n| `2935t/2934n` | `2908t/2909n` | `2909t/2908n` |\n| `2909t/2908n` | `2934t/2935n` | `2935t/2934n` |\n| `2907t/2906n` | `2936t/2937n` | `2937t/2936n` |\n| `2905t/2904n` | `2938t/2939n` | `2939t/2938n` |\n\nNo endpoint-specific adjustment is used.\n\n### 13.4 All four periods: full closure versus partial overlap\n\nUniformly applying each four-cycle total to every node gives:\n\n| Four-cycle total | Nodes inside the fixed paired-Mirror set | Outside |\n|---:|---:|---:|\n| `5840=4×1460` | 8 | 4 |\n| `5842=4×1460.5` | 12 | 0 |\n| `5844=4×1461` | 8 | 4 |\n| `5846=4×1461.5` | 4 | 8 |\n\nThe other totals remain valid selected-route relations, including `5840→5844` and `5842→5846`. They do not each permute the whole fixed field.\n\nIn general:\n\n\\[\nM(T_L(X))=X+(5842-L).\n\\]\n\nThe four totals therefore correspond to displacements `+2,0,−2,−4` after inverse Mirror. Their overlap counts are entailed by the local Gear set.\n\nFor upper/lower Nisan labels `U,D`, the corresponding-phase cross-Mirror span is `U+D`. The complete matrix is:\n\n| `U \\ D` | 2904 | 2906 | 2908 |\n|---|---:|---:|---:|\n| 2934 | 5838 | 5840 | 5842 |\n| 2936 | 5840 | 5842 | 5844 |\n| 2938 | 5842 | 5844 | 5846 |\n\nThe `2935t/2934n` to the Mirror of `2909t/2908n` route has `5842`; the route to the Mirror of `2907t/2906n` has `5840`. These are respectively half-step and ordinary raw examples.\n\n### 13.5 Conditional uniqueness\n\nFor a fixed centrally symmetric template `E`, demand:\n\n\\[\nT_{5842}(c+E)=M(c+E).\n\\]\n\nComparing centers gives `c+5842=−c`, hence `c=−2921`. With the inherited `30`, local `±2`, and phase pattern fixed, this placement is unique.\n\nThe template shape is not determined by the period alone. However, the **specific placement** is determined once the source-controlled template and full closure are specified. Furthermore, a finite non-degenerate subset of the real line has no affine self-permutation other than identity or, when symmetric, reflection about its center: preservation of width forces `|a|=1` for `ax+b`.\n\n### 13.6 Opposed macro rails\n\nThe nested `±720` comparison follows exactly:\n\n\\[\nT_{5842}(X+k)=M(X-k).\n\\]\n\nOpposed shifts cancel in every `U+D` span. The union generated by:\n\n\\[\nx=-2921+720m+15r+2g+p/4,\n\\]\n\nwith `m,g∈{−1,0,1}`, has 36 nodes and the same whole-field involution. For example:\n\n\\[\n3657t/3656n\\text{ BC}\\xrightarrow{5842}\\text{AD }2186t/2187n.\n\\]\n\nSame-direction shifts do not cancel. The proof applies to the declared nested macro field; it does not imply that an arbitrarily distant SKL Creation node returns under the unchanged four-cycle length. Propagation through the full SKL source lists and `360:1` scaling remains a separate test. [Files 21/34; State Vocabulary Register §D.38]\n\n### 13.7 Why this center: the Sothic–Mosaic selection mechanism\n\nInternal symmetry alone would allow many shapes. The Mosaic–Joshua comparison supplies the placement rationale: the principal flanks stand one ordinary Sothic cycle before Joshua's birth and the plague/Exodus packet.\n\nThe corresponding January centers are:\n\n\\[\n2936\\rightarrow1476=1460,\n\\qquad2906\\rightarrow1446=1460.\n\\]\n\nThus the source midpoint is:\n\n\\[\n\\boxed{1460+\\frac{1476+1446}{2}=2921.}\n\\]\n\nThe previously controlled source anchors and target packet co-register. The `1380→1500` Priestly route supplies another operator-based compatibility check, not independent source testimony.\n\n#### 13.7.1 The twenty-year calendar interchange\n\nAt the fixed Exodus target:\n\n\\[\n2906-1446=1460=4\\times365,\n\\]\n\n\\[\n2886-1446=1440=4\\times360.\n\\]\n\nTherefore:\n\n\\[\n\\boxed{2906-2886=20=4(365-360).}\n\\]\n\nThe inherited `30|20|30` SKL corridor contains exactly the displacement required to interchange these two fourfold calendar-body counts without moving Exodus. `720+720=1440` is the 360-based realization; `1460` is the 365-based realization. They are structurally comparable counts, not equal elapsed durations or an unannounced calendar conversion. [Files 21/34; inherited Supplement source corridor]\n\n#### 13.7.2 A smaller reconstruction of the corridor\n\nLet `e=1446`, `Q=4×365=1460`, and `F=4×360=1440`. With the inherited 30-year rail:\n\n\\[\n\\boxed{(e+Q+30,\\ e+Q,\\ e+F,\\ e+F-30)=(2936,2906,2886,2856).}\n\\]\n\nIts spacings are `30`, `Q−F=20`, and `30`. The Moses/Joshua comparisons become:\n\n\\[\n(e+Q)-(e+80)=Q-80=1380,\n\\]\n\n\\[\n(e+F-30)-(e+30)=F-60=1380.\n\\]\n\nTheir 50-year rectangle is consequently compatible with:\n\n\\[\n80-30=30+(Q-F)=50.\n\\]\n\nThis clarifies evidence accounting. The corridor, both `1380` differences, the `20`, and the `50` are not independent after the listed inputs are fixed. The explanatory advance is that a small input packet reconstructs all of them. A probability claim would have to charge for the choices of calendar bodies, anchors, rail, and endpoint classes.\n\n### 13.8 Joshua to the paired Mirror of Exodus\n\nThe paired target is `AD 1446t/1447n`. Writing that set in reverse order does not change its members, but component-wise pairing must be stated.\n\n| Span | Length |\n|---|---:|\n| `1477t BC→AD 1446t` | 2922 |\n| `1476n BC→AD 1447n` | 2922 |\n| Outer cross-phase `1477t BC→AD 1447n` | 2922.5 |\n| Inner cross-phase `1476n BC→AD 1446t` | 2921.5 |\n\nHence:\n\n\\[\n2922=2\\times1461=1460.5+1461.5,\n\\]\n\n\\[\n2922.5=1461+1461.5=\\frac{2\\times1461+2\\times1461.5}{2},\n\\]\n\n\\[\n2921.5=1460.5+1461.\n\\]\n\nThe `2922.5` value is the average of the two doubled completed totals; the one-period average is `1461.25`.\n\nThe exact outer-span midpoint is `x=−15`, January 1, 15 BC. The corresponding-phase midpoints are `16t BC` and `15n BC`, straddling that January center. The interval `1t BC→AD 1n` does straddle the epoch datum, but it is not automatically the midpoint or an internal-cycle landing of these Joshua/Exodus paths. No epoch-straddle landing is inferred from the midpoint calculation.\n\n### 13.9 The Long SKL family and the Moses–Joshua fifty\n\nThe Long branch has its own legitimate roles:\n\n\\[\n2888n\\text{ BC}\\rightarrow\\text{AD }33n=2920=2\\times1460,\n\\]\n\n\\[\n2886n\\text{ BC}\\rightarrow\\text{AD }35n=2920,\n\\]\n\n\\[\n2856n\\text{ BC}\\rightarrow\\text{AD }65n=2920.\n\\]\n\nAD 33n retains its preferred Passion comparison, AD 35 its separate comparison role, and AD 65 the schematic Christ-generation terminus—not the literal duration of Jesus' earthly life. [Files 13, 43, 54, 68]\n\nThe reversed 50-year relation is exact:\n\n\\[\n2905t/2904n\\text{ BC}\\rightarrow\\text{AD }1476t/1477n=4380,\n\\]\n\n\\[\n2855t/2854n\\text{ BC}\\rightarrow\\text{AD }1526t/1527n=4380.\n\\]\n\nMoving the BC source forward 50 and its mirrored target forward 50 preserves the span. In source-year magnitudes, the source labels decrease while the target AD labels increase. This is the appropriate reversed orientation of the Moses–Joshua birth separation.\n\nThe complete fixed-field test uses exactly the three Long-source phase pairs `2859t/2858n`, `2857t/2856n`, and `2855t/2854n BC`:\n\n| Source | To AD 1526t | To AD 1527n |\n|---|---:|---:|\n| 2859t BC | 4384 | 4384.5 |\n| 2858n BC | 4383.5 | 4384 |\n| 2857t BC | 4382 | 4382.5 |\n| 2856n BC | 4381.5 | 4382 |\n| 2855t BC | 4380 | 4380.5 |\n| 2854n BC | 4379.5 | 4380 |\n\nThe matrix contains `3×1460`, `3×1460.5`, and `3×1461.5`, but **not `3×1461=4383`**. No additional adjacent/single-date variant is admitted here to supply the missing member. A future extended test may specify such a field before calculation; the fixed matrix remains unchanged.\n\nThe Long twelve-node field is centered at January 1, 2871 BC. Its own self-Mirror translation is `5742`, not `5842`. Its genuine Sothic paths are not evidence that both variants separately satisfy the same four-cycle whole-field theorem.\n\n### 13.10 Scope guards\n\nMachine Guard [SOTHIC PAIRED MIRROR FIELD]:\nUse File_09's January-centered paired-phase reflection for the Sothic twelve-node theorem, with `x=0` at January 1, AD 1 and schematic Nisan/Tishri offsets `1/4` and `3/4`. Keep it distinct from single-date same-label Mirror, Rounded Protocol 1, SKL mod-10 Mirror, and inverse-number reversal. The source field has exactly the declared twelve phase-nodes.\n\nMachine Guard [SOTHIC FULL FIELD AND OVERLAPS]:\nOnly `5842=4×1460.5` translates all twelve declared source nodes onto their paired-Mirror set. The fixed-set uniform overlap counts for `5840/5842/5844/5846` are `8/12/8/4`. Selected-route completions do not make each total a whole-field permutation. Conditional uniqueness fixes placement only after the rail, Gear, phase template, and full-closure requirement are fixed.\n\nMachine Guard [SOTHIC ANCHORED SELECTION DEPENDENCE]:\nThe Mosaic–Joshua packet locates the SKL template within the repository's declared chronology. It does not independently establish historical Exodus or Joshua dates. The `30|20|30` corridor, equal `1380` routes, and `50` rectangle are correlated consequences of their common input packet, not independent statistical witnesses or proof of scribal transmission direction.\n\nMachine Guard [SOTHIC MACRO AND REMOTE SCOPE]:\nOpposed `±720` shifts preserve the declared cross-Mirror sums and the 36-node nested comparison field. Same-direction shifts do not cancel. This finite-field theorem does not establish an unchanged four-Sothic-cycle closure for remote SKL Creation/Flood nodes; full source-chain, scaling, and phase propagation require a separately declared test.\n\nMachine Guard [SOTHIC LONG MOSES FIXED FIELD]:\nFor the exact six-source Long field `2859t/2858n`, `2857t/2856n`, `2855t/2854n BC` and fixed paired-Moses target `AD 1526t/1527n`, the span `4383=3×1461` is absent. Do not introduce an adjacent date, a different Mirror, or an additional phase silently to claim all four three-cycle totals. AD 33, AD 35, and AD 65 retain their distinct Christological node classes.\n\nMachine Guard [SOTHIC SUPPLEMENT INHERITED PROOF]:\nThe new Sothic module leaves the inherited 446-row manifest, evidence weights, registered 53 guards, and earlier Enoch-centered theorems unchanged. The `2921 BC` common center is an existing generated-center co-registration, not a new Primary anchor. Appendix H's arithmetic inventory is separate from the inherited evidence count, and the six new local Sothic guards are centrally registered at State Vocabulary Register v1.52 §D.42, bringing the Supplement to `59/59` registered guards.\n\n# Appendix A. Consolidated `446`-Row Arithmetic Manifest\n\nPass 1B preserves all `324` inherited equations, results, functions, and IDs, promotes `22` decisive inherited rows, and appends `122` newly admitted rows (`96` original new relations, `KEY019`, `20` exact LXX corroboration rows, and `5` Appendix-level LXX leveling rows). Parent-owned equations and control checks remain in separate non-counted ledgers.\n\n## A.1 Family inventory\n\n| Family | Function | Rows | PASS |\n|---|---|---:|---:|\n| `A` | native ladder and Christological continuation | `23` | `23/23` |\n| `K` | Key and calendrical flank grammar | `18` | `18/18` |\n| `I` | intercalation cycle | `6` | `6/6` |\n| `E` | legacy 34.5 envelope | `14` | `14/14` |\n| `O` | Actual outer openings | `11` | `11/11` |\n| `P` | legacy phase extremities | `15` | `15/15` |\n| `G` | Long-anchor grooves | `17` | `17/17` |\n| `C` | cumulative fractal | `16` | `16/16` |\n| `R` | 2700 corollary | `3` | `3/3` |\n| `S` | legacy SKL close | `9` | `9/9` |\n| `CTR` | center/scalar-coordinate algebra | `33` | `33/33` |\n| `PHA` | PhaseNorm40 and 70/120 | `45` | `45/45` |\n| `VAR` | Short/Long source reconciliation | `27` | `27/27` |\n| `ENO` | Enoch anchor lattice | `24` | `24/24` |\n| `KEY` | bilateral Keys and biblical translation | `21` | `21/21` |\n| `SCL` | scale, Pillars, and calendar-body branch | `43` | `43/43` |\n| `MTP` | MT gain compensation | `6` | `6/6` |\n| `LAD` | ladder, companion, and double translation | `18` | `18/18` |\n| `ALT` | alternative-center objection control | `10` | `10/10` |\n| `FLD` | upper-MT Flood partition | `11` | `11/11` |\n| `PIL` | Pillar common-parent field | `16` | `16/16` |\n| `CUM` | cumulative common-parent field | `14` | `14/14` |\n| `CAI` | cumulative Cainan continuation | `6` | `6/6` |\n| `DAN` | Danielic seam and refined anatomy | `15` | `15/15` |\n| `LXX` | LXX–MT Terah-pair, outer-register, Priestly-route, and conjectural leveling family | `25` | `25/25` |\n\n## A.2 Inherited legacy `132`-row manifest\n\n| ID | Weight | Equation | Result | Function |\n|---|---|---:|---:|---|\n| `A001` | `primary` | `4326−4296` | `30` | first Rounded `+30` rail |\n| `A002` | `primary` | `4296−3606` | `690` | first crossed corridor |\n| `A003` | `primary` | `3606−3576` | `30` | second `+30` rail |\n| `A004` | `primary` | `3576−2886` | `690` | second crossed corridor |\n| `A005` | `primary` | `2886−2856` | `30` | SKL terminal rail |\n| `A006` | `primary` | `2856−2166` | `690` | third crossed corridor |\n| `A007` | `primary` | `2166−2136` | `30` | fourth `+30` rail |\n| `A008` | `primary` | `2136−1446` | `690` | fourth crossed corridor |\n| `A009` | `primary` | `1446−1416` | `30` | Exodus-side rail |\n| `A010` | `primary` | `4326−1416` | `2910` | complete five-pair Rounded ladder |\n| `A011` | `primary` | `5×30+4×690` | `2910` | component check of the Rounded ladder |\n| `A012` | `primary` | `3606−2136` | `1470` | six-node inner field |\n| `A013` | `primary` | `30+690+30+690+30` | `1470` | six-node component check |\n| `A014` | `primary` | `1416−726` | `690` | continuation to the Samaria schematic node |\n| `A015` | `primary` | `726−696` | `30` | Samaria-to-Hezekiah seam rail |\n| `A016` | `primary` | `696−6` | `690` | Hezekiah seam to Christ birth |\n| `A017` | `primary` | `6+25−1` | `30` | `6 BC → AD 25` civil span |\n| `A018` | `primary` | `1446+25−1` | `1470` | Exodus to ministry civil span |\n| `A019` | `primary` | `30+690+30+690+30` | `1470` | Exodus-to-ministry component check |\n| `A020` | `secondary` | `726+25−1` | `750` | `726 BC → AD 25` outer Christological bracket |\n| `A021` | `secondary` | `724+27−1` | `750` | local Gear companion bracket |\n| `A022` | `primary` | `720−30` | `690` | cross-rail contraction |\n| `A023` | `primary` | `720+30` | `750` | cross-rail expansion |\n| `K001` | `primary` | `23×30` | `690` | Priestly denominator factorization |\n| `K002` | `primary` | `69×10` | `690` | Prophetic denominator factorization |\n| `K003` | `primary` | `690×70/69` | `700` | Prophetic expansion |\n| `K004` | `primary` | `690×25/23` | `750` | Priestly expansion |\n| `K005` | `primary` | `700−690` | `10` | Prophetic gain |\n| `K006` | `primary` | `750−690` | `60` | Priestly gain |\n| `K007` | `primary` | `690+30` | `720` | native one-flank span |\n| `K008` | `primary` | `700+30` | `730` | Prophetic one-flank span |\n| `K009` | `primary` | `750+30` | `780` | Priestly one-flank span |\n| `K010` | `primary` | `2×360` | `720` | double Prophetic year |\n| `K011` | `primary` | `2×365` | `730` | double common solar year |\n| `K012` | `primary` | `2×364` | `728` | double Enochian year |\n| `K013` | `primary` | `730−2` | `728` | local Gear descent to the Enochian double |\n| `K014` | `secondary` | `2×390` | `780` | double `390` |\n| `K015` | `secondary` | `6×130` | `780` | Atonement/Minor-Note factorization |\n| `K016` | `primary` | `30+690+30` | `750` | complete native bracket |\n| `K017` | `secondary` | `690+780` | `1470` | native core plus Priestly flank |\n| `K018` | `secondary` | `720+750` | `1470` | native flank plus Priestly core |\n| `I001` | `secondary` | `6×(6×360+30)+(4×360+30)` | `14610` | forty-year intercalation cycle |\n| `I002` | `secondary` | `6×360+30` | `2190` | six-year closed block |\n| `I003` | `secondary` | `4×360+30` | `1470` | seventh four-year block |\n| `I004` | `secondary` | `14610/40` | `365.25` | Julian mean |\n| `I005` | `secondary` | `30×49` | `1470` | thirty Jubilees |\n| `I006` | `secondary` | `3×490` | `1470` | three Danielic weeks |\n| `E001` | `primary` | `2+2+0.5` | `4.5` | full local Gear-plus-phase addition |\n| `E002` | `primary` | `30+4.5` | `34.5` | maximum phase-and-Gear rail |\n| `E003` | `secondary` | `30−4.5` | `25.5` | minimum phase-and-Gear rail |\n| `E004` | `secondary` | `34.5−25.5` | `9` | full extremal spread |\n| `E005` | `primary` | `690/20` | `34.5` | one-twentieth relation |\n| `E006` | `primary` | `34.5×70/69` | `35` | Prophetic completion |\n| `E007` | `primary` | `34.5×25/23` | `37.5` | Priestly completion |\n| `E008` | `primary` | `35−34.5` | `0.5` | Prophetic gain |\n| `E009` | `primary` | `37.5−34.5` | `3` | Priestly gain |\n| `E010` | `primary` | `690+34.5` | `724.5` | half-field seed |\n| `E011` | `primary` | `724.5×70/69` | `735` | expanded half-field |\n| `E012` | `primary` | `2×735` | `1470` | paired-half closure |\n| `E013` | `primary` | `37.5−30` | `7.5` | Creation phase-spread remainder |\n| `E014` | `secondary` | `35−30` | `5` | Prophetic remainder above the rail |\n| `O001` | `primary` | `4336−4306` | `30` | actual apparent-age rail |\n| `O002` | `primary` | `4306−3606` | `700` | upper outer Prophetic opening |\n| `O003` | `primary` | `3606−3576` | `30` | retained rail |\n| `O004` | `primary` | `3576−2886` | `690` | retained inner corridor |\n| `O005` | `primary` | `2886−2856` | `30` | SKL terminal rail |\n| `O006` | `primary` | `2856−2166` | `690` | retained inner corridor |\n| `O007` | `primary` | `2166−2136` | `30` | retained rail |\n| `O008` | `primary` | `2136−1436` | `700` | lower outer Prophetic opening |\n| `O009` | `primary` | `1436−1406` | `30` | Conquest-side rail |\n| `O010` | `primary` | `4336−1406` | `2930` | full outer-opened Nisan span |\n| `O011` | `primary` | `30+700+30+690+30+690+30+700+30` | `2930` | component check |\n| `P001` | `primary` | `4339−4337` | `2` | upper Tishri local tooth |\n| `P002` | `primary` | `4337−4335` | `2` | lower Tishri local tooth |\n| `P003` | `primary` | `4338−4336` | `2` | upper Nisan local tooth |\n| `P004` | `primary` | `4336−4334` | `2` | lower Nisan local tooth |\n| `P005` | `primary` | `4342−4339` | `3` | Creation-side Priestly gain |\n| `P006` | `primary` | `1405−1402` | `3` | Conquest-side Priestly gain |\n| `P007` | `primary` | `4342−1402` | `2940` | Tishri-to-Tishri closure |\n| `P008` | `primary` | `4341−1401` | `2940` | Nisan-to-Nisan closure |\n| `P009` | `primary` | `2930+5+5` | `2940` | two-sided extension |\n| `P010` | `primary` | `2+3` | `5` | local tooth plus Priestly gain per side |\n| `P011` | `primary` | `2×1470` | `2940` | double `1470` |\n| `P012` | `primary` | `6×490` | `2940` | six Danielic weeks |\n| `P013` | `secondary` | `60×49` | `2940` | Jubilee factorization |\n| `P014` | `primary` | `4342−4312` | `30` | Tishri apparent-age placement at Creation opening |\n| `P015` | `primary` | `4341−4311` | `30` | Nisan apparent-age placement at Creation opening |\n| `G001` | `secondary` | `2856−2166` | `690` | Abram/Noah-overlay groove |\n| `G002` | `secondary` | `2856−2156` | `700` | Sarah groove |\n| `G003` | `secondary` | `2856−2106` | `750` | base Noah-death groove |\n| `G004` | `secondary` | `2886−2166` | `720` | double `360` |\n| `G005` | `secondary` | `2886−2156` | `730` | double `365` |\n| `G006` | `secondary` | `2886−2106` | `780` | double `390` |\n| `G007` | `secondary` | `2166−2106` | `60` | Terah-variant-width correspondence |\n| `G008` | `secondary` | `3576−2886` | `690` | Enochian-anchor native corridor |\n| `G009` | `secondary` | `3576−2876` | `700` | Enochian-anchor Prophetic corridor |\n| `G010` | `secondary` | `3606−2226` | `1380` | two `690` units to Terah age-70 firstborn state |\n| `G011` | `secondary` | `2×690` | `1380` | two-unit factorization |\n| `G012` | `secondary` | `4296−2226` | `2070` | three `690` units |\n| `G013` | `secondary` | `3×690` | `2070` | three-unit factorization |\n| `G014` | `secondary` | `2070×70/69` | `2100` | threefold Prophetic expansion |\n| `G015` | `secondary` | `2100−2070` | `30` | regenerated `+30` rail |\n| `G016` | `secondary` | `4296−2196` | `2100` | generated Prophetic companion |\n| `G017` | `secondary` | `2226−2196` | `30` | companion displacement |\n| `C001` | `primary` | `34.5×364` | `12558` | local Enochian day-volume / cumulative root scalar |\n| `C002` | `primary` | `14004−1446` | `12558` | cumulative Creation close to Exodus |\n| `C003` | `primary` | `12558×300/299` | `12600` | Enochian completion |\n| `C004` | `primary` | `12558×70/69` | `12740` | Prophetic expansion |\n| `C005` | `primary` | `14006−1406` | `12600` | cumulative Year-6 to Conquest |\n| `C006` | `primary` | `35×360` | `12600` | thirty-five Prophetic years |\n| `C007` | `primary` | `35×364` | `12740` | thirty-five Enochian years |\n| `C008` | `secondary` | `12600−12558` | `42` | Enochian gain |\n| `C009` | `secondary` | `12740−12558` | `182` | Prophetic gain |\n| `C010` | `primary` | `12600×364` | `12740×360` | equal day-volume identity |\n| `C011` | `primary` | `12600×364` | `4586400` | common day volume |\n| `C012` | `primary` | `34.5×70/69×360` | `12600` | local `34.5` Prophetic day lock |\n| `C013` | `primary` | `34.5×364×300/299` | `12600` | local `34.5` Enochian completion |\n| `C014` | `primary` | `34.5×364×70/69` | `12740` | local `34.5` Prophetic expansion |\n| `C015` | `appendix` | `34.5×(336023/920)−12600` | `0.8625` | Residue-Protocol calibrated remainder; optional only |\n| `C016` | `appendix` | `69/80` | `0.8625` | exact residue display for C015 |\n| `R001` | `appendix` | `4106−1406` | `2700` | Rounded Creation to Conquest |\n| `R002` | `appendix` | `4146−1446` | `2700` | apparent-age Creation state to Exodus |\n| `R003` | `appendix` | `7.5×360` | `2700` | phase-spread scalar |\n| `S001` | `appendix` | `27366−2856` | `24510` | SKL Long whole-year source span |\n| `S002` | `appendix` | `690×70/69−690` | `10` | Prophetic Key gain |\n| `S003` | `appendix` | `24510−10` | `24500` | adjacent Jubilee-completed companion |\n| `S004` | `appendix` | `50×490` | `24500` | fifty-Jubilee factorization |\n| `S005` | `appendix` | `27366−2866` | `24500` | terminal-side generated companion |\n| `S006` | `appendix` | `27356−2856` | `24500` | Flood-side generated companion |\n| `S007` | `appendix` | `458646−6` | `458640` | single permitted remote scale echo |\n| `S008` | `appendix` | `1260×364` | `458640` | Enochian factorization |\n| `S009` | `appendix` | `1274×360` | `458640` | Prophetic factorization |\n\n## A.3 Inherited renewed `192`-row manifest\n\nThe equations, results, functions, and IDs are unchanged. The `22` targeted weight promotions occur within this block.\n\n| ID | Weight | Equation | Result | Function |\n|---|---|---:|---:|---|\n| `CTR001` | `primary` | `1470/2` | `735` | half of the native 1470 field |\n| `CTR002` | `primary` | `3606−2871` | `735` | upper arm of the native Long field |\n| `CTR003` | `primary` | `2871−2136` | `735` | lower arm of the native Long field |\n| `CTR004` | `primary` | `(3606+2136)/2` | `2871` | midpoint of the native Long field |\n| `CTR005` | `primary` | `2886−2871` | `15` | upper half of the central 30-year rail |\n| `CTR006` | `primary` | `2871−2856` | `15` | lower half of the central 30-year rail |\n| `CTR007` | `primary` | `(2886+2856)/2` | `2871` | center of the source Long anchor pair |\n| `CTR008` | `primary` | `4341−2871` | `1470` | Nisan upper arm of the completed 2940 corridor |\n| `CTR009` | `primary` | `2871−1401` | `1470` | Nisan lower arm of the completed 2940 corridor |\n| `CTR010` | `primary` | `4342−2872` | `1470` | Tishri-label upper arm of the completed corridor |\n| `CTR011` | `primary` | `2872−1402` | `1470` | Tishri-label lower arm of the completed corridor |\n| `CTR012` | `secondary` | `3366−2876` | `490` | Enochian schematic generation-to-generation translation, opening |\n| `CTR013` | `secondary` | `3359−2869` | `490` | Enochian schematic generation-to-generation translation, close |\n| `CTR014` | `secondary` | `3361−2871` | `490` | Year-6 center translation |\n| `CTR015` | `primary` | `2884−2871` | `13` | upper contracted local-Gear offset from Long center |\n| `CTR016` | `primary` | `2871−2858` | `13` | lower contracted local-Gear offset from Long center |\n| `CTR017` | `primary` | `2884−2858` | `26` | contracted local-Gear pair |\n| `CTR018` | `primary` | `13+724.5` | `737.5` | complete coordinate arm from Long center |\n| `CTR019` | `primary` | `2×737.5` | `1475` | phase-and-Gear coordinate envelope |\n| `CTR020` | `primary` | `724.5+26+724.5` | `1475` | component form of the 1475 coordinate envelope |\n| `CTR021` | `primary` | `3608.5−2133.5` | `1475` | continuous-coordinate check for 3609t to 2134t |\n| `CTR022` | `primary` | `724.5+21+724.5` | `1470` | abstract scalar half-field before the 735 completion |\n| `CTR023` | `primary` | `735−724.5` | `10.5` | gain per abstract half-field |\n| `CTR024` | `primary` | `2×10.5` | `21` | central scalar gap absorbed by the two gains |\n| `CTR025` | `secondary` | `2884−2156` | `728` | lower crossed Enochian double |\n| `CTR026` | `secondary` | `3586−2858` | `728` | upper crossed Enochian double |\n| `CTR027` | `secondary` | `700+15+13` | `728` | centered anatomy of the crossed Enochian double |\n| `CTR028` | `secondary` | `3656−2921` | `735` | upper arm of the parallel Short 1470 ladder |\n| `CTR029` | `secondary` | `2921−2186` | `735` | lower arm of the parallel Short 1470 ladder |\n| `CTR030` | `secondary` | `(3656+2186)/2` | `2921` | midpoint of the parallel Short ladder |\n| `CTR031` | `secondary` | `(2936+2906)/2` | `2921` | midpoint of the Short source anchor pair |\n| `CTR032` | `secondary` | `2921−2871` | `50` | translation between Short- and Long-ladder centers |\n| `CTR033` | `secondary` | `3656−2186` | `1470` | complete parallel Short ladder |\n| `PHA001` | `primary` | `2888.5−2854` | `34.5` | outer cross-phase envelope of 2889t/2888n to 2855t/2854n |\n| `PHA002` | `secondary` | `2889−2855` | `34` | same-Tishri label width before normalization |\n| `PHA003` | `secondary` | `2888−2854` | `34` | same-Nisan label width before normalization |\n| `PHA004` | `primary` | `40−37.5` | `2.5` | residual from Priestly completion to corresponding-suffix 40 |\n| `PHA005` | `primary` | `2892−2852` | `40` | Tishri-label normalized bracket |\n| `PHA006` | `primary` | `2891−2851` | `40` | Nisan-label normalized bracket |\n| `PHA007` | `secondary` | `2892−2889` | `3` | upper endpoint movement from the original Tishri label |\n| `PHA008` | `secondary` | `2855−2852` | `3` | lower endpoint movement from the original Tishri label |\n| `PHA009` | `secondary` | `40−34` | `6` | same-suffix gain from 34 to 40 |\n| `PHA010` | `secondary` | `2×3` | `6` | two-sided endpoint movement |\n| `PHA011` | `primary` | `40−2.5−2.5` | `35` | symmetric inward contraction of the 40 bracket |\n| `PHA012` | `primary` | `35+35` | `70` | two half-generations |\n| `PHA013` | `primary` | `30+40` | `70` | upstream +30 plus the bilateral reconciliation span |\n| `PHA014` | `primary` | `2916−2876` | `40` | bilateral reconciliation interval |\n| `PHA015` | `primary` | `2946−2911` | `35` | upper half of Enoch generation |\n| `PHA016` | `primary` | `2911−2876` | `35` | lower half of Enoch generation |\n| `PHA018` | `primary` | `50+30` | `80` | Short/Long gap plus upstream pre-Flood rail |\n| `PHA019` | `secondary` | `2892+80` | `2972` | upper Tishri translated endpoint |\n| `PHA020` | `secondary` | `2891+80` | `2971` | upper Nisan translated endpoint |\n| `PHA021` | `secondary` | `2852+80` | `2932` | lower Tishri translated endpoint |\n| `PHA022` | `secondary` | `2851+80` | `2931` | lower Nisan translated endpoint |\n| `PHA023` | `secondary` | `2972−2932` | `40` | upper translated Tishri bracket |\n| `PHA024` | `secondary` | `2932−2892` | `40` | middle Tishri bracket |\n| `PHA025` | `secondary` | `2971−2931` | `40` | upper translated Nisan bracket |\n| `PHA026` | `secondary` | `2931−2891` | `40` | middle Nisan bracket |\n| `PHA027` | `primary` | `2972−2852` | `120` | full Tishri-label expanded field |\n| `PHA028` | `primary` | `2971−2851` | `120` | full Nisan-label expanded field |\n| `PHA029` | `primary` | `(2972+2852)/2` | `2912` | Tishri-label center of the 120 field |\n| `PHA030` | `primary` | `(2971+2851)/2` | `2911` | Nisan-label center of the 120 field |\n| `PHA031` | `primary` | `2972−2912` | `60` | upper half of the Tishri 120 field |\n| `PHA032` | `primary` | `2912−2852` | `60` | lower half of the Tishri 120 field |\n| `PHA033` | `primary` | `2947−2912` | `35` | upper phase-resolved half of Enoch generation |\n| `PHA034` | `primary` | `2912−2877` | `35` | lower phase-resolved half of Enoch generation |\n| `PHA035` | `primary` | `2972−2947` | `25` | upper Priestly flank around Enoch generation |\n| `PHA036` | `primary` | `2877−2852` | `25` | lower Priestly flank around Enoch generation |\n| `PHA037` | `primary` | `25+70+25` | `120` | Priestly flanks plus Prophetic center |\n| `PHA038` | `primary` | `25+35+35+25` | `120` | fully resolved Key-completed envelope |\n| `PHA039` | `primary` | `3×40` | `120` | three consecutive Mosaic units |\n| `PHA040` | `primary` | `2×60` | `120` | two equal outer arms |\n| `PHA041` | `primary` | `23×25/23` | `25` | Priestly Key completion value |\n| `PHA042` | `primary` | `69×70/69` | `70` | Prophetic Key completion value |\n| `PHA043` | `secondary` | `(2892+2852)/2` | `2872` | Tishri-label center of the lower 40 bracket |\n| `PHA044` | `secondary` | `(2972+2932)/2` | `2952` | Tishri-label center of the upper 40 bracket |\n| `PHA045` | `secondary` | `2952−2912` | `40` | upper bracket-center displacement |\n| `PHA046` | `secondary` | `2912−2872` | `40` | lower bracket-center displacement |\n| `VAR001` | `secondary` | `25×720` | `18000` | pure Short post-Flood multiple |\n| `VAR002` | `secondary` | `18000−20` | `17980` | Short source total |\n| `VAR003` | `secondary` | `34×720` | `24480` | pure Long post-Flood multiple |\n| `VAR004` | `secondary` | `24480+30` | `24510` | Long source total |\n| `VAR005` | `primary` | `24510−17980` | `6530` | difference of transmitted Short/Long totals |\n| `VAR006` | `primary` | `9×720` | `6480` | nine macro gears / precessional quarter |\n| `VAR007` | `primary` | `6480+50` | `6530` | source-total difference decomposed by anchor gap |\n| `VAR008` | `secondary` | `2906−2856` | `50` | physical-anchor separation |\n| `VAR009` | `primary` | `2936−2886` | `50` | +30-anchor separation |\n| `VAR010` | `secondary` | `20886−2906` | `17980` | Short physical Flood-to-anchor span |\n| `VAR011` | `secondary` | `20916−2936` | `17980` | Short +30 Flood-to-anchor span |\n| `VAR012` | `secondary` | `27396−2886` | `24510` | Long +30 Flood-to-anchor span |\n| `VAR013` | `secondary` | `27366−20886` | `6480` | physical Flood-variant separation |\n| `VAR014` | `secondary` | `27396−20916` | `6480` | +30 Flood-variant separation |\n| `VAR015` | `secondary` | `27366−20916` | `6450` | lower +30-rail envelope |\n| `VAR016` | `secondary` | `27396−20886` | `6510` | upper +30-rail envelope |\n| `VAR017` | `secondary` | `15×430` | `6450` | alternate-quarter lower envelope |\n| `VAR018` | `secondary` | `90×72` | `6480` | standard precessional-quarter state |\n| `VAR019` | `secondary` | `7×930` | `6510` | upper rail-envelope factorization |\n| `VAR020` | `secondary` | `20916−20886` | `30` | Short Flood +30 rail |\n| `VAR021` | `secondary` | `27396−27366` | `30` | Long Flood +30 rail |\n| `VAR022` | `primary` | `20916−18000` | `2916` | Short +30 pure-720 landing |\n| `VAR023` | `primary` | `27396−24480` | `2916` | Long +30 pure-720 landing |\n| `VAR024` | `secondary` | `20886−18000` | `2886` | Short physical pure-720 landing |\n| `VAR025` | `secondary` | `27366−24480` | `2886` | Long physical pure-720 landing |\n| `VAR026` | `secondary` | `2916−2886` | `30` | pure-720 companion rail |\n| `VAR027` | `secondary` | `9×720+50` | `6530` | complete source-total difference anatomy |\n| `ENO001` | `secondary` | `2946−2936` | `10` | Enoch opening to Short +30 anchor |\n| `ENO002` | `secondary` | `2936−2916` | `20` | Short +30 anchor to pure-720 companion |\n| `ENO003` | `secondary` | `2916−2906` | `10` | pure-720 companion to Short physical anchor |\n| `ENO004` | `secondary` | `2906−2886` | `20` | Short physical to Long +30 anchor |\n| `ENO005` | `secondary` | `2886−2876` | `10` | Long +30 anchor to Enoch close |\n| `ENO006` | `secondary` | `2876−2856` | `20` | Enoch close to Long physical anchor |\n| `ENO007` | `primary` | `10+20+10+20+10` | `70` | palindromic Enoch-generation core |\n| `ENO008` | `secondary` | `10+20+10+20+10+20` | `90` | complete anchor field |\n| `ENO009` | `primary` | `2946−2876` | `70` | translated Enoch generation |\n| `ENO010` | `secondary` | `2946−2856` | `90` | complete Enoch/SKL anchor field |\n| `ENO012` | `primary` | `10+50+10` | `70` | Enoch generation with +50 body |\n| `ENO013` | `primary` | `(2946+2876)/2` | `2911` | midpoint of Enoch generation |\n| `ENO014` | `secondary` | `(2936+2886)/2` | `2911` | midpoint of the +50 anchor body |\n| `ENO015` | `secondary` | `(2916+2906)/2` | `2911` | midpoint of inner pure-720/physical pair |\n| `ENO016` | `secondary` | `2936−2911` | `25` | upper half of the +50 anchor body |\n| `ENO017` | `secondary` | `2911−2886` | `25` | lower half of the +50 anchor body |\n| `ENO018` | `secondary` | `2916−2911` | `5` | upper half of the inner 10-year pair |\n| `ENO019` | `secondary` | `2911−2906` | `5` | lower half of the inner 10-year pair |\n| `ENO020` | `primary` | `2946−2916` | `30` | upper generated reconciliation rail |\n| `ENO021` | `primary` | `2906−2876` | `30` | lower source/generated reconciliation rail |\n| `ENO022` | `primary` | `30+10+30` | `70` | four-node reconciliation lattice |\n| `ENO023` | `secondary` | `2946−2906` | `40` | left side of the reconciliation rectangle |\n| `ENO024` | `primary` | `2916+30` | `2946` | upstream +30 companion of reverse-Key node |\n| `ENO025` | `primary` | `2876+30` | `2906` | upstream +30 companion of forward-Key node |\n| `KEY001` | `secondary` | `3626−2936` | `690` | Short earlier-side native core |\n| `KEY002` | `primary` | `3626−750` | `2876` | Short/Priestly forward reconciliation |\n| `KEY003` | `secondary` | `3626−3576` | `50` | earlier-side variant separation |\n| `KEY004` | `secondary` | `750−700` | `50` | difference between complementary Key spans |\n| `KEY005` | `secondary` | `2906−2216` | `690` | Short later-side native core |\n| `KEY006` | `primary` | `2216+700` | `2916` | Short/Prophetic reverse reconciliation |\n| `KEY007` | `primary` | `2166+750` | `2916` | Long/Priestly reverse reconciliation |\n| `KEY008` | `secondary` | `2216−2166` | `50` | later-side variant separation |\n| `KEY009` | `secondary` | `60+10` | `70` | sum of Priestly and Prophetic gains |\n| `KEY010` | `secondary` | `60−10` | `50` | difference of Priestly and Prophetic gains |\n| `KEY011` | `secondary` | `750+700−40` | `1410` | overlapped expanded arms |\n| `KEY012` | `secondary` | `690+30+690` | `1410` | native interior corridor |\n| `KEY013` | `primary` | `2946−1476` | `1470` | Enoch opening to Joshua birth |\n| `KEY014` | `primary` | `2916−1446` | `1470` | reverse-Key node to Exodus |\n| `KEY015` | `primary` | `2906−1436` | `1470` | Short physical anchor to generated lower rail |\n| `KEY016` | `primary` | `2876−1406` | `1470` | forward-Key node to Conquest |\n| `KEY017` | `secondary` | `1476−1446` | `30` | lower quartet first interval |\n| `KEY018` | `secondary` | `1446−1436` | `10` | lower quartet center interval |\n| `KEY020` | `secondary` | `1476−1406` | `70` | translated lower quartet |\n| `KEY021` | `secondary` | `1446−1406` | `40` | Exodus–Conquest counterpart of reconciliation pair |\n| `SCL001` | `secondary` | `3606−2936` | `670` | ordinary upper 670-year segment |\n| `SCL002` | `secondary` | `3606−2886` | `720` | ordinary upper complete carrier |\n| `SCL003` | `secondary` | `3576−2906` | `670` | ordinary lower 670-year segment |\n| `SCL004` | `secondary` | `3576−2856` | `720` | ordinary lower complete carrier |\n| `SCL005` | `secondary` | `670+50` | `720` | ordinary fractal partition |\n| `SCL006` | `secondary` | `262116−20916` | `241200` | +30 Creation-to-Short-Flood segment |\n| `SCL007` | `secondary` | `670×360` | `241200` | scaled 670 segment |\n| `SCL008` | `secondary` | `20916−2916` | `18000` | +30 Flood-to-pure-terminal segment |\n| `SCL009` | `secondary` | `50×360` | `18000` | scaled 50 segment |\n| `SCL010` | `secondary` | `262116−2916` | `259200` | +30 complete 720×360 carrier |\n| `SCL011` | `secondary` | `720×360` | `259200` | scaled 720 carrier |\n| `SCL012` | `secondary` | `262086−20886` | `241200` | physical Creation-to-Short-Flood segment |\n| `SCL013` | `secondary` | `20886−2886` | `18000` | physical Flood-to-pure-terminal segment |\n| `SCL014` | `secondary` | `262086−2886` | `259200` | physical complete 720×360 carrier |\n| `SCL015` | `secondary` | `27366−2886` | `24480` | Long Flood-to-+30 anchor pure 68×360 |\n| `SCL016` | `secondary` | `68×360` | `24480` | 68 macro generations |\n| `SCL017` | `secondary` | `27366−2166` | `25200` | Long Flood to Abraham/Noah field |\n| `SCL018` | `secondary` | `70×360` | `25200` | amplified Enoch generation |\n| `SCL019` | `secondary` | `68×360+2×360` | `70×360` | 68+2 macro-Gear completion |\n| `SCL020` | `secondary` | `20886−720` | `20166` | Short Flood Gear-1 macro member |\n| `SCL021` | `secondary` | `262086−20166` | `241920` | 672×360 Creation-to-Flood branch |\n| `SCL022` | `secondary` | `672×360` | `241920` | Priestly double-body scaled branch |\n| `SCL023` | `secondary` | `20166−2166` | `18000` | Gear-1 Flood to Abraham/Noah field |\n| `SCL024` | `secondary` | `262086−2166` | `259920` | complete 722×360 branch |\n| `SCL025` | `secondary` | `722×360` | `259920` | scaled 361+361 body |\n| `SCL026` | `secondary` | `3608−2936` | `672` | ordinary Priestly double-body segment |\n| `SCL027` | `secondary` | `3608−2886` | `722` | ordinary 361+361 complete carrier |\n| `SCL028` | `secondary` | `2×336` | `672` | Priestly double |\n| `SCL029` | `secondary` | `336+25` | `361` | 361-body half |\n| `SCL030` | `secondary` | `2×361` | `722` | 361+361 calendar double |\n| `SCL031` | `secondary` | `672+50` | `722` | Priestly double plus variant gap |\n| `SCL032` | `appendix` | `1406+1844−1` | `3249` | Conquest to Baháʼí Era civil span |\n| `SCL033` | `appendix` | `9×361` | `3249` | nine 361-body cycles |\n| `SCL034` | `appendix` | `57×57` | `3249` | square display |\n| `SCL035` | `appendix` | `19×19` | `361` | nineteen-squared calendrical body |\n| `SCL036` | `appendix` | `3×3` | `9` | three-squared multiplier |\n| `SCL037` | `secondary` | `2936+29465−1` | `32400` | Short +30 anchor to Boaz Pillar |\n| `SCL038` | `secondary` | `2886+29515−1` | `32400` | Long +30 anchor to Jachin Pillar |\n| `SCL039` | `secondary` | `2911+29490−1` | `32400` | center-to-center Pillar translation |\n| `SCL040` | `secondary` | `29515−29465` | `50` | Pillar separation |\n| `SCL041` | `secondary` | `29490−29465` | `25` | lower Pillar half-gap |\n| `SCL042` | `secondary` | `29515−29490` | `25` | upper Pillar half-gap |\n| `SCL043` | `secondary` | `90×360` | `32400` | SKL day-year/Pillar projection |\n\n## A.4 Newly admitted Pass-1B `122`-row manifest\n\nThe `122` rows comprise `99` main-body rows, `22` appendix-weight rows, and the omitted forward-convergence body equation `KEY019`.\n\n| ID | Weight | Equation | Result | Function |\n|---|---|---:|---:|---|\n| `MTP006` | `secondary` | `4346−4114` | `232` | Priestly contraction amount |\n| `MTP013` | `secondary` | `4346−4304` | `42` | Prophetic contraction amount |\n| `MTP014` | `primary` | `4304−4114` | `190` | distance between the two MT variant states |\n| `MTP015` | `primary` | `60+130` | `190` | Terah plus restored-second-Cainan variant package |\n| `MTP016` | `primary` | `232−42` | `190` | Key-gain difference absorbs MT variant package |\n| `MTP017` | `secondary` | `2940−2900` | `40` | completed-span difference |\n| `LAD007` | `primary` | `4346−2946` | `1400` | twenty generations before Enoch opening |\n| `LAD009` | `primary` | `1400+70` | `1470` | first 1470 arm resolved as 20+1 generations |\n| `LAD010` | `secondary` | `2876−2871` | `5` | Enoch close to Long-corridor center handoff |\n| `LAD011` | `secondary` | `35+35+5` | `75` | Enoch 70 plus bounded five-year handoff |\n| `LAD012` | `secondary` | `4346−4341` | `5` | upper ladder five-year companion shift |\n| `LAD013` | `secondary` | `1406−1401` | `5` | Conquest-extremity five-year companion shift |\n| `LAD014` | `secondary` | `70−65` | `5` | Temple companion beyond carrier terminus |\n| `LAD015` | `secondary` | `1401+70−1` | `1470` | generated Conquest extremity to AD 70 |\n| `LAD016` | `secondary` | `4341+70−1` | `4410` | complete five-year companion ladder |\n| `LAD021` | `secondary` | `6+70−1` | `75` | Christ 70 plus five-year companion envelope |\n| `LAD022` | `primary` | `1476−6` | `1470` | Joshua birth to Christ birth hinge |\n| `LAD023` | `primary` | `1441+30−1` | `1470` | Joshua midpoint to Christ midpoint |\n| `LAD024` | `primary` | `2946−6` | `2940` | Enoch opening to Christ birth hinge |\n| `LAD025` | `primary` | `2911+30−1` | `2940` | Enoch midpoint to Christ midpoint |\n| `LAD026` | `primary` | `2876+65−1` | `2940` | Enoch close to Christ carrier terminus |\n| `LAD027` | `secondary` | `2871+70−1` | `2940` | Long-corridor center to Temple companion |\n| `LAD028` | `secondary` | `2916+25−1` | `2940` | reverse-Key node to AD 25 comparison |\n| `LAD029` | `secondary` | `2906+35−1` | `2940` | Short physical anchor to AD 35 comparison |\n| `ALT001` | `appendix` | `2936−2921` | `15` | upper half of Short source pair |\n| `ALT002` | `appendix` | `2921−2906` | `15` | lower half of Short source pair |\n| `ALT003` | `appendix` | `2921+1470` | `4391` | Short-center upper extremity |\n| `ALT004` | `appendix` | `2921−1470` | `1451` | Short-center lower extremity |\n| `ALT005` | `appendix` | `4391−2921` | `1470` | Short-center upper arm |\n| `ALT006` | `appendix` | `2921−1451` | `1470` | Short-center lower arm |\n| `ALT007` | `appendix` | `2916+1470` | `4386` | pure-720 upper extremity |\n| `ALT009` | `appendix` | `4386−2916` | `1470` | pure-720 upper arm |\n| `ALT010` | `appendix` | `4391−4341` | `50` | Short versus Long upper-extremity displacement |\n| `ALT011` | `appendix` | `1451−1401` | `50` | Short versus Long lower-extremity displacement |\n| `FLD001` | `secondary` | `4304−2648` | `1656` | upper-MT Creation to generated Flood seam |\n| `FLD002` | `secondary` | `2648−1406` | `1242` | generated Flood seam to Conquest |\n| `FLD003` | `secondary` | `1656+1242` | `2898` | raw partition recombines to Prophetic input |\n| `FLD007` | `secondary` | `1656×70/69` | `1680` | Prophetic expansion of upper component |\n| `FLD009` | `secondary` | `5×336` | `1680` | Priestly calendar-body factorization of 1680 |\n| `FLD010` | `secondary` | `1242×70/69` | `1260` | Prophetic expansion of lower component |\n| `FLD012` | `secondary` | `3.5×360` | `1260` | Prophetic half-week factorization of 1260 |\n| `FLD013` | `secondary` | `1680+1260` | `2940` | expanded components recombine to 2940 |\n| `FLD014` | `secondary` | `1406+1260` | `2666` | generated transformed seam |\n| `FLD015` | `secondary` | `2666+1680` | `4346` | generated transformed head |\n| `FLD016` | `secondary` | `10×1260` | `12600` | regular-to-cumulative scalar homology |\n| `PIL001` | `secondary` | `4346+29465−1` | `33810` | common parent to fixed Projective Pillar |\n| `PIL002` | `secondary` | `69×490` | `33810` | native Pillar-side coefficient state |\n| `PIL004` | `secondary` | `7×4830` | `33810` | seven base-span partition |\n| `PIL005` | `secondary` | `33810×70/69` | `34300` | Prophetic completion of Pillar span |\n| `PIL007` | `secondary` | `34300−33810` | `490` | Prophetic endpoint gain |\n| `PIL008` | `secondary` | `4346+490` | `4836` | landing on cumulative Flood |\n| `PIL009` | `secondary` | `4836+29465−1` | `34300` | completed Prophetic Pillar span |\n| `PIL010` | `secondary` | `33810×25/23` | `36750` | Priestly completion of Pillar span |\n| `PIL013` | `secondary` | `36750−33810` | `2940` | Priestly endpoint gain |\n| `PIL014` | `secondary` | `4346+2940` | `7286` | generated outer bracket head |\n| `PIL015` | `secondary` | `7286+29465−1` | `36750` | completed Priestly Pillar span |\n| `PIL016` | `secondary` | `7286−4346` | `2940` | upper half of generated 2940 bracket |\n| `PIL017` | `secondary` | `7286−1406` | `5880` | generated outer Creation–Conquest bracket |\n| `PIL020` | `appendix` | `14006+29465−1` | `43470` | full cumulative Creation-to-Pillar span |\n| `PIL021` | `appendix` | `9×4830` | `43470` | full field base-span factorization |\n| `PIL022` | `appendix` | `9660+33810` | `43470` | 2\\|7 partition of full field |\n| `CUM002` | `secondary` | `69×140` | `9660` | native cumulative-side coefficient state |\n| `CUM006` | `secondary` | `9660+2940` | `12600` | native cumulative Creation-to-Conquest total |\n| `CUM011` | `secondary` | `4346+9800` | `14146` | generated Prophetic Creation head |\n| `CUM012` | `secondary` | `14146−1406` | `12740` | generated Enochian-body span to Conquest |\n| `CUM015` | `secondary` | `14146−14006` | `140` | intercalary head displacement |\n| `CUM017` | `secondary` | `12740−12600` | `140` | difference between Enochian and Prophetic registers |\n| `CUM018` | `secondary` | `9660×25/23` | `10500` | Priestly completion of upper cumulative segment |\n| `CUM020` | `secondary` | `4346+10500` | `14846` | generated Priestly Creation head |\n| `CUM021` | `secondary` | `14846−1406` | `13440` | generated Priestly-body span to Conquest |\n| `CUM023` | `secondary` | `40×336` | `13440` | Priestly forty-years-of-years register |\n| `CUM024` | `secondary` | `9800−9660` | `140` | Prophetic gain on upper segment |\n| `CUM025` | `secondary` | `10500−9660` | `840` | Priestly gain on upper segment |\n| `CUM026` | `secondary` | `14846−14006` | `840` | Priestly head displacement |\n| `CUM027` | `secondary` | `13440−12600` | `840` | Priestly versus native completed-total gain |\n| `CAI004` | `secondary` | `23×440` | `10120` | Priestly-ready Cainan span |\n| `CAI005` | `secondary` | `10120×25/23` | `11000` | Priestly completion of Cainan span |\n| `CAI007` | `appendix` | `4346+11000` | `15346` | generated expanded Cainan head |\n| `CAI008` | `secondary` | `10120−9660` | `460` | native cumulative Cainan insertion |\n| `CAI009` | `secondary` | `11000−10500` | `500` | expanded Cainan insertion |\n| `CAI011` | `appendix` | `15346−14846` | `500` | generated-head insertion after expansion |\n| `DAN001` | `primary` | `4836−4346` | `490` | opening seven-generation packet |\n| `DAN002` | `primary` | `4346−6` | `4340` | central sixty-two-generation body |\n| `DAN008` | `primary` | `490+4340` | `4830` | 4346 seam resolves the formerly undivided 4830 |\n| `DAN011` | `primary` | `62×70` | `4340` | central body in seventy-year units |\n| `DAN013` | `primary` | `7+62+0.5+0.5` | `70` | seventy-generation Danielic anatomy |\n| `DAN014` | `primary` | `1470+1470+1400` | `4340` | dual reconciliation plus Conquest-to-Christ body |\n| `DAN015` | `primary` | `21+21+20` | `62` | internal resolution of the sixty-two generations |\n| `DAN016` | `primary` | `147+147+140` | `434` | Danielic-scale internal resolution of 434 |\n| `DAN018` | `primary` | `7+20+1+21+20+0.5+0.5` | `70` | fine-resolution seventy-generation sequence |\n| `DAN019` | `primary` | `49+140+7+147+140+3.5+3.5` | `490` | fine-resolution Danielic-scale sequence |\n| `DAN020` | `primary` | `140+7+147+140` | `434` | internal fine resolution of 434 |\n| `DAN021` | `primary` | `490+1400+70+1470+1400+35+35` | `4900` | full coordinate execution from cumulative Flood to AD 65 |\n| `DAN024` | `appendix` | `4906−4836` | `70` | File_45 front packet to new cumulative packet translation |\n| `DAN025` | `appendix` | `4416−4346` | `70` | File_45 front packet close to common-parent seam translation |\n| `DAN028` | `secondary` | `4900−4830` | `70` | one final generation added by Prophetic completion |\n| `KEY019` | `primary` | `3576−700` | `2876` | Long/Prophetic forward reconciliation |\n| `LXX001` | `secondary` | `5584−5554` | `30` | LXX Maximum endpoint upper apparent-age flank |\n| `LXX002` | `secondary` | `5554−4144` | `1410` | LXX Maximum to MT apparent endpoint interior corridor |\n| `LXX003` | `secondary` | `4144−4114` | `30` | MT endpoint apparent-age flank |\n| `LXX004` | `secondary` | `5584−4114` | `1470` | complete endpoint outer register |\n| `LXX005` | `secondary` | `5586−5556` | `30` | LXX Maximum Year-6 upper apparent-age flank |\n| `LXX006` | `secondary` | `5556−4146` | `1410` | LXX Maximum Year-6 to MT apparent Year-6 interior corridor |\n| `LXX007` | `secondary` | `4146−4116` | `30` | MT Year-6 apparent-age flank |\n| `LXX008` | `secondary` | `5556−4836` | `720` | LXX Maximum Year-6 to cumulative Flood half-bracket |\n| `LXX009` | `secondary` | `4836−4116` | `720` | cumulative Flood to MT Year-6 half-bracket |\n| `LXX010` | `secondary` | `5554−60` | `5494` | remove LXX Maximum Terah +60 to actual endpoint |\n| `LXX011` | `secondary` | `5494−4114` | `1380` | actual LXX to actual MT endpoint body |\n| `LXX012` | `secondary` | `5494−1446` | `4048` | actual LXX endpoint to Exodus Priestly input |\n| `LXX013` | `secondary` | `4048÷23` | `176` | Priestly-input denominator units |\n| `LXX014` | `secondary` | `4048×25/23` | `4400` | Priestly completion of LXX-to-Exodus span |\n| `LXX015` | `secondary` | `1446+4400` | `5846` | generated LXX–Exodus Priestly head |\n| `LXX016` | `secondary` | `5846−2906` | `2940` | generated head to Short physical SKL anchor |\n| `LXX017` | `secondary` | `5554−4174` | `1380` | `+60 Terah` endpoint-to-endpoint body |\n| `LXX018` | `secondary` | `5556−4176` | `1380` | `+60 Terah` Year-6-to-Year-6 body |\n| `LXX019` | `secondary` | `5496−4116` | `1380` | no-`+60` Year-6-to-Year-6 body |\n| `LXX020` | `secondary` | `690+690` | `1380` | double-`690` core of every matched Terah pair |\n| `LXX021` | `appendix` | `5846−4346` | `1500` | conjectural-leveling upper unlevelled arm |\n| `LXX022` | `appendix` | `4346−2906` | `1440` | conjectural-leveling lower unlevelled arm |\n| `LXX023` | `appendix` | `5846−30` | `5816` | conjectural leveled LXX Priestly companion |\n| `LXX024` | `appendix` | `5816−4346` | `1470` | conjectural leveled upper carrier arm |\n| `LXX025` | `appendix` | `5816−2876` | `2940` | conjectural leveled LXX-to-Enoch/SKL pair |\n\n## A.5 Evidence-weight summary\n\n| Weight | Inherited after promotion | New Pass-1B | Consolidated |\n|---|---:|---:|---:|\n| `primary` | `153` | `23` | `176` |\n| `secondary` | `152` | `77` | `229` |\n| `appendix` | `19` | `22` | `41` |\n\n## A.6 Non-counted execution ledgers\n\n| Ledger class | Rows | Evidence count |\n|---|---:|---|\n| dependency-reference | `33` | excluded |\n| control-only | `42` | excluded |\n| existing/reweight reference | `24` | excluded |\n\nAll non-counted equations execute exactly and remain available in the machine-readable Pass-1B ledgers.\n\n# Appendix B. Pass-1B Node-State, Common-Parent, and Center Matrix\n\n| Field | Upper / first state | Center / joint | Lower / last state | Node-class control |\n|---|---|---|---|---|\n| Long native field | `3606 BC` | `2872t/2871n BC` | `2136 BC` | principal source/generated Long corridor |\n| Long source anchor pair | `2886 BC` | `2872t/2871n BC` | `2856 BC` | source +30/base pair around generated center |\n| Short ladder | `3656 BC` | `2922t/2921n BC` | `2186 BC` | generated comparison ladder |\n| Short source anchor pair | `2936 BC` | `2922t/2921n BC` | `2906 BC` | source +30/base pair around generated center |\n| lower PhaseNorm40 bracket | `2892t/2891n` | `2872t/2871n` | `2852t/2851n BC` | generated corresponding-suffix bracket |\n| expanded `120` field | `2972t/2971n` | `2912t/2911n` | `2852t/2851n BC` | generated `60\\|60` envelope |\n| Enoch generation | `2947t/2946n` | `2912t/2911n` | `2877t/2876n BC` | dependency-controlled schematic `35\\|35` generation |\n| full Enoch/SKL lattice | `2946/2936/2916` | `2911` common center | `2906/2886/2876 BC` | mixed schematic/source/generated sequence |\n| direct Key convergence | reverse `2916 BC` | directional Key exchange | forward `2876 BC` | generated convergence nodes |\n| four-node reconciliation field | `2946/2916` | `30\\|10\\|30` | `2906/2876 BC` | Primary generated/source co-registration |\n| translated biblical quartet | `1476/1446` | `1436` companion | `1406 BC` | Joshua birth / Exodus / generated rail / Conquest |\n| MT contracted states | `4114 BC` | `4346 BC` common parent | `4304 BC` | standard/expanded variants under distinct anchors |\n| LXX–MT endpoint outer register | `5584/5554 BC` | `30\\|1410\\|30` | `4144/4114 BC` | LXX Maximum, generated apparent, and MT states remain distinct |\n| LXX–cumulative–MT Year-6 register | `5586/5556 BC` | `4836 BC` bisects `5556/4116` | `4146/4116 BC` | apparent companions and `±720` midpoint; not one chronology |\n| LXX–MT matched Terah pairs | endpoint `5554/5494 BC` | `1380=690+690` | endpoint `4174/4114 BC` | `+60` and no-`+60` compared only within endpoint node-class |\n| LXX–MT matched Year-6 pairs | Year-6 `5556/5496 BC` | `1380=690+690` | Year-6 `4176/4116 BC` | `+60` and no-`+60` compared only within Year-6 node-class |\n| LXX Priestly route | actual `5494 BC` | fixed Exodus `1446 BC` | generated `5846 BC → 2906 BC` | `25/23` completion; `5846` generated, `2906` Short physical anchor |\n| conjectural leveled LXX/SKL pair | generated `5816 BC` | `4346 BC` common MT parent | `2876 BC` reconciliation node | Appendix-only `1470\\|1470`; `5816` is not a source date |\n| MT→SKL first carrier arm | `4346 BC` | `2946 BC` Enoch opening | `2876 BC` Enoch close | `20+1` seventy-year units; exact execution complete |\n| reconciliation ladder | `4346 BC` | `2876/1406 BC` joints | `AD 65` | repeated carrier-close architecture |\n| five-year companion ladder | `4341 BC` | `2871/1401 BC` joints | `AD 70` | generated/historical companion; not carrier close |\n| cumulative native side | `14006 BC` | `4346 BC` hinge | — | `69×140` parent span |\n| Pillar native side | — | `4346 BC` hinge | `AD 29465` | `69×490` parent span; Pillar fixed |\n| cumulative calendar matrix | native `35×360` | companion `35×364` | companion `40×336` | distinct coordinate executions |\n| Danielic seam | `4836 BC` | `4346 BC` | `6 BC` | opening `7` and middle `62` boundary |\n| Christ generation | `6 BC` | `AD 30` | `AD 65` | `35\\|35`; `AD 33n` preferred Passion unchanged |\n| Christological quartet | `6 BC/AD 25` | `AD 30` center | `AD 35/65` | translated `30\\|10\\|30`; comparison nodes controlled |\n| Enoch/Christ five-year fields | `2946 BC / 6 BC` | `2911 BC / AD 30` | `2876→2871 BC / AD 65→70` | `35\\|35\\|5`; only `2871 BC` is a center |\n| raw upper-MT Flood partition | `4304 BC` | local `2648 BC` seam | `1406 BC` | generated state; not BJ Ham identity |\n| transformed Flood partition | generated upper head | local `2666 BC` seam | `1406 BC` | transformed coordinate state; not genealogy |\n| source/companion SKL close | `27366 BC` | `24510 / 24500` | `2856/2866 BC` | source duration / generated Jubilee companion |\n| Projective Pillar pair | `AD 29465` | `AD 29490` | `AD 29515` | Projective Boundaries, not historical chronology |\n# Appendix C. Bounded Echoes, Generated Heads, Collision Routing, and Exclusions\n\n## C.1 `2700=7.5×360`\n\nThe fuller Creation-to-Exodus/Conquest argument remains controlled elsewhere. The compact crossed pair remains:\n\n```text\n4106−1406 = 2700,\n4146−1446 = 2700,\n2700 = 7.5×360.\n```\n\nIt is corroborative only.\n\n## C.2 Physical residue\n\nThe optional calibrated solar comparison remains appendix-only:\n\n```text\n34.5 solar years − 12600 days = 0.8625 day.\n```\n\nThe exact main proof uses whole-number Key conversions and does not feed the residue back into civil chronology.\n\n## C.3 Remote `458640`\n\nThe retained remote echo is:\n\n```text\n458646−6 = 458640,\n458640 = 1260×364 = 1274×360.\n```\n\nIt remains one scale echo inside the same evidence family.\n\n## C.4 Mirror continuation\n\n```text\nAD 30+690 = AD 720.\n```\n\nThis is an ordinary continuation only; no formal Mirror operator is opened.\n\n## C.5 `90×360` Pillar routing\n\nThe exact Projective-Pillar spans are executed in §8.7. Files 21/10 remain controlling, and the civil `BC+AD−1` operator is mandatory.\n\n## C.6 `361` and Baháʼí reception history\n\nFile_36/P19 supplies the repository precedent for:\n\n```text\n1406 BC → AD 1844\n= 1406+1844−1\n= 3249\n= 9×361\n= 57².\n```\n\nThe Supplement uses **361-day calendrical body**, not “361-day solar year.” This is reception-history/providential corroboration only. It does not prove historical SKL use of the modern Baháʼí calendar.\n\n## C.7 Wider `+50` family\n\nKings, Berossus, SKL Short/Long, Jubilee `49/50`, Pillar, and local `25+25` displays form a comparison family. Their source states and operators remain distinct.\n\n## C.8 Explicit exclusions\n\nThe following remain outside the canonical proof:\n\n- `313×7×30×7`;\n- `23030|24500|25970`;\n- `23000|24500|26000`;\n- any claim that `24500` replaces `24510`;\n- any claim that `120` is one Key-ratio output;\n- any claim that `361` proves historical SKL use of the Baháʼí calendar;\n- any remote factorization catalogue that obscures the Creation–Conquest–Christ spine.\n## C.9 Generated outer heads and Cainan continuation\n\nPass 1B verifies:\n\n```text\n4346+2940 = 7286 BC,\n4346+9800 = 14146 BC,\n4346+10500 = 14846 BC,\n4346+11000 = 15346 BC,\n460×25/23 = 500.\n```\n\nThese exact appendix-generated heads cannot carry the main proof, enter the Primary-anchor inventory, or duplicate File_53 evidence.\n\n## C.10 Collision register for `2648/2666 BC`\n\n| Label | Existing parent use | Local proposed use | Control |\n|---:|---|---|---|\n| `2648 BC` | BJ/Jubilees Ham birth | raw upper-MT Flood partition seam | tradition/state/node-class non-collapse |\n| `2666 BC` | genealogical/Enochic translated labels | transformed upper-MT coordinate seam | generated-coordinate and parent-proof firewall |\n\nThe safest public wording always includes the local state: **generated upper-MT raw Flood seam `2648 BC`** or **generated transformed seam `2666 BC`**.\n# Appendix D. Reopened Pass-1B Frozen-Parent and Dependency Ledger\n\nAll sources and controls below remain read-only. Hashes are those recorded by Reopened Pass 0; no dependency or control source is modified in Pass 1B.\n\n| Class | Dependency | SHA-256 | Function | Handling |\n|---|---|---|---|---|\n| `TARGET` | `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail (2).md` | `8e7431c3cfbd76a06fa263a7278e8072659289c1847689816c8b7dc463e92cc8` | Current Final Supplement A reopening target | frozen/read-only |\n| `RECIPROCAL-PARENT` | `File_70.Genesis_Toledot_Atonement_Weave(9)(1).md` | `08aa940bd061ed4102d0370d752ae03628258629f0f8c60472cc66931aaf665b` | Current reciprocal Final File_70 reopening parent; remains frozen | frozen/read-only |\n| `CONTROL` | `490d_Repository_Style_Guide_v2.5(6)(1).md` | `037e9094d1cba56928db23168e3ad951bf462c502efaf1c135629ea3fe1469a4` | Canonical source/style and state-safe revision rules | frozen/read-only |\n| `CONTROL` | `Project_Procedures_v3.5(4)(1).md` | `a460b3efc90ccb02125b15d6576d4f0a3905a073aa66f07fc650f4d648e1c128` | Pass workflow; Pass 0 intake/lint only | frozen/read-only |\n| `CONTROL` | `Restart_Capsule_v11.49(1).md` | `7bf6ff07c6069b2672cfea4d269f53b71afc3f84f396b5417b4dddc9af564c61` | Repository-wide current anchor/operator/state control | frozen/read-only |\n| `CONTROL` | `State_Vocabulary_Register_v1.50 (1).md` | `f420286122cd622063b552d41c6649fb9a13c68f75f9e45625590e8f49edcbdc` | Current Supplement A §D.40 registration and Machine Guards | frozen/read-only |\n| `FOUNDATION` | `File_00.Repository_Foundation_Axiom_Engine_Source_Map(2).md` | `6b4cc688ab995f23574f9f7422bd38acfd659130347f1d14ce47220fa919b5b3` | Foundational state, node-class, Key, and source-map control | frozen/read-only |\n| `EXEMPLAR` | `File_51a.Rounded_Scaffold_Mod5_Architecture(6).md` | `31dfe17ef8b50bf583503af256cbae4e29a75b30613548047f4dc233473bacb4` | Procedural/state-register and Rounded/Actual firewall precedent | frozen/read-only |\n| `EXEMPLAR` | `File_54.Luke_70_Year_Genealogical_Lattice(5).md` | `1ff1914fa180de2aba3e8bf1bb81a3478dc1f8b0153dc722019ff392c3c87899` | Later-file claim-status and comparative restraint exemplar | frozen/read-only |\n| `SKL` | `File_21.SKL_Unified_Protocol(4).md` | `e42eb010a7fa499a08cc16249679f1069c8080a3beb4d2cf05ed5e0b728f27f8` | SKL Short/Long, +30, Pillars, scale state | frozen/read-only |\n| `SKL` | `File_34.Unified_Chronology_SKL_Berossus_Bible(4).md` | `4fa811c80332e002497ea326ba5e5ac273b3d35f4491383c0e721fb3ab17793b` | Full SKL/Berossus source-state and corridor controller | frozen/read-only |\n| `TABLE` | `File_18.Chronological_Data_Tables(20260825-214608).md` | `9f35b1e1915517052def2d490c113974aa324a7cad7e137bae1d93c86ad4a4a2` | Raw source tables; also controls existing 2648 BC BJ Ham label | frozen/read-only |\n| `LXX-MAX` | `File_14.Biological_Numerical_Fractals(5).md` | `8b65ac5e4538c36d9c873595597f8f92fd544b404126d885b7a2ce93ca12dcf2` | Controls LXX Maximum `5554/5555/5556 BC` endpoint/Year-7/Year-6 node classes | frozen/read-only |\n| `MT-CUMULATIVE` | `File_22.Cumulative_MT_Harmonics(10).md` | `bb722b0df2161a74911097f81c30e8cb51cc6a3e4ec76d0ca22f9d3112befc7c` | Dual 4346 BC MT convergence; cumulative 12600/12740 controls | frozen/read-only |\n| `CUMULATIVE` | `File_09.Cumulative_Architecture(8).md` | `a7910c13c2d1f471fbdc47d46ad0494c5f8f8c78951f74feb804173f04d40594` | Cumulative Creation/Flood/Cainan endpoint anatomy | frozen/read-only |\n| `ENOCH` | `File_68.Enochic_Seven_Week_Core(20260819-145634).md` | `2fb72e6c1267ac3e4f82549c0202cfe3c277131af7c07a4f7326f514adc8f303` | Enoch 70/72 carriers; 2946/2876 and 2666 comparison states | frozen/read-only |\n| `GENEALOGICAL` | `File_69.Enoch_Centered_Genealogical_Accordion(20260823-145801).md` | `e415d58136a6e9bcc5af3a34074a16c0a8a5925822349584fe5e37ad75c26efc` | 4346/2876/1406/AD 65 ladder and Enoch/Christ states | frozen/read-only |\n| `DANIELIC` | `File_45.Superstructure_14000_1400_Fractal.md` | `b2fcad8dd16316ccf82329e34e02b4c180631205af5f6085d3f5c3616af5d610` | Daniel 9 pattern-template and no-434-year-lock control | frozen/read-only |\n| `OPERATOR` | `File_46.Harmonic_Expansion_Protocols (1).md` | `aee775e8f23a477411d69ed3f009bc9232cafba7d27e982b58a99e123aeefb0d` | 4830/9660, 70/69, 25/23, 4900 operator mechanics | frozen/read-only |\n| `JUBILEES` | `File_53.Jubilees_22Fold_Creation_Genealogy_Witness(4).md` | `9f0e41022cab59a43c090c98224e55fe45e622a15e094dacad6721bea0aee8f3` | Pre-existing 4346/9660/9800/10120 ladder; non-overcount dependency | frozen/read-only |\n| `JUBILEES` | `File_20.Jubilees_Fourth_Witness(2).md` | `c8822cb5bb81a7ac72eac44774c0aba5e1470c1b1ba63b612a1364a393a440fe` | Controls existing 2648 BC BJ Ham birth node-class | frozen/read-only |\n| `GENEALOGICAL` | `File_43.Genealogical_Bridge(2).md` | `dde4eca7c1f64eaef93f1084cd6aef99776b38c7673c680e8ff8185c0fc5a987` | Controls existing 2666 BC genealogical interval labels | frozen/read-only |\n| `CALENDAR` | `File_12.Calendrical_Physics(5).md` | `89e3af8692c36cb3251880bc62db013441668dd3eabb3b8fd7770be96b6208fe` | 336/360/364 calendar-body non-collapse | frozen/read-only |\n| `ANCHOR` | `File_05.Exodus_Target_Fulcrum_Anchor(4).md` | `4f1b1d870a98eb23439df482bd3aa6956c8fbc5affbf1c10b90aae2a04dc8860` | Primary 1446 BC Exodus and Christological target controls | frozen/read-only |\n| `ANCHOR` | `File_06.Judges_Bridge(9).md` | `74c4c76b599f2af3759133a7c45da2bd7a0320ceb244b401956cddff9b3eb551` | 1406 BC Conquest and land-rest controls | frozen/read-only |\n| `CHRIST` | `File_13.Christological_Matrix(4).md` | `9d6543955ac330676fa8eca9d5db6bffdfef7c675106921f0ac15b99a8823d0c` | AD 30/65/70 and Passion-date hierarchy | frozen/read-only |\n| `KINGS` | `File_08.Kings_Resolution(20260815-183558).md` | `09ec95a5cf8e23c3fd55214065a2dc613a5d1f67e9623dca510f327851ad5640` | AD 70 historical Temple-destruction node | frozen/read-only |\n\nFile-Library-only dependencies remain read-only:\n\n| Dependency | Reference | Handling |\n|---|---|---|\n| `File_36 current Final` | `File Library reference: File_36_Final_Post_Final_Pressure_Tested.md` | appendix-only/read-only |\n| `File_33/File_36 P19 source-history` | `File Library reference: File_33_File36_Target_Mirror_Dependency_Update_Full_Replacement.md` | source-history/read-only |\n| `File_52e — The Subordinate LXX Inverse` | `File Library reference: Pasted text (9).txt / File_52e source-history copy` | read-only dependency for the independent Secondary `5816 BC` node and `5816→1406=4410`; does not control or prove the conjectural `5846→5816` rail assignment |\n# Appendix E. Reopened Pass-1B Arithmetic and Argument Verification\n\n## E.1 Protected-region result\n\n| Protected object | Pass-1B result |\n|---|---:|\n| frozen Final Supplement parent | hash exact |\n| frozen reciprocal File_70 parent | hash exact |\n| immediate Pass-1A parent | hash exact |\n| inherited §§1–7 | byte-exact |\n| inherited §§8.1–8.9 | byte-exact |\n| inherited `324` equations/results/IDs | exact |\n| inherited `52` Pass-1A Machine Guards | exact and unique |\n| superseding LXX Terah-pair / leveling guard | `1/1`; total `53/53` unique |\n\n## E.2 Arithmetic execution\n\n| Ledger | Rows | Result |\n|---|---:|---:|\n| consolidated evidence manifest | `446` | `446/446 PASS` |\n| newly admitted canonical rows | `122` | `122/122 PASS` |\n| bounded LXX family rows | `25` | `25/25 PASS` |\n| dependency-reference executions | `33` | `33/33 PASS` |\n| control-only executions | `42` | `42/42 PASS` |\n| existing/reweight references | `24` | `24/24 PASS` |\n| complete Pass-0 intake re-execution | `193` | `193/193 PASS` |\n\n## E.3 Evidence-accounting result\n\n| Object | Result |\n|---|---:|\n| inherited row-weight promotions | `22` Secondary → Primary |\n| inherited arithmetic mutations | `0` |\n| exact frozen-row duplicates added | `0` |\n| omitted body equation admitted | `1` (`KEY019`) |\n| parent-owned equations re-owned | `0` |\n| control equations counted as evidence | `0` |\n| generated coordinates promoted to Primary anchors | `0` |\n\n## E.4 Current trust disposition\n\nPass 1B, including the bounded LXX Terah-parallel, File_52e co-registration, and conjectural-leveling refinement, completed arithmetic and argument integration but was not an independent verification pass. Appendix G supersedes that pending disposition: Independent Pass 2, the combined pressure test, author-invoked Finalization, central registration, the affected-only no-change reciprocal review, and expanded File_70 routing are complete. Publication replacement remains separate.\n\n# Appendix F. Pass-1B Family/Weight Map and Pass-2 Handoff\n\n| Family / source | Rows | Pass-1B disposition |\n|---|---:|---|\n| inherited manifest | `324` | equations/results/IDs preserved; `22` targeted weight promotions |\n| original newly admitted canonical rows | `97` | `96` new relations plus `KEY019` |\n| bounded LXX exact corroboration rows | `20` | Principal corroboration; row-level Secondary |\n| bounded LXX leveling rows | `5` | Appendix-led conjectural corollary |\n| total newly admitted canonical rows | `122` | original Pass-1B plus bounded LXX exact/conjectural amendment |\n| dependency-reference executions | `33` | exact; cited rather than re-owned |\n| control-only executions | `42` | exact; outside evidence count |\n| existing/reweight references | `24` | exact; outside evidence count |\n| consolidated manifest | `446` | `176` Primary; `229` Secondary; `41` Appendix |\n\nMachine-readable Pass-1B artifacts are listed in the companion report and verification package. Appendix G records the completed independent rebuild rather than a mere rereading of those ledgers.\n\n# Appendix G. Independent Pass-2 Verification and Combined Pressure Test\n\n## G.1 Independent arithmetic reconstruction\n\n| Object | Result |\n|---|---:|\n| canonical arithmetic rows | `446/446 PASS` in independent Fraction and SymPy engines |\n| source-manifest rows | `446/446 exact` against the consolidated TSV |\n| inherited frozen-parent arithmetic | `324/324` equations, results, and IDs preserved; seven inherited function-cell backticks mechanically restored |\n| full-source parseable equality chains | `326/326 PASS` |\n| one-token arithmetic mutations | `446/446 rejected` |\n\n## G.2 State and argument pressure test\n\n| Control family | Result |\n|---|---:|\n| critical theorem and claim controls | `60/60 PASS` |\n| arithmetic wrong-state/operator/anchor attacks | `42/42 rejected` |\n| LXX claim-ceiling assertions | `4/4 PASS` |\n| Machine Guards | `53/53` unique; first `52/52` exact against Pass 1A; superseding LXX guard retained |\n| mounted dependency hashes | `27/27 PASS` |\n| mounted dependency content assertions | `14/14 PASS` |\n| File_52e read-only assertion | `PASS` — `5816→1406 BC=4410=9×490`; no proof of the `5846→5816` rail assignment |\n| proof-bearing region | equations/results/weights/IDs exact; seven inherited function-cell backticks restored |\n| headings / tables / fences | `126` headings clean; `42/42` tables valid; `402` fence markers balanced |\n\n## G.3 LXX disposition after attack\n\nThe exact LXX evidence survives as Principal cross-tradition corroboration:\n\n```text\n1380 = 690+690 = 60×23 = 20×69,\n30|1410|30,\n5556−4836 = 4836−4116 = 720,\n5494−1446 = 4048,\n4048×25/23 = 4400,\n1446+4400 = 5846 BC.\n```\n\nThe proposed leveling also survives arithmetically:\n\n```text\n5846−30 = 5816,\n5816−4346 = 1470,\n4346−2876 = 1470.\n```\n\nIts **state assignment does not graduate beyond conjecture**. File_52e independently corroborates `5816 BC`, but no source establishes `5846 BC` as an applied `+30` member. Therefore `LXX021–LXX025` remain Appendix-weight, `5846 BC` remains generated, and `5816 BC` remains a provisional leveled companion rather than a transmitted LXX date or Primary anchor.\n\n## G.4 Pass-2 conclusion\n\nIndependent Pass 2 and the combined pressure test identify no proof-bearing defect. The integrated source is Final by explicit author instruction. The combined pre-Finalization pressure test remains the current proof trust basis. Central registration of all `53/53` guards, affected-only no-change review, and expanded File_70 reciprocal routing are complete; publication artifacts remain separate actions.\n\n# Appendix H. Sothic module verification and unresolved applications\n\nThis appendix belongs only to the bounded September 6 2026 addition. Appendix A's inherited `446` rows and their evidence weights are unchanged. The current package verifies `116` scalar rows in Fraction and SymPy and `141` phase/set/sensitivity/rejection assertions across the coordinated File_12/File_22/Supplement amendment family. These are executable test counts, not `257` independent witnesses and not a new full pressure test of this source.\n\nThe compact source arithmetic is `4×1460=5840`, `4×1460.5=5842`, `4×1461=5844`, `4×1461.5=5846`, with the exact `8/12/8/4` overlap inventory. `R(x)=−5842−x` squares to identity and gives six transpositions. Opposed macro shifts preserve the sum; the full nested comparison contains `36` nodes. The fixed Long–Moses matrix in §13.9 preserves the missing `4383` as a negative result.\n\nOpen scope: remote SKL Creation/Flood source-chain propagation; any separately specified adjacent-state completion of the missing Long member; historical interpretation and formal statistical evaluation. The distinct File_22 Pillar residual `4.5` remains unresolved and is not filled by this supplement's inherited similarly numbered operators.\n\nThe package retains a runnable verification program, exact scalar manifest, every fixed-field image, source fingerprints, and the complete amendment diff. Historical verification assertions elsewhere in this inherited file refer to the frozen earlier Final source unless explicitly dated September 6 2026.\n\n## Revision Log\n\n### August 28 2026 — Central registration, affected-only reciprocal review, and expanded File_70 routing\n\n- Registered the `17` reopening guards verbatim at State Vocabulary Register v1.51 Part D §D.41; the inherited `36` guards remain byte-exact at §D.40, giving `53/53` centrally registered Supplement guards.\n- Replaced—not supplemented—the prior File_70 reciprocal guard with one expanded guard registered verbatim at §D.41; File_70 remains `58/58` current guards (`57` inherited plus one reciprocal).\n- Completed the affected-only review of the new common-parent, Danielic, cumulative, LXX, seam-collision, and File_52e interfaces. No content-source amendment is required beyond the bounded reciprocal File_70 replacement.\n- Refreshed only current trust-state, control-pointer, dependency-routing, and disposition text in this source. Appendix A, all `446` arithmetic rows, all `53` guard bodies, evidence weights, equations, node classes, claim ceilings, and Primary-anchor boundaries remain unchanged.\n- Publication layers remain separate.\n\n### August 28 2026 — Renewed author-invoked Finalization\n\n- Finalized `File_70_Supplement_A.Key_of_23_Fine_Resolution_720_30_Rail.md` by explicit author instruction.\n- Changed only active status, workflow and trust-state framing, §0.9, §12.2, Appendix E.4, Appendix G.4, the Revision basis, and Revision-Log wording.\n- Preserved all `446/446` canonical arithmetic rows, the `176/229/41` evidence-weight inventory, all `53/53` Machine Guards, all dependency boundaries, the File_52e read-only assertion, the LXX conjecture ceiling, and every proof-bearing equation and conclusion.\n- Focused Finalization-diff verification found only permitted changes; no new full post-Finalization pressure test is claimed.\n- Central registration of the `17` reopening guards, affected-only reciprocal review, reciprocal File_70 routing, and publication layers remain separate.\n- Status: Final; no source-level blocker.\n\n### August 28 2026 — Reopened Independent Pass 2 and combined pressure test\n\n- Preserved the integrated LXX endpoint/Year-6 Terah-parallel matrix, doubled `690` body, `30|1410|30` grammar, `±720` cumulative-Flood center, and Priestly `5846 BC` head.\n- Independently rebuilt and re-executed all `446` canonical rows in Fraction and SymPy.\n- Rejected `446` one-token arithmetic mutations and `42` arithmetic wrong-state, wrong-anchor, wrong-Key, year-zero, center-collapse, seam-collapse, and conjecture-promotion attacks.\n- Verified `60` critical theorem/claim controls, `4` LXX claim-ceiling assertions, all `53` guards, `27` mounted dependency hashes, `14` mounted dependency content assertions, the File_52e `5816 BC` read-only assertion, inherited-row preservation, and Markdown structure.\n- Retained `LXX001–LXX020` at Secondary row weight and `LXX021–LXX025` at Appendix weight. The `5846→5816` state assignment remains conjectural despite exact arithmetic and independent File_52e coordinate recurrence.\n- No arithmetic, anchor, node-class, operator, evidence weight, claim ceiling, or principal conclusion changed.\n- Historical stage status: Independent Pass 2 Verification and the combined pressure test complete; ready for author-invoked Finalization and not Final at that stage.\n\n### August 28 2026 — Reopened Pass 1B\n\n- Executed the arithmetic and completed the argument for the four-node Enochian–SKL, MT common-parent, reconciliation-ladder, Cumulative–Pillar, Flood-partition, Cainan-continuation, and Danielic-seam families.\n- Partitioned the original `193`-row intake into `97` newly admitted canonical rows (`96` new relations plus `KEY019`), `30` dependency references, `42` controls, and `24` remaining existing/reweight references.\n- Preserved all `324` inherited equations/results/IDs and promoted `22` inherited rows without arithmetic mutation.\n- Added `KEY019` for `3576−700=2876`.\n- Retained the correction of the discussion shorthand `4106` to the required MT Year-6 node `4116 BC`.\n- Added matched endpoint and Year-6 Terah-pair controls: `5554/5494 ↔ 4174/4114 BC` and `5556/5496 ↔ 4176/4116 BC`, each `1380=690+690`.\n- Added five Appendix-weight arithmetic rows for the conjectural positional leveling `5846→5816 BC`, yielding the candidate `5816→4346→2876 BC = 1470|1470` ladder without promoting `5816 BC` to a source date.\n- Refined the Terah-parallel body as `1380=60×23=20×69`, routed its `1400/1500` Key completions as dependency-reference executions, and registered File_52e’s independent Secondary `5816 BC` occurrence as coordinate corroboration only.\n- Established the refined working `446`-row manifest at `176` Primary, `229` Secondary, and `41` Appendix rows.\n- Preserved all `52` Pass-1A Machine Guards and superseded the prior LXX guard in place with one expanded Terah-pair / conjectural-leveling guard, leaving `53/53` current guards.\n- Historical stage status: Reopened Pass 1B with bounded LXX Terah-parallel, File_52e co-registration, and conjectural-leveling refinement complete; Independent Pass 2 and combined pressure test pending, and not Final at that stage.\n\n\n## September 6 2026 bounded Sothic amendment record\n\nPrepared under the author's explicit consolidation/update instruction and delegated implementation choice. Intake, additive structure/state preparation, arithmetic/argument review, and bounded verification were performed within the current response. The complete earlier Final parent is preserved, and all pre-existing proof equations, node classes, and guard bodies remain unchanged. The new additions are verification-complete bounded working text, centrally registered but not separately author-Finalized or full-file pressure tested. Active controls are Capsule v11.51 / Register v1.52 / Style Guide v2.5 / Procedures v3.5.\n\nOpen scope and adoption: explicit Finalization; registration of the new local states/guards; remote SKL source-chain test; the absent fixed-field `4383`; the actual-Apparent-Adam `4.5` residual. Source/control review proposals and complete diffs are supplied in the consolidation package. No publication manifest, archive replacement, deployment, or external preservation capture is claimed.\n", "evidenceLinks": [{"id": "d-45851004c5864229", "title": "File 09"}, {"id": "d-ed718a9e579978a9", "title": "File 00"}, {"id": "d-e415d58136a6e9bc", "title": "File 69"}, {"id": "d-0066d07fd7bf2db4", "title": "File 29"}, {"id": "d-1ff1914fa180de2a", "title": "File 54"}, {"id": "d-dde4eca7c1f64eae", "title": "File 43"}, {"id": "d-c2511c7710955ad5", "title": "File 16"}, {"id": "d-9f0e41022cab59a4", "title": "File 53"}, {"id": "d-4f1b1d870a98eb23", "title": "File 05"}, {"id": "d-1d981a97f78fbbfb", "title": "File 01"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-9a1eff41920cd0f8", "title": "File 12"}, {"id": "d-e42eb010a7fa499a", "title": "File 21"}, {"id": "d-c8822cb5bb81a7ac", "title": "File 20"}, {"id": "d-2fb72e6c1267ac3e", "title": "File 68"}, {"id": "d-18e8c54ff1663fb1", "title": "File 46"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}, {"id": "d-1c77fd504afbf59b", "title": "File 22"}, {"id": "d-0f5ab858ab7f6e1f", "title": "File 17"}, {"id": "d-c4ad12833900f43d", "title": "File 11"}, {"id": "d-4fa811c80332e002", "title": "File 34"}, {"id": "d-0fa80217c94b3951", "title": "File 70"}, {"id": "d-8b65ac5e4538c36d", "title": "File 14"}]}