{"id": "d-dde4eca7c1f64eae", "title": "File_43 — Genealogical Bridge", "filename": "06-File_43.Genealogical_Bridge-2-.md", "role": "Source", "step": null, "sha256": "dde4eca7c1f64eaef93f1084cd6aef99776b38c7673c680e8ff8185c0fc5a987", "bytes": 86095, "origins": ["Attached repository/06-File_43.Genealogical_Bridge-2-.md", "C480–C1634/Research_Cycles/C0732_C0831/evidence/sources/06-File_43.Genealogical_Bridge-2-.md", "C480–C1634/Research_Cycles/C0832_C0931/evidence/sources/06-File_43.Genealogical_Bridge-2-.md", "C480–C1634/Research_Cycles/C0932_C1131/evidence/sources/06-File_43.Genealogical_Bridge-2-.md", "C480–C1634/Research_Cycles/C1132_C1431_Recovered/evidence/sources/06-File_43.Genealogical_Bridge-2-.md"], "download": "/sources/dde4eca7c1f64eaef93f1084cd6aef99776b38c7673c680e8ff8185c0fc5a987.md", "format": "md", "derived": false, "tags": ["Cumulative", "Rounded", "Inverse", "Calendar Keys", "Covenant", "Counts & NT", "Mirror / 529"], "excerpt": "File: File_43\nTitle: Genealogical Bridge\nEntity: Genealogical Bridge (Matthew / Luke)\nClassification: Theological Lattice / Genealogical Harmonics\nUUID: GEN_BRIDGE_LUKE_MATT_SPLIT\nStatus: Final; File_44 terminology-harmonization cycle integrated and focused pressure tested during trust-status equalization; prior post-f", "content": "File: File_43\nTitle: Genealogical Bridge\nEntity: Genealogical Bridge (Matthew / Luke)\nClassification: Theological Lattice / Genealogical Harmonics\nUUID: GEN_BRIDGE_LUKE_MATT_SPLIT\nStatus: Final; File_44 terminology-harmonization cycle integrated and focused pressure tested during trust-status equalization; prior post-final pressure-tested status retained as source-history; source status DEFINED retained; bounded Final File_69 reciprocal pointer applied August 17 2026; bounded Final File_69 August 18 thematic reciprocal extension applied and focused verified August 18 2026.\nPressure-test status: Current; focused pressure test complete for the File_44 terminology-harmonization finalization and public-clean cleanup; prior June 8 2026 post-final and Alpha-Omega 22-fold focused tests retained; focused reciprocal-routing verification complete August 17 2026 for the bounded File_69 pointer; no new full pressure test claimed; focused reciprocal-routing verification complete August 18 2026 for the bounded File_69 August 18 extension; no new full pressure test claimed.\nReciprocal-routing verification status: Bounded Final File_69 pointer applied and focused machine-diff, dependency, guard, Markdown-structure, and publication-clean checks completed August 17 2026; no new full pressure test was performed for this pointer-only update; bounded Final File_69 August 18 pointer applied and focused machine-diff, dependency, guard, Markdown-structure, and publication-clean checks completed August 18 2026; no new full pressure test.\nRegister Agreement status: Checked against State_Vocabulary_Register v1.17 and active companion controls; convergence / pointer update only; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries changed; File_69 reciprocal guard registered at State_Vocabulary_Register v1.41 Part D §D.33 and routed through Restart Capsule v11.40; no pre-existing proof-bearing state or Primary anchor changed; File_69 August 18 reciprocal guard registered at State_Vocabulary_Register v1.42 Part D §D.33 and routed through Restart Capsule v11.41; no pre-existing proof-bearing state or Primary anchor changed.\nPublication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive; bounded File_69 reciprocal replacement incorporated into the Manifest v22 non-archive release package; no live deployment or external archival capture claimed; bounded File_69 August 18 reciprocal replacement incorporated into the Publication Manifest v23 release package; no live deployment or external archival capture claimed.\nSource status: DEFINED (Harmonized with v10.1 capsule protocol)\nPrimary domain: NT Genealogical; Theological; Comparative; Structural\nTraditions: NT / Luke; NT / Matthew; Davidic typological framing by dependency\nCanonical source: Markdown\nPrimary anchors: 5326 BC; 5286 BC; 5256 BC; 2806 BC; 2876 BC; 6 BC; 36 BC; AD 25; AD 65; AD 135; 2450; 8050; 8750; 700; 14006 BC\nDependency-controlled explanatory anchors: 5356/5286 BC; 36 BC/AD 35; AD 5285/5355; AD 5355; 10710; 10780; 153; 154; 22 × 490; 22 × 7 × 70\nRelated files: File_00; File_13; File_15; File_32 by bounded P2 dependency; File_33 by Prime–Civil / Polarity Namespace reinforcement; File_42 by bounded geometry-first source-history support; File_44 as downstream / reciprocal scaling-law context; File_53 by File_54 dependency; File_54; Restart Capsule v11.15; State Vocabulary Register v1.17; 490d Repository Style Guide v2.5; Project Procedures v3.2; File_69\nMajor operators: 70-year generational carrier; LukeSpan; LukeIntervals; MattSpan_BirthHinge; MattSpan_Carrier; File_32 / File_33 positive-polarity date-output / rails-space `B/M` state where the P2 positive rails-window is opened; File_32 / File_33 negative-polarity / signed A-space bridge where the P2 bridge is opened; P2 positive rails-window local Operator A; P2 negative-polarity / signed A-space local Operator B; 25/23; 50 × 49; 5 × 490; 125 × 70; 5³ × 70; civil cross-axis span `BC + AD − 1`\nMajor modal states: LukeSpan names-span state; LukeIntervals interval-count state; Luke birth-hinge bracket state; Luke P2 rail-bracket state; MattSpan_BirthHinge state; Matthean head-envelope marker state; MattSpan_Carrier state; File_32 / File_33 Prime–Civil / Polarity Namespace state; P2 positive rails-window local Operator A state; P2 negative-polarity / signed A-space local Operator B state by bounded File_32 dependency; P2 local-label restraint state; display-table-only genealogy ledger; author-resolved figurative God bookend label state; bounded File_32 P2 namespace state; File_44 reciprocal scaling-law context state; double-generational knot compositional state; Job-only restoration warrant state; outer Luke rail / overlapped middle-generation state by File_54 dependency; Alpha-Omega 22-fold bracket state by File_54 / File_53 dependency; Revelation threefold Alpha-Omega reception-history note; Jubilee bridge state; MirrorVolume span-provenance state; ordinary Key-of-23 whole-year expansion state; Seal700 state; cumulative cube lock state; optional 40/70/100 display motif state; inactive Residue Protocol state\nMajor claim-status labels: textual / genealogy-count datum by dependency; arithmetic fact; exact-ratio arithmetic fact; structural inference; structural / compositional operator; display motif; typological framing; author-clarified theological note; author-clarified typological note; reception-history note; shared-tradition evidence; source-retained structural label; dependency-controlled; Machine Guard; argument-control result; audit note\nRevision basis: 490d Repository Style Guide v2.5; Restart Capsule v11.15; State Vocabulary Register v1.17; Project Procedures v3.2; source `FILE_43: GENEALOGICAL_BRIDGE.md`; File_54 Final comparison; File_32 / File_33 Prime–Civil / Polarity Namespace controls; File_44 Final Post-Final Pressure Tested reciprocal scaling-law controls; prior finalized File_43 source; Repository_Change_Archive (non-controlling history); Final File_69; State Vocabulary Register v1.41; Restart Capsule v11.40; Publication Manifest v22 non-archive release package; Final File_69 August 18 thematic reopening; State Vocabulary Register v1.42; Restart Capsule v11.41; Repository Change Archive v1.51; Publication Manifest v23.\nCurrent refresh note: Public-clean trust-status equalization aligns active control pointers to 490d Repository Style Guide v2.5, Restart Capsule v11.15, State_Vocabulary_Register v1.17, and Project Procedures v3.2. Register Agreement status is recorded in the header; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries are changed. Detailed pass logs, pressure-test records where applicable, pointer-refresh history, and replacement-workflow notes are preserved in Repository_Change_Archive; Bounded File_69 reciprocal routing applied August 17 2026; the registered guard changes no pre-existing arithmetic, anchor, source duration, node-class, operator, sign convention, calendar definition, Mirror protocol, claim-status label, theological claim, or dependency boundary; Bounded File_69 August 18 reciprocal routing applied; the registered guard changes no pre-existing arithmetic, anchor, source duration, node-class, operator, sign convention, calendar definition, Mirror protocol, claim-status label, theological claim, or dependency boundary.\n\n# File_43 — Genealogical Bridge\n\n## Related Repository Files\n\n| File | Function for `File_43` |\n|---|---|\n| `File_00` | Foundational source-map discipline, arithmetic-control / argument-control layering, Machine Guard style, and civil / Mirror / inverse firewalling. |\n| `File_13` | Christological and Luke/Matthew dependency controls where broader Christological anchors are opened. |\n| `File_15` | Generational-unit controls for the 70-year Jacobean carrier and optional 40/70/100 display motif. |\n| `File_32` | Current bounded Prime–Civil / Polarity Namespace control for the P2 positive rails-window `6 BC / 36 BC` and the P2 negative-polarity / signed A-space bridge `6 BC / AD 25`; this is the active P2 dependency route after author decision. No broader prime-system proof is imported here. |\n| `File_33` | Reinforces the File_32 Prime–Civil / Polarity Namespace, especially polarity-before-Mirror hierarchy, positive-polarity rails-space `B/M`, negative-polarity / signed A-space output, and Coordinate Mirror as secondary agreement. File_33 Ordinal Authentication is not opened locally. |\n| `File_42` | Geometry-first source-history support for the P2 dual-operator split, MirrorVolume, Key-of-23 expansion, and Seal700. It is not reactivated as File_43's primary P2 dependency route; active P2 terminology remains routed through File_32 / File_33. |\n| `File_44` | Downstream / reciprocal scaling-law module that depends on File_43's P2 non-straddling, MirrorVolume, Seal700, double-generational knot, and display-vs-lock controls. File_44 is context for terminology restraint, not a proof source for File_43. |\n| `File_53` | Dependency opened only through `File_54` for the BJ / Jubilees 22-fold Creation-genealogy witness and its 22-created-works / covenantal-heads pattern. No full `File_53` proof burden is imported here. |\n| `File_54` | Later comparative synthesis that depends on `File_43` for LukeSpan, LukeIntervals, the 70-year carrier, the `6 BC` hinge, and the `36 BC` rail. It also supplies the outer Luke rail / Alpha-Omega 22-fold clarification used dependency-controlled in §6.3. |\n| `Restart Capsule v11.15` | Repository-wide anchors, operators, modal states, and File_54 dependency controls. |\n| `490d Repository Style Guide v2.5` | Source formatting, terminology, modal-state control, claim-status labels, no-comma numbers, and cross-axis span discipline. |\n| `Project Procedures v3.2` | Project workflow controls, authorial-direction protocol, audit-note discipline, Context Economy, Novelty Verification Rule, and canonical Markdown / derived-format boundary. |\n| `State Vocabulary Register v1.17` | Current per-file modal-state vocabulary, convention entries, and Machine Guards. |\n\nFile_69 genealogical-bridge reciprocal note:\nFinal File_69 extends the File_43 bridge through the Jeconiah-overlap `42`-slot state, the `21+42=63` composite, and Enoch-centered multi-resolution tables. File_43's original LukeSpan and MattSpan locks remain unchanged.\n\nMachine Guard [FILE_43 FILE_54 FILE_69 GENEALOGICAL-BRIDGE ROUTING]:\nFinal File_69 may register the Jeconiah exile-overlap `42`-slot state, the `21+42=63` composite, and the Enoch-centered Luke/Matthew tables by dependency. File_43 retains control of LukeSpan, LukeIntervals, MattSpan_BirthHinge, MattSpan_Carrier, the `6 BC` hinge, the `36 BC` rail, and its `2806/2876 BC` node-class distinction. File_54 retains control of the Rounded Scaffold / BJ comparison. File_69 does not replace either proof spine or promote its generated coordinates into those files' Primary anchors.\n\nFile_69 Matthean-microcosm reciprocal note:\nFinal File_69 now treats Matthew's undoubled `14|13|14=41` as the local textual microcosm containing both `14+13` and `13+14`, while Jeconiah completes the declared `14|14|14=42`. The reduced `62` and leading `63` composites, and the paired `2806/2876` and `2888/2960 BC` Abraham-head states, remain downstream File_69 applications only.\n\nMachine Guard [FILE_43 FILE_54 FILE_69 MATTHEAN-MICROCOSM ROUTING]:\nFinal File_69 may register Matthew's undoubled `14|13|14=41`, Jeconiah-completed `14|14|14=42`, the reduced `62=21+41` composite, the leading `63=21+42` full-outer composite, and the `2806/2876 BC` primary and `2888/2960 BC` companion Abraham-head distinctions. File_43 retains control of LukeSpan, LukeIntervals, MattSpan_BirthHinge, MattSpan_Carrier, the `6 BC` hinge, the `36 BC` rail, and the original `2806/2876 BC` node-class distinction. File_54 retains control of the Rounded Scaffold / BJ comparison. No File_69 generated coordinate becomes a parent-file Primary anchor.\n\n## 0. File-function\n\n`File_43` defines the Matthew / Luke Genealogical Bridge by harmonizing the Lukan and Matthean genealogical schemata through a locked 70-year carrier while preserving mandatory split states.\n\nThe file enforces four primary non-collapse rules:\n\n1. `LukeSpan` and `LukeIntervals` remain distinct.\n2. `MattSpan_BirthHinge` and `MattSpan_Carrier` remain distinct.\n3. The P2 rails-window operator remains distinct from the P2 A-space bridge operator.\n4. No `30`-year straddling operator is permitted.\n\nThis file supplies upstream locks used by `File_54`, especially LukeSpan, LukeIntervals, the `6 BC` hinge, the `36 BC` rail, the 70-year carrier, MirrorVolume `8050`, the `25/23` expansion to `8750`, and Seal700.\n\nThis reopened harmonization cycle also records `File_44` as downstream / reciprocal context. `File_44` uses `File_43` for scaling-law controls, but `File_44` does not become a proof source for `File_43`.\n\nTerminology-control rule:\nWhere this file preserves the local shorthand `Operator A` and `Operator B`, those labels are confined to the P2 split only: local Operator A is the P2 positive rails-window `6 BC / 36 BC`; local Operator B is the P2 negative-polarity / signed A-space bridge `6 BC / AD 25`. These labels must not be exported to unrelated ratio expansions, scaling operators, or later prime-grid systems.\n\nThis file does not replace `File_13`, `File_15`, `File_32`, `File_33`, `File_42`, `File_44`, or `File_54`. It depends on them only where their local states are active.\n\nPublication-cleanup note:\nThis public-clean source preserves the Final status, prior post-final pressure-tested source-history, and the caution that the current File_44 terminology-harmonization finalization was focused pressure tested during trust-status equalization. Detailed pass ledgers, pressure-test records, harmonization logs, and revision-log material are archived rather than repeated in the public body.\n\nArgument-control rule:\nArithmetic locks and span provenance carry the file’s base layer. Display motifs and compositional warrants may frame the genealogy ledger, but they do not create arithmetic drivers.\n\nModal-state rule:\nA shared value, date, span, or generation count does not create identity unless state, node-class, tradition, and operator agree.\n\n## 0.1 Working state register\n\n| State | Value or anchor | Node-class / function | Handling in `File_43` |\n|---|---:|---|---|\n| Locked generational carrier | 70 years | Jacobean carrier unit | Active unit for Luke and Matthew displays. |\n| LukeSpan names-span state | 5320 = 76 × 70 | names-span | Adam → Christ as names; not the interval count. |\n| LukeIntervals interval-count state | 5250 = 75 × 70 | interval count | Intervals between 76 names; active MirrorVolume input. |\n| Luke `6 BC` birth-hinge bracket | 6 BC → 5326 BC | birth-hinge projection | Uses LukeSpan from the Christ-side hinge. |\n| Luke `36 BC` rail bracket | 36 BC → 5286 BC | P2 rails-window bracket | Rails-window display only; not the A-space bridge to AD 25. |\n| MattSpan_BirthHinge state | 2800 = 40 × 70 | Abraham → 6 BC bracket | Active MirrorVolume input. |\n| Matthean head-envelope marker | 2876 BC | envelope marker | `2806 BC + 70`; not a distinct span lock. |\n| MattSpan_Carrier state | 2870 = 41 × 70 | Abraham → AD 65 carrier | Carrier bracket; not a MirrorVolume input. |\n| Display genealogy ledger | 5326 BC → AD 135 | display table | Mechanized 70-year ledger; non-lock. |\n| Figurative God bookend label | God → Adam → Christ | theological / display bookend | Author-resolved Luke-derived label; signifies `Adam, son of God` and Christ the Son of God, not divine origination or literal birth chronology for God. |\n| Jubilee bridge state | 2450 = 5 × 490 = 50 × 49 | head-to-head bridge | Luke head bracket to Matthean head bracket. |\n| MirrorVolume state | 8050 = 5250 + 2800 | hard span-provenance volume | Uses LukeIntervals and MattSpan_BirthHinge only. |\n| Key-of-23 expansion state | 8050 × 25/23 = 8750 | exact expansion | Ordinary Key-of-23 whole-year expansion; not Residue Protocol. |\n| Seal700 state | 700 = 8750 − 8050 = 10 × 70 | expansion seal | Generated by the `25/23` expansion. |\n| Double-generational knot | compositional end-cap operator | display / literary framing | Not an arithmetic input. |\n| Job-only restoration warrant | Job `140`; restored double-fold display `280`; four-generation witness | typological / compositional warrant | Author-clarified Job-only analogy for doubled restoration; unclear secondary warrant removed. |\n| Outer Luke rail / overlapped middle generation | `5356 BC → AD 5355 = 10710 = 153 × 70`; `10710 + 70 = 10780 = 154 × 70 = 22 × 490` | File_54 dependency-controlled Mirror coordinate-completion / appendix support | Explains the 153 + 1 structure and the doubled central Christ-generation; does not alter local File_43 span locks. |\n| Alpha-Omega 22-fold bracket state | `22 × 490 = 22 × 7 × 70`; Revelation 1:8; Revelation 21:6; Revelation 22:13 | typological / reception-history display by File_54 / File_53 dependency | Reads the outer Luke rail as a start / center / end Alpha-Omega bracket aligned with Hebrew 22-letter symbolism and the BJ / Jubilees 22-fold Creation-genealogy witness; not a local arithmetic driver. |\n| Cumulative cube lock | 14006 BC → 5256 BC = 8750 = 125 × 70 = 5³ × 70 | dependency-controlled cumulative lock | Preserved where already authorized by the capsule anchor set. |\n| Optional 40/70/100 triad | 40; 70; 100 | display motif | Non-lock; not a driver for deriving spans. |\n| File_32 / File_33 Prime–Civil / Polarity Namespace | positive-polarity rails-space `B/M`; negative-polarity / signed A-space; Coordinate Mirror secondary | terminology-control state | Active only for naming the P2 split; no broader prime proof burden is opened. |\n| P2 local-label restraint state | Operator A; Operator B | local shorthand control | Operator A/B labels are local to the P2 split and must not be reused for unrelated ratio or scaling operators. |\n| File_44 reciprocal scaling-law context | MirrorVolume; Seal700; P2 non-straddling; display-vs-lock discipline | downstream context | Registered for terminology restraint only; not proof-bearing upstream. |\n| Anti-straddling guard | 36 BC ↔ 6 BC; 6 BC ↔ AD 25 | P2 operator split | Operator A and Operator B must not be chained. |\n\n## 0.2 File map\n\n| Section | Function | Active state / operator |\n|---|---|---|\n| §0 | File-function and state controls | file-level modal states and dependency boundaries |\n| §0.9 | Records final arithmetic-control verification | same-side spans; cross-axis spans; exact ratios; ledger rows |\n| §0.11 | Registers final author decisions | File_32 routing; resolved God bookend label; Job-only warrant; File_54 outer Luke rail note; Alpha-Omega 22-fold clarification |\n| §0.12 | Confirms harmonized modal-state boundaries | File_32 / File_33 namespace; File_42 source-history support; File_44 reciprocal context |\n| §0.13 | Confirms harmonized arithmetic controls | no arithmetic correction; operator preservation |\n| §0.14 | Confirms harmonized argument status | proof-burden separation; claim-status calibration; non-driver guards |\n| §1 | Defines the 70-year unit and Davidic display motif | Jacobean carrier; display-only `30 + 40` motif |\n| §2 | Separates LukeSpan from LukeIntervals | LukeSpan; LukeIntervals; P2 rail bracket |\n| §3 | Separates MattSpan_BirthHinge from MattSpan_Carrier | Matthew dual-bracket protocol; display table |\n| §4 | Establishes the Luke / Matthew head-to-head Jubilee bridge | 2450 = 5 × 490 = 50 × 49 |\n| §5 | Defines MirrorVolume, Key-of-23 expansion, and Seal700 | 8050; 8750; 700; `25/23` |\n| §6 | Defines the double-generational knot and God / Alpha-Omega bookend logic | compositional operator only; figurative God bookend label; Alpha-Omega 22-fold bracket state |\n| §7 | Prohibits 30-year straddling | File_32 / File_33 P2 namespace; local Operator A / Operator B separation |\n| §8 | Preserves the cumulative cube lock | dependency-controlled `8750` cube lock |\n| §9 | Restricts the 40/70/100 triad | display motif only; anti-overfitting guard |\n| Revision sections | Records completed passes, source-history finalization, pressure-test status, and current File_44 terminology-harmonization cycle | no arithmetic or argument-status overclaim; current harmonized final source focused pressure tested during trust-status equalization |\n\n## 0.3 Machine Guards\n\nMachine Guard [SPAN SPLIT]:\nDo not use `LukeSpan` where the file requires `LukeIntervals`. Do not use `LukeIntervals` where the file requires `LukeSpan`.\n\nMachine Guard [MATTHEW SPLIT]:\nBare `Matthew span` is disallowed. Specify either `MattSpan_BirthHinge = 2800` or `MattSpan_Carrier = 2870`.\n\nMachine Guard [P2 NON-STRADDLING]:\nDo not chain `36 BC ↔ 6 BC ↔ AD 25` as a single operator. `36 BC ↔ 6 BC` belongs to the P2 positive rails-window, locally retained as Operator A. `6 BC ↔ AD 25` belongs to the P2 negative-polarity / signed A-space bridge, locally retained as Operator B.\n\nMachine Guard [DISPLAY TABLE ONLY]:\nThe genealogy ledger is a mechanized 70-year display table. It must not overwrite LukeSpan, LukeIntervals, MattSpan_BirthHinge, MattSpan_Carrier, MirrorVolume, Expanded volume, or Seal700.\n\nMachine Guard [MIRRORVOLUME PROVENANCE]:\nMirrorVolume `8050` uses `LukeIntervals = 5250` and `MattSpan_BirthHinge = 2800` only. `MattSpan_Carrier = 2870` must not be substituted into `8050`, `8750`, or Seal700.\n\nMachine Guard [P2 FILE_32 / FILE_33 ROUTE]:\nThe former skipped-prime dependency label is removed by author decision. Active P2 terminology in `File_43` is routed through bounded File_32 / File_33 Prime–Civil / Polarity Namespace controls: P2 positive rails-window `6 BC / 36 BC` and P2 negative-polarity / signed A-space bridge `6 BC / AD 25` remain separate.\n\nMachine Guard [P2 LOCAL-LABEL RESTRAINT]:\n`Operator A` and `Operator B` are local shorthand labels for the File_43 P2 split only. Do not export those labels to unrelated ratio expansions, scaling-law operators, File_44 exact-ratio expansions, File_33 Ordinal Authentication, File_35 Half-Step, File_36 target-Mirror machinery, or later prime-grid systems.\n\nMachine Guard [FILE_42 SOURCE-HISTORY NON-REACTIVATION]:\n`File_42` may be noted as geometry-first source-history support for P2, MirrorVolume, Key-of-23 expansion, and Seal700. It does not replace the active File_32 / File_33 P2 namespace in `File_43` and must not revive the former skipped-prime active dependency label.\n\nMachine Guard [FILE_44 RECIPROCAL NON-IMPORT]:\n`File_44` is downstream / reciprocal scaling-law context. It confirms terminology restraint and display-vs-lock discipline, but it does not import File_44 scaling-law proof burden, File_44 Creation-head triad logic, or File_45 exact-sweep statistics into `File_43`.\n\nMachine Guard [GOD BOOKEND LABEL]:\nThe display-ledger `God` label is author-resolved as a figurative Luke-derived bookend label. It refers to `Adam, son of God` and Christ the Son of God, completing the bookend frame. It must not be read as a claim that God came into existence or as a literal chronological generation for God.\n\nMachine Guard [JOB-ONLY WARRANT]:\nThe double-generational knot may use Job as a typological restoration warrant. The unclear secondary warrant is removed because the local source-control basis is unclear.\n\nMachine Guard [FILE_54 NON-IMPORT]:\n`File_54` may use `File_43` as an upstream source for LukeSpan, LukeIntervals, the 70-year carrier, the `6 BC` hinge, and the `36 BC` rail. `File_43` does not import `File_54`'s Rounded Scaffold, BJ / Jubilees comparison, inverse-number material, or later Mirror classifications unless a local section explicitly opens those states.\n\n## 0.4 Modal-state processing rules\n\nActive state:\n`File_43` Genealogical Bridge; NT / Luke and NT / Matthew witness states; 70-year Jacobean carrier; bounded File_32 / File_33 P2 namespace state; P2 local-label restraint state; display-table-only genealogy ledger; MirrorVolume span-provenance state; File_44 reciprocal scaling-law context state.\n\n1. `File_43` is a genealogical bridge file. Its Luke, Matthew, P2, display-ledger, Jubilee, MirrorVolume, Key-of-23, and cumulative-cube states are simultaneous unless a local section explicitly narrows the working state.\n2. A shared value, date-label, span, range, theological phrase, or genealogy name does not create identity unless state, node-class, tradition, and operator agree.\n3. `LukeSpan = 5320` is a names-span state. `LukeIntervals = 5250` is an interval-count state. They must not be substituted for one another.\n4. `MattSpan_BirthHinge = 2800` is the Abraham → `6 BC` birth-hinge bracket. `MattSpan_Carrier = 2870` is the Abraham → `AD 65` carrier bracket. They must not be collapsed into bare `Matthew span`.\n5. `36 BC` is the P2 positive rails-window bracket where this file uses the alternate Luke rail. It is not the `AD 25` negative-polarity / signed A-space bridge target.\n6. `6 BC → AD 25` is the P2 negative-polarity / signed A-space bridge state by dependency. It is not the Luke `36 BC` rails-window and is not a genealogical ledger row.\n7. `36 BC ↔ 6 BC ↔ AD 25` is not an allowed single operator in `File_43`. Local Operator A / B labels must remain confined to this P2 split.\n8. The display genealogy ledger is a mechanized 70-year ledger. It may show names, row boundaries, and end-cap overlap, but it does not replace the locked span states.\n9. The double-generational knot is a compositional display state. It may justify literary framing, Job-like double-restoration framing, or end-cap overlap, but it is not an arithmetic input.\n10. MirrorVolume is a genealogical span-provenance volume, not a local Mirror protocol. Its `Mirror` label is source-retained terminology, not a license to import Protocol 1, Protocol 2, Coordinate Mirror, target-Mirror, or inverse-number machinery.\n11. The `25/23` operation in this file is an ordinary Key-of-23 whole-year expansion. It is not the Residue Protocol unless a later section explicitly opens residue arithmetic.\n12. The cumulative cube lock is dependency-controlled. Its arithmetic is verified locally; its authorization remains governed by the capsule anchor set.\n13. `Cainan (2nd)` in the genealogy ledger is a Luke-genealogy display label in this file. It does not locally open LXX Genesis 5 / 11 source-reconstruction unless a later dependency explicitly opens that state.\n14. `File_54` may use `File_43` locks downstream. `File_43` may cite `File_54` for the outer Luke rail / overlapped middle-generation clarification and the Alpha-Omega 22-fold bracket note, but `File_54` does not redefine `File_43` or import Rounded Scaffold, BJ, LXX, Mirror, or inverse-number proof burden into this local file.\n15. The Alpha-Omega 22-fold bracket is typological / reception-history framing. It may coordinate `22 × 490`, the Hebrew 22-letter symbolic field, BJ / Jubilees 22-fold Creation-genealogy by `File_53` dependency, and Revelation 1:8 / 21:6 / 22:13. It does not create a local proof of direct Lukan, Johannine, or BJ dependence.\n\n## 0.5 Node-class and display-state register\n\n| Date / value / display | Node-class | Active state | Do not collapse with |\n|---|---|---|---|\n| `70 years` | generational carrier unit | Jacobean carrier state | Davidic `30 + 40` display decomposition |\n| `30 + 40` | display decomposition | Davidic display motif | arithmetic driver; span derivation operator |\n| `LukeSpan = 5320` | names-span | Luke names-span state | `LukeIntervals = 5250`; display ledger row count |\n| `LukeIntervals = 5250` | interval count | Luke interval-count state | `LukeSpan = 5320`; Matthew spans |\n| `6 BC` | Christ-side birth hinge | Luke / Matthew birth-hinge state | `36 BC` rail; `AD 25` A-space target; table row terminal by itself |\n| `36 BC` | P2 positive rail bracket | Luke alternate positive rails-window state | `6 BC`; `AD 25`; continuous straddling operator |\n| `AD 25` | P2 negative-polarity / signed A-space bridge target by dependency | P2 bridge state | `36 BC` positive rail; Luke projection bracket; genealogy ledger row |\n| `5326 BC` | Lukan head bracket | LukeSpan from `6 BC` | `5286 BC`; `5256 BC`; Matthean head bracket |\n| `5286 BC` | Lukan rail bracket | LukeIntervals from `36 BC` rail | `5326 BC`; `5256 BC`; Rounded Scaffold states in `File_54` |\n| `5256 BC` | ledger boundary / cumulative-cube endpoint by dependency | first 70-year ledger boundary and cumulative cube target state | `5286 BC` rail bracket; `5326 BC` Lukan head bracket |\n| `2806 BC` | Abraham anchor | MattSpan_BirthHinge endpoint | `2876 BC` head-envelope marker; MattSpan_Carrier target |\n| `2876 BC` | head-envelope marker | Matthean head bracket | independent span lock; `2806 BC` Abraham anchor |\n| `AD 65` | carrier target / ledger terminal | MattSpan_Carrier target and display-table row endpoint | MirrorVolume input; `6 BC` birth hinge |\n| `AD 135` | display-table terminal | final-generation display row | span lock; Passion / Christological anchor |\n| `2450` | head-to-head bridge value | Jubilee bridge state | MirrorVolume; Key-of-23 expansion; display ledger row count |\n| `8050` | span-provenance volume | Genealogical MirrorVolume state | Protocol Mirror; expanded volume `8750`; MattSpan_Carrier substitution |\n| `8750` | expanded volume / cumulative cube value | Key-of-23 expanded volume and dependency-controlled cumulative cube lock | MirrorVolume `8050`; Seal700 `700` |\n| `700` | expansion seal | Seal700 state | independent genealogy span; display motif |\n| `22 × 490` | dependency-controlled Alpha-Omega bracket display | File_54 / File_53 22-fold field | local arithmetic driver; proof of direct dependence; substitute for File_43 locks |\n| `God` in Matthew-side display row | figurative Luke-derived bookend label | author-resolved display / theological state | literal divine origination; Matthean textual datum; arithmetic input |\n| `14006 BC` | cumulative anchor by dependency | cumulative cube lock state | local Luke / Matthew genealogy origin |\n| `Cainan (2nd)` | genealogy label | Luke-genealogy display label | local LXX Genesis 5 / 11 source-reconstruction proof |\n\n## 0.6 Range, arrow, and sign-convention register\n\n| Form | Local function | Guard |\n|---|---|---|\n| `5326–5256 BC` and other BC-only ledger ranges | 70-year generation-display rows | Display-table-only unless a section opens a specific span operator. |\n| `6 BC–AD 65` | cross-axis display-table row | Do not use as a substitute for `MattSpan_Carrier = 2870`; final arithmetic-control checks preserve the cross-axis distinction. |\n| `AD 65–AD 135` | AD-side display-table row | Display-table-only; not a new span lock. |\n| `→` | bracket / projection relation | Not a Mirror operator unless a local section opens a Mirror protocol. |\n| `↔` | relation marker for bridge, window, or lock | State must be named: rails-window, A-space bridge, Jubilee bridge, or other local state. |\n| `=` | asserted equality or definition | Verified or retained under final arithmetic-control notes; do not silently correct in later use. |\n| `:=` | definition marker | Preserved for MirrorVolume definition. |\n| slash-pairs | none active in `File_43` source | Do not introduce slash-pair logic from `File_13` or calendar files. |\n| calendar suffixes | none active in `File_43` source | Do not add `n` / `t` suffixes unless a later dependency explicitly opens calendar-state refinement. |\n| no-year-0 rule | active only where stated | Explicit in `MattSpan_Carrier`; final arithmetic-control checks preserve cross-axis arithmetic. |\n\n## 0.7 Mirror, Key, and Residue protocol register\n\n| Term / protocol | Local classification | Handling in `File_43` |\n|---|---|---|\n| MirrorVolume | span-provenance volume label | Preserved as source terminology for `8050 = 5250 + 2800`; not treated as formal Mirror coordinate-completion. |\n| Expanded volume | exact-ratio output state | `8750` under the ordinary Key-of-23 whole-year expansion. |\n| Seal700 | expansion-residue seal in ordinary whole-year arithmetic | `700`; generated only after the `25/23` expansion. |\n| Formal Mirror coordinate-completion | inactive locally | Not opened in this file except by dependency vocabulary; ordinary civil spans remain distinct. |\n| P2 positive rails-window | active by bounded File_32 / File_33 dependency | `36 BC ↔ 6 BC`; local Operator A only. |\n| P2 negative-polarity / signed A-space bridge | active by bounded File_32 / File_33 dependency | `6 BC ↔ AD 25`; local Operator B only. |\n| Residue Protocol | inactive | Do not import residue arithmetic into §5. |\n| Cumulative cube lock | dependency-controlled | Preserved only where capsule authorization is already active. |\n\n## 0.8 Dependency-state register\n\n| Dependency state | Local handling | Harmonization control |\n|---|---|---|\n| `File_32` bounded P2 route | Current active control for P2 positive rails-window and P2 negative-polarity / signed A-space bridge terminology | Used only for the P2 split; no broader prime-system proof is imported. This replaces the former skipped-prime dependency label by author decision. |\n| `File_33` namespace reinforcement | Reinforces File_32 polarity-before-Mirror hierarchy, positive-polarity rails-space `B/M`, negative-polarity / signed A-space output, and Coordinate Mirror as secondary agreement | Terminology-control only in File_43. File_33 Ordinal Authentication is not locally opened. |\n| `File_42` geometry-first source-history support | Supports P2 split, MirrorVolume, Key-of-23 expansion, and Seal700 as background / source-history control | Does not reactivate the removed skipped-prime active dependency label; File_32 / File_33 remain the current P2 namespace. |\n| `File_44` downstream / reciprocal context | Downstream scaling-law module using File_43's P2 split, MirrorVolume, Seal700, and display-vs-lock discipline | Context for terminology restraint only; it does not supply proof burden to File_43. |\n| `File_13` Christological dependency | Parallel / downstream Christological matrix using File_43 locks | Confirms that File_43 terms remain distinct where Christological states are opened. |\n| `File_15` generational-unit dependency | 70-year Jacobean carrier and optional 40/70/100 display motif | Supports the carrier-unit state without turning display motifs into arithmetic drivers. |\n| `File_54` comparative synthesis | Later comparative use of LukeSpan, LukeIntervals, `6 BC`, `36 BC`, the 70-year carrier, outer Luke rail, and Alpha-Omega 22-fold display | File_54 depends on File_43; File_43 cites File_54 only for dependency-controlled explanatory material and does not import File_54’s rounded / BJ / inverse proof burden. |\n| `File_53` BJ / Jubilees 22-fold witness | Opened only through `File_54` for the 22 created works / covenantal-heads symbolic field | Supports the Alpha-Omega 22-fold bracket as shared-tradition / reception-history context; no full File_53 proof burden is imported. |\n| LXX / Smith source-reconstruction witness | Not locally opened | No Smith note required in this file unless a later dependency materially opens LXX Genesis 5 / 11 reconstruction. |\n\n## 0.9 Arithmetic-control register\n\nActive state:\nharmonization arithmetic-control state; same-side BC projection; same-side BC span; same-side AD span; civil cross-axis span `BC + AD − 1`; exact-ratio checks; display-ledger row-width check.\n\nArithmetic-control scope:\nThis register records the verified arithmetic and confirms that the File_44 terminology harmonization does not disturb it. It preserves the active operators needed to prevent later state collapse. It does not change anchors, operators, modal states, node-classes, theological claims, or dependency status.\n\nArithmetic operators active in this file:\n\n| Operator | Local use | Control |\n|---|---|---|\n| Same-side BC projection | project backward from a BC hinge by addition | Example: `6 BC + 5320 = 5326 BC`. |\n| Same-side BC span | subtract later BC from earlier BC | Example: `5326 − 2876 = 2450`. |\n| Same-side AD span | subtract earlier AD from later AD | Example: `AD 135 − AD 65 = 70`. |\n| Civil cross-axis span | `BC + AD − 1` | Example: `2806 BC → AD 65 = 2806 + 65 − 1 = 2870`. |\n| Exact-ratio expansion | multiply by stated ratio | Example: `8050 × 25/23 = 8750`. |\n| Display-ledger row width | each row spans 70 years under its local same-side or cross-axis rule | Display-table-only; not a new lock. |\n\nArithmetic verification ledger:\n\n| Item | Calculation | Arithmetic-control status |\n|---|---|---|\n| Davidic display decomposition | `30 + 40 = 70` | verified; display motif only |\n| LukeSpan | `76 × 70 = 5320` | verified |\n| LukeIntervals | `75 × 70 = 5250` | verified |\n| Luke birth-hinge projection | `6 BC + 5320 = 5326 BC` | verified as same-side BC projection |\n| Luke P2 rail projection | `36 BC + 5250 = 5286 BC` | verified as same-side BC projection |\n| MattSpan_BirthHinge | `40 × 70 = 2800` | verified |\n| Matthew birth-hinge projection | `6 BC + 2800 = 2806 BC` | verified as same-side BC projection |\n| Matthean head-envelope marker | `2806 BC + 70 = 2876 BC` | verified as same-side BC projection |\n| MattSpan_Carrier | `41 × 70 = 2870` | verified |\n| Matthean carrier cross-axis span | `2806 BC → AD 65 = 2806 + 65 − 1 = 2870` | verified under no-year-0 rule |\n| Matthean carrier component check | `2806 BC → 1 BC = 2805`; `1 BC → AD 65 = 65`; `2805 + 65 = 2870` | verified |\n| P2 rails-window span | `36 BC − 6 BC = 30` | verified; Operator A only |\n| P2 A-space bridge span | `6 BC → AD 25 = 6 + 25 − 1 = 30` | verified; Operator B only |\n| Prohibited composite P2 chain | `36 BC → AD 25 = 36 + 25 − 1 = 60` | arithmetic fact only; not an allowed single operator in this file |\n| Luke-head / Matthew-head bridge | `5326 − 2876 = 2450` | verified |\n| Jubilee bridge | `2450 = 5 × 490 = 50 × 49` | verified |\n| MirrorVolume | `5250 + 2800 = 8050` | verified; uses locked inputs only |\n| Key-of-23 divisor | `8050 ÷ 23 = 350` | verified |\n| Key-of-23 expansion | `8050 × 25/23 = 8750` | verified as exact-ratio whole-year expansion |\n| Seal700 | `8750 − 8050 = 700 = 10 × 70` | verified |\n| Cumulative cube same-side span | `14006 BC → 5256 BC = 14006 − 5256 = 8750` | verified; dependency-controlled lock |\n| Cumulative cube factorization | `125 × 70 = 8750`; `5³ × 70 = 8750` | verified |\n| Display ledger row width | all 78 displayed rows span 70 years under their local same-side or cross-axis rule | verified; display-table-only |\n| Ledger primary terminal check | `5326 BC → AD 65 = 5326 + 65 − 1 = 5390 = 77 × 70` | verified as display-ledger check only |\n| Ledger final-generation terminal check | `5326 BC → AD 135 = 5326 + 135 − 1 = 5460 = 78 × 70` | verified as display-ledger check only |\n\nArithmetic result:\nNo arithmetic correction is required. All checked calculations compute as written when the active operator and state are preserved.\n\nMachine Guard [ARITHMETIC NON-COLLAPSE]:\nA verified shared numeric value does not create an identity across states. The `30`-year P2 rails-window span and the `30`-year P2 A-space bridge span are both verified, but they remain separate operators. MirrorVolume `8050`, expanded volume `8750`, and Seal700 `700` are verified, but they remain distinct node-classes.\n\n\n## 0.10 Argument-control and claim-status register\n\nActive state:\nfinal argument-control state; claim-status control; proof-burden separation; dependency-boundary restraint.\n\nArgument-control scope:\nThis register separates arithmetic facts from interpretive claims and dependency-controlled claims. It does not change arithmetic, anchors, modal states, node-classes, sign conventions, ranges, operators, Mirror protocols, theological claims, or cross-file dependencies.\n\nArgument-control rule:\nThe file's proof sequence is layered:\n\n1. NT / Luke and NT / Matthew genealogy structures supply the local genealogy-count frame by dependency.\n2. The 70-year carrier supplies the local generational measuring unit by `File_15` dependency and source usage.\n3. Arithmetic facts verify products, projections, cross-axis spans, exact-ratio expansion, and ledger-row widths.\n4. Structural inferences name the verified structures as `LukeSpan`, `LukeIntervals`, `MattSpan_BirthHinge`, `MattSpan_Carrier`, Jubilee bridge, MirrorVolume, Seal700, double-generational knot, and cumulative cube lock.\n5. Typological, theological, or compositional language may explain why the structures matter, but it does not replace arithmetic verification or dependency control.\n\nNo local claim in `File_43` is promoted to proof of direct Lukan or Matthean compositional intent. Such intent would require source-critical argument beyond the local arithmetic bridge. This file establishes state-controlled structural coherence and preserves the author's theological / harmonic interpretation under claim-status control.\n\n| Claim / term | Claim-status in `File_43` | Argument handling |\n|---|---|---|\n| 70-year carrier | dependency-controlled generational unit; arithmetic base | Active local measuring unit; not rederived here. |\n| Davidic `30 + 40` decomposition | typological / display motif | May frame the carrier compositionally; cannot derive or alter locked spans. |\n| `LukeSpan = 5320` | arithmetic fact once the 76-name frame and 70-year carrier are active | Names-span label; not interchangeable with `LukeIntervals`. |\n| `LukeIntervals = 5250` | arithmetic fact once the 75-interval frame and 70-year carrier are active | Interval-count label; active MirrorVolume input. |\n| Luke `6 BC` and `36 BC` projections | arithmetic fact with dependency-controlled P2 rail guard | `36 BC` is a rail bracket only; it does not open the A-space bridge. |\n| `MattSpan_BirthHinge = 2800` | arithmetic fact and structural birth-hinge label | Active MirrorVolume input. |\n| `MattSpan_Carrier = 2870` | arithmetic fact and structural carrier label | Valid Matthew carrier bracket; excluded from MirrorVolume. |\n| Matthean head bracket `2876 BC` | arithmetic fact and structural head-envelope marker | Envelope marker only; not a third Matthew span. |\n| Genealogy ledger | display-table-only | Mechanized 70-year display; not a textual chronology and not a span source. |\n| `God` display entry | author-resolved figurative Luke-derived bookend label; theological / display note | Refers to `Adam, son of God` and Christ the Son of God. It completes the bookend frame and does not imply that God came into existence 70 years before Adam. |\n| Jubilee bridge `2450` | arithmetic fact for equality; structural inference for Jubilee framing | The arithmetic is verified; the Jubilee label is interpretive / structural. |\n| MirrorVolume `8050` | arithmetic fact plus source-retained structural label | Span-provenance volume only; not a local formal Mirror protocol. |\n| Key-of-23 expansion `8050 × 25/23 = 8750` | exact-ratio arithmetic fact; structural expansion state | Ordinary whole-year expansion; not Residue Protocol. |\n| Seal700 | arithmetic fact plus structural seal label | Generated by expansion difference; not an independent span input. |\n| Double-generational knot | structural / compositional operator with Job-only typological warrant | May justify literary end-cap overlap or doubled-restoration framing; not an arithmetic input. The unclear secondary warrant is removed. |\n| Alpha-Omega 22-fold bracket | typological reading; reception-history note; shared-tradition evidence by dependency | Coordinates `22 × 490 = 22 × 7 × 70`, Hebrew 22-letter symbolism, BJ / Jubilees 22-fold Creation-genealogy, and Revelation 1:8 / 21:6 / 22:13; does not carry the local arithmetic burden. |\n| P2 non-straddling correction | Machine Guard and argument-control result | Separate verified 30-year operators remain separate; no continuous straddling operator. |\n| Cumulative cube lock | arithmetic fact; dependency-controlled claim | Preserved only under capsule authorization; not locally rederived. |\n| `Cainan (2nd)` in ledger | Luke-genealogy display label | Does not locally open LXX Genesis 5 / 11 source reconstruction. |\n\nMachine Guard [ARGUMENT BURDEN]:\nArithmetic facts carry computation. Structural inferences name the architecture created by those facts. Typological, theological, and display motifs explain meaning or composition. Do not use a structural label, display motif, or theological interpretation as a substitute for the arithmetic or dependency that supports it.\n\n## 0.11 Author-decision integration register\n\nActive state:\nfinal author-decision state; dependency-label cleanup; resolved display label; narrowed compositional warrant; File_54 explanatory dependency.\n\n| Decision area | Integrated state | Guard |\n|---|---|---|\n| Former skipped-prime dependency label | Removed from active dependencies | Active P2 routing now uses bounded `File_32` controls only. |\n| `God` display label | Author-resolved figurative Luke-derived bookend label | Does not imply divine origination or literal chronology for God. |\n| Prior compound warrant phrase | Narrowed to Job-only warrant | The unclear secondary warrant was removed because its local source-control basis is unclear. |\n| Job restoration warrant | Typological / compositional doubled-restoration note | Not an arithmetic input and not a local chronology proof about Job. |\n| Outer Luke rail / `153 + 1` structure | Dependency-controlled explanatory note from `File_54` | Does not overwrite File_43 span locks or import broader File_54 proof burden. |\n| Alpha-Omega `22 × 490` bracket | Author-clarified typological / reception-history note by `File_54` / `File_53` dependency | Coordinates Hebrew 22-letter symbolism, BJ / Jubilees 22-fold Creation-genealogy, and Revelation Alpha-Omega passages; not a new local arithmetic lock. |\n| Johannine `153` note | Typological resonance only | Does not prove Johannine authorial dependence. |\n| File_32 / File_33 terminology harmonization after File_44 | Current terminology-control state | Keeps File_43's local Operator A/B labels but explicitly confines them to the P2 split. |\n| File_44 reciprocal registration | Downstream context added to dependency registers | File_44 confirms scaling-law and display-vs-lock terminology but does not become File_43's proof source. |\n\nIntegration rule:\nThese author decisions resolve the prior audit issues. They clarify state labels and source-control routing without changing File_43's arithmetic locks. The current harmonization confirms the same modal-state boundaries for File_32 / File_33 terminology consistency, File_42 source-history support, File_44 reciprocal registration, and P2 local Operator A/B restraint.\n\n## 0.12 Harmonization modal-state confirmation register\n\nActive state:\nFile_44 terminology harmonization; File_32 / File_33 Prime–Civil / Polarity Namespace state; File_42 geometry-first source-history support state; File_44 downstream / reciprocal scaling-law context state; P2 local Operator A/B restraint state.\n\nModal-state scope:\nThis register confirms modal-state boundaries created or sharpened by the reopened harmonization cycle. It does not change arithmetic, anchors, node-classes, sign conventions, Mirror protocols, theological claims, or dependency-lock status.\n\n| Modal-state field | Harmonization resolution | Boundary preserved |\n|---|---|---|\n| File_32 / File_33 Prime–Civil / Polarity Namespace | Active namespace for P2 terminology in File_43. | Positive-polarity rails-space `B/M`, negative-polarity / signed A-space bridge, Coordinate Mirror / Protocol 1, and civil cross-axis span remain distinct. |\n| P2 positive rails-window | `6 BC / 36 BC`; local Operator A where shorthand is retained. | `36 BC` is the positive rail, not AD 25. |\n| P2 negative-polarity / signed A-space bridge | `6 BC / AD 25`; local Operator B where shorthand is retained. | AD 25 is bridge output, not the positive P2 `M` rail and not a Luke genealogy ledger row. |\n| P2 local Operator A/B labels | Retained only as local File_43 shorthand for the P2 split. | Not exportable to ratio expansions, scaling-law operators, Ordinal Authentication, Half-Step, target-Mirror, or later prime-grid operators. |\n| File_33 reinforcement | Terminology reinforcement for File_32 namespace and polarity-before-Mirror hierarchy. | File_33 Ordinal Authentication is not opened locally in File_43. |\n| File_42 source-history support | Geometry-first background support for P2 split, MirrorVolume, Key-of-23 expansion, and Seal700. | Does not reactivate the former skipped-prime active dependency label and does not replace File_32 / File_33 as active P2 namespace. |\n| File_44 reciprocal context | Downstream / reciprocal scaling-law context for terminology restraint and display-vs-lock discipline. | Does not become proof-bearing upstream and does not import File_44 Creation-head triad logic or File_45 exact-sweep statistics. |\n| Coordinate Mirror / Protocol 1 | Secondary agreement where explicitly opened. | Not the positive rail, not the negative-polarity bridge generator, and not the civil elapsed-span operator. |\n| MirrorVolume | Span-provenance label for `8050 = 5250 + 2800`. | Not formal Mirror coordinate-completion and not formed with `MattSpan_Carrier = 2870`. |\n| Alpha-Omega `22 × 490` bracket | Typological / reception-history framing by File_54 / File_53 dependency. | Not a local arithmetic driver, new Mirror protocol, or proof of direct textual dependence. |\n| Cumulative cube lock | Arithmetic verified by source-history; authorization remains dependency-controlled. | Not promoted into an independent File_43 proof. |\n| Smith LXX source-reconstruction witness | Not active in File_43. | `Cainan (2nd)` remains a Luke-genealogy display label and does not locally open LXX Genesis 5 / 11 reconstruction. |\n\nModal-state result:\nNo modal-state correction is required beyond confirming and recording these boundaries.\n## 0.13 Harmonization arithmetic confirmation register\n\nActive state:\nFile_44 terminology harmonization arithmetic confirmation; same-side BC span state; civil cross-axis span state; exact-ratio arithmetic fact; display-ledger row-width check; P2 local Operator A/B arithmetic restraint; File_32 / File_33 terminology already confirmed by the modal-state register.\n\nArithmetic-control scope:\nThis register confirms that terminology harmonization did not disturb existing arithmetic. It does not alter the modal-state decisions, does not promote dependency-controlled locks, and does not import File_44 scaling-law proof burden into File_43.\n\n| Arithmetic field | Recheck | Arithmetic-control result | Boundary preserved |\n|---|---|---|---|\n| Davidic display decomposition | `30 + 40 = 70` | verified | display motif only |\n| LukeSpan | `76 × 70 = 5320` | verified | names-span state only |\n| LukeIntervals | `75 × 70 = 5250` | verified | interval-count state only |\n| Luke birth-hinge projection | `6 BC + 5320 = 5326 BC` | verified | same-side BC projection |\n| Luke P2 rail projection | `36 BC + 5250 = 5286 BC` | verified | P2 positive rails-window / local Operator A only |\n| MattSpan_BirthHinge | `40 × 70 = 2800`; `6 BC + 2800 = 2806 BC` | verified | birth-hinge input to MirrorVolume |\n| Matthean head-envelope marker | `2806 BC + 70 = 2876 BC` | verified | envelope marker, not a third span lock |\n| MattSpan_Carrier | `41 × 70 = 2870`; `2806 + 65 − 1 = 2870` | verified | valid carrier bracket; excluded from MirrorVolume |\n| P2 positive rails-window | `36 − 6 = 30` | verified | local Operator A only |\n| P2 negative-polarity / signed A-space bridge | `6 + 25 − 1 = 30` | verified | local Operator B only |\n| Prohibited P2 composite chain | `36 + 25 − 1 = 60` | verified as arithmetic fact only | not a single P2 operator |\n| Luke-head / Matthew-head bridge | `5326 − 2876 = 2450` | verified | Jubilee bridge structural inference |\n| Jubilee bridge factorization | `2450 = 5 × 490 = 50 × 49` | verified | arithmetic fact plus structural inference |\n| MirrorVolume | `5250 + 2800 = 8050` | verified | span provenance only; no `2870` substitution |\n| Key-of-23 expansion | `8050 ÷ 23 = 350`; `350 × 25 = 8750` | verified | ordinary whole-year expansion; not Residue Protocol |\n| Seal700 | `8750 − 8050 = 700 = 10 × 70` | verified | generated seal, not independent input |\n| Cumulative cube lock | `14006 − 5256 = 8750`; `125 × 70 = 8750`; `5³ × 70 = 8750` | verified | dependency-controlled lock |\n| Display-ledger row widths | all 78 displayed rows span `70` years under their local same-side or cross-axis rule | verified | display-table-only |\n| Ledger primary terminal check | `5326 BC → AD 65 = 5326 + 65 − 1 = 5390 = 77 × 70` | verified | display-ledger check only |\n| Ledger final-generation terminal check | `5326 BC → AD 135 = 5326 + 135 − 1 = 5460 = 78 × 70` | verified | display-ledger check only |\n| File_54 outer Luke rail dependency | `5356 BC → AD 5355 = 5356 + 5355 − 1 = 10710 = 153 × 70`; `10710 + 70 = 10780 = 154 × 70 = 22 × 490` | verified as dependency-controlled explanatory arithmetic | does not overwrite File_43 locks |\n\nArithmetic-control result:\nNo arithmetic correction is required. Terminology and modal-state harmonization do not disturb the same-side spans, cross-axis handling, exact-ratio locks, display-ledger row widths, MirrorVolume, Seal700, cumulative cube arithmetic, or dependency-controlled Alpha-Omega explanatory arithmetic.\n\n\n## 0.14 Harmonization argument-status confirmation register\n\nActive state:\nFile_44 terminology harmonization argument-control confirmation; claim-status calibration state; File_32 / File_33 terminology restraint; File_44 reciprocal context boundary; proof-burden separation.\n\nArgument-control scope:\nThis register confirms that the File_32 / File_33 terminology harmonization, File_42 source-history note, File_44 reciprocal registration, and P2 local Operator A/B restraint do not alter File_43's claim-status hierarchy. This register does not change arithmetic, anchors, modal states, node-classes, sign conventions, ranges, operators, Mirror protocols, theological claims, or dependency locks.\n\nArgument-control result:\nThe harmonization controls preserve the prior File_43 argument architecture. Arithmetic facts compute the spans and expansions. Exact-ratio arithmetic facts verify Key-of-23 and related whole-year expansions. Structural inferences name the bridge architecture. Display motifs and typological framing explain composition. Dependency-controlled explanatory material stays bounded to its source file. Theological and reception-history notes remain interpretive and non-driver unless a local section explicitly gives them proof burden.\n\n| Claim field | Claim-status classification | Guard |\n|---|---|---|\n| File_32 / File_33 P2 terminology | dependency-controlled terminology state | Controls wording for positive-polarity rails-space `B/M`, negative-polarity / signed A-space bridge, and Coordinate Mirror as secondary agreement. |\n| P2 local Operator A | local shorthand for P2 positive rails-window | Equivalent local label for `6 BC / 36 BC`; not a general repository operator. |\n| P2 local Operator B | local shorthand for P2 negative-polarity / signed A-space bridge | Equivalent local label for `6 BC / AD 25`; not a general repository operator. |\n| P2 non-straddling correction | Machine Guard and argument-control result | Separate verified `30`-year spans remain separate operators; the `60`-year composite is not a P2 operator. |\n| File_42 | source-history / geometry-first support | Supports the split but does not replace File_32 / File_33 terminology or revive the former skipped-prime active dependency label. |\n| File_44 | downstream / reciprocal context | Confirms scaling-law and display-vs-lock discipline; not proof-bearing upstream for File_43. |\n| LukeSpan and LukeIntervals | arithmetic facts with structural labels | `LukeSpan = 5320` and `LukeIntervals = 5250` remain distinct; only `LukeIntervals` enters MirrorVolume. |\n| MattSpan_BirthHinge and MattSpan_Carrier | arithmetic facts with structural labels | `MattSpan_BirthHinge = 2800` enters MirrorVolume; `MattSpan_Carrier = 2870` remains valid but excluded. |\n| MirrorVolume | arithmetic fact plus source-retained structural label | Span-provenance volume only; not formal Mirror coordinate-completion. |\n| Key-of-23 expansion | exact-ratio arithmetic fact | Whole-year expansion; not Residue Protocol. |\n| Seal700 | arithmetic fact plus structural seal label | Generated by expansion difference; not an independent genealogy span input. |\n| Genealogy ledger | display-table-only | Mechanized display of 70-year rows; not a textual chronology and not a proof source. |\n| Figurative `God` bookend label | author-clarified theological / display note | Luke-derived bookend label only; not ontological chronology and not arithmetic input. |\n| Jubilee bridge | arithmetic fact plus structural inference | `2450 = 5 × 490 = 50 × 49` computes; Jubilee framing is structural. |\n| Double-generational knot | structural / compositional operator | May frame overlap and doubled-restoration typology; not arithmetic input. |\n| Job-only restoration warrant | typological framing | Supports the doubled-restoration analogy only; not a local chronology proof about Job. |\n| Outer Luke rail / `153 + 1` structure | dependency-controlled explanatory material by File_54 | Preserved as explanatory / reception-history material; does not overwrite File_43 locks. |\n| Alpha-Omega `22 × 490` bracket | typological framing; reception-history note; shared-tradition evidence by dependency | Coordinates Hebrew 22-letter symbolism, BJ / Jubilees 22-fold witness, Revelation Alpha-Omega framing, and Johannine `153` resonance; not a local arithmetic driver. |\n| Cumulative cube lock | arithmetic fact; dependency-controlled claim | Arithmetic remains verified; authorization remains dependent on upstream capsule / anchor controls. |\n| Smith LXX source-reconstruction witness | inactive in File_43 | Not added because LXX Genesis 5 / 11 reconstruction is not locally opened. |\n\nMachine Guard [PASS 4 PROOF BURDEN]:\nDo not use File_43's typological, theological, reception-history, display, or dependency-controlled explanatory material as an arithmetic driver. Do not use File_44's downstream scaling-law controls as proof for File_43. Do not export File_43's local Operator A/B labels to File_44, File_33, File_35, File_36, File_45, or later files.\n\nArgument result:\nNo claim-status correction requires arithmetic, anchor, modal-state, node-class, sign-convention, operator, Mirror-protocol, theological-claim, or dependency-lock revision.\n\n## 1. Locked unit and Davidic display motif\n\nActive state:\nJacobean 70-year carrier; Davidic `30 + 40` display motif; non-lock interpretive framing.\n\nClaim-status: arithmetic fact for `30 + 40 = 70`; typological / display motif for the Davidic decomposition.\n\nThe locked generational carrier unit is 70 years. This file treats the 70-year unit as the Jacobean standard.\n\nDisplay motif:\nThe 70-year generational carrier may be read compositionally as `30 + 40`, reflecting the Davidic template:\n\n| Component | Value | Function |\n|---|---:|---|\n| David accession hinge | 30 years | display component |\n| David reign length | 40 years | display component |\n| Davidic decomposition | 70 := 30 + 40 | interpretive framing only |\n\nGuard:\nThis decomposition is a compositional display motif only. It must not overwrite or substitute for any arithmetic locks:\n\n| Lock | Required distinction |\n|---|---|\n| Luke side | `LukeSpan = 5320` vs `LukeIntervals = 5250` |\n| Matthew side | `MattSpan_BirthHinge = 2800` vs `MattSpan_Carrier = 2870` |\n| MirrorVolume | `8050` and expansion to `8750` remain bound to their locked inputs |\n| Seal700 | `700` remains generated by the locked expansion |\n| P2 operator protocol | `36 BC ↔ 6 BC` and `6 BC ↔ AD 25` must not be chained |\n\nThe decomposition may be cited as literary framing, including end-cap overlap or double-generational-knot warrant, but never as an arithmetic driver.\n\n## 2. Luke — two distinct numbers\n\nActive state:\nNT / Luke genealogy; 70-year carrier; mandatory split between names-span and interval-count states.\n\n### 2.1 LukeSpan: names-span state\n\nActive state:\nLuke names-span state; Adam → Christ as names.\n\nClaim-status: arithmetic fact for `76 × 70 = 5320`; structural genealogy-span label for `LukeSpan`.\n\n`LukeSpan = 5320 = 76 × 70`.\n\nThis is the names-span state: Adam → Christ as names.\n\nLock:\n`LukeSpan = 5320`.\n\n### 2.2 LukeIntervals: interval-count state\n\nActive state:\nLuke interval-count state; intervals between 76 names.\n\nClaim-status: arithmetic fact for `75 × 70 = 5250`; structural interval-count label for `LukeIntervals`.\n\n`LukeIntervals = 5250 = 75 × 70`.\n\nThis is the interval-count state: the intervals between 76 names.\n\nLock:\n`LukeIntervals = 5250`.\n\n### 2.3 Luke-side BC projection brackets\n\nActive state:\nLuke birth-hinge bracket; Luke P2 rails-window bracket; same-side BC projection display.\n\nClaim-status: arithmetic fact; dependency-controlled P2 rail-state guard.\n\nUsing the locked birth hinge `6 BC` as the Christ-side bracket:\n\n```markdown\n6 BC + 5320 = 5326 BC\n```\n\nArithmetic check:\n`6 + 5320 = 5326`. Verified as same-side BC projection.\n\nLock:\n`LukeSpan` bracket from `6 BC` → `5326 BC`.\n\nUsing the quad-window mate `36 BC` as an alternate Christ-side rail bracket, explicitly mapped to civil BC for display:\n\n```markdown\n36 BC + 5250 = 5286 BC\n```\n\nArithmetic check:\n`36 + 5250 = 5286`. Verified as same-side BC projection.\n\nLock:\n`LukeIntervals` bracket from `36 BC` → `5286 BC`.\n\nGuard:\nThe use of `36 BC` here is the P2 positive rails-window bracket, local Operator A under the current bounded File_32 / File_33 Prime–Civil / Polarity Namespace. It must not be conflated with the P2 negative-polarity / signed A-space bridge that yields `AD 25`, local Operator B.\n\n## 3. Matthew — explicit dual-bracketed requirement\n\nActive state:\nNT / Matthew genealogy; birth-hinge bracket; head-envelope marker; carrier bracket; display-table-only ledger.\n\n### 3.1 MattSpan_BirthHinge\n\nActive state:\nMatthean Abraham → `6 BC` birth-hinge bracket.\n\nClaim-status: arithmetic fact for `40 × 70 = 2800`; structural birth-hinge label for `MattSpan_BirthHinge`.\n\n`MattSpan_BirthHinge = 2800 = 40 × 70`.\n\nThis is the Abraham → `6 BC` bracket.\n\nFrom the birth hinge `6 BC`:\n\n```markdown\n6 BC + 2800 = 2806 BC\n```\n\nArithmetic check:\n`6 + 2800 = 2806`. Verified as same-side BC projection.\n\nLock:\n`MattSpan_BirthHinge` bracket: Abraham anchor = `2806 BC`.\n\n### 3.2 Matthean head bracket\n\nActive state:\nMatthean head-envelope marker; 42-name presentation envelope.\n\nClaim-status: arithmetic fact for `2806 + 70 = 2876`; structural marker for the head-envelope function.\n\nTo express the head-envelope marker for the 42-name presentation, as an envelope only and not as a distinct span lock:\n\n```markdown\n2806 BC + 70 = 2876 BC\n```\n\nArithmetic check:\n`2806 + 70 = 2876`. Verified as same-side BC projection.\n\nLock:\nMatthean head bracket = `2876 BC`.\n\n### 3.3 MattSpan_Carrier\n\nActive state:\nMatthean Abraham → `AD 65` carrier bracket; civil cross-axis no-year-0 state.\n\nClaim-status: arithmetic fact for `41 × 70 = 2870`; structural carrier-bracket label for `MattSpan_Carrier`.\n\n`MattSpan_Carrier = 2870 = 41 × 70`.\n\nThis is the Abraham → `AD 65` bracket, with no year 0.\n\nCivil arithmetic check:\n\n```markdown\n2806 BC → 1 BC = 2805 years\n1 BC → AD 65 = 65 years\n2805 + 65 = 2870\n```\n\nArithmetic check:\nEquivalent civil cross-axis check: `2806 + 65 − 1 = 2870`. Verified under the no-year-0 rule.\n\nLock:\n`MattSpan_Carrier`: `2806 BC → AD 65 = 2870`.\n\nGuard:\nBare `Matthew span` is disallowed. All references must specify `MattSpan_BirthHinge = 2800` or `MattSpan_Carrier = 2870`.\n\n### 3.4 Genealogy chart\n\nActive state:\ndisplay-table-only genealogy ledger; 70-year carrier display; non-lock schematic placement state.\n\nStatus: display table only.\n\nClaim-status: display-table-only; author-resolved figurative God bookend label state; no literal divine-origin chronology claim.\n\nThis chart is a mechanized ledger of the 70-year carrier applied to the dual-bracket schema. It must not be used to overwrite any capsule locks: `MattSpan_BirthHinge = 2800`, `MattSpan_Carrier = 2870`, `LukeSpan = 5320`, or `LukeIntervals = 5250`.\n\nDisplay-label audit state:\nThe author-resolved `God` entry in the Matthew-side display column is a figurative Luke-derived bookend label. It refers to `Adam, son of God` and to Christ the Son of God, completing the bookend frame of `1 + 75 + 1` generations. It is not a Matthean textual datum, not an arithmetic input, and not a claim that God came into existence before Adam.\n\n| Primary 70-year generation | Matthew's genealogy | Luke's genealogy |\n|---|---|---|\n| 5326–5256 BC |  | God |\n| 5256–5186 BC |  | Creation of Adam |\n| 5186–5116 BC |  | Seth |\n| 5116–5046 BC |  | Enosh |\n| 5046–4976 BC |  | Kenan |\n| 4976–4906 BC |  | Mahalalel |\n| 4906–4836 BC |  | Jared |\n| 4836–4766 BC |  | Enoch |\n| 4766–4696 BC |  | Methuselah |\n| 4696–4626 BC |  | Lamech |\n| 4626–4556 BC |  | Noah |\n| 4556–4486 BC |  | Shem |\n| 4486–4416 BC |  | FLOOD & Arphaxad |\n| 4416–4346 BC |  | Cainan (2nd) |\n| 4346–4276 BC |  | Shelah |\n| 4276–4206 BC | God | Eber |\n| 4206–4136 BC | Creation of Adam | Peleg |\n| 4136–4066 BC | Seth | Reu |\n| 4066–3996 BC | Enosh | Serug |\n| 3996–3926 BC | Kenan | Nahor |\n| 3926–3856 BC | Mahalalel | Terah |\n| 3856–3786 BC | Jared | Abraham |\n| 3786–3716 BC | Enoch | Isaac |\n| 3716–3646 BC | Methuselah | Jacob |\n| 3646–3576 BC | Lamech | Judah |\n| 3576–3506 BC | Noah | Perez |\n| 3506–3436 BC | Shem | Hezron |\n| 3436–3366 BC | FLOOD & Arphaxad | Ram |\n| 3366–3296 BC | Cainan (2nd) | Amminadab |\n| 3296–3226 BC | Shelah | Nahshon (Aaron's brother-in-law) |\n| 3226–3156 BC | Eber | Salmon |\n| 3156–3086 BC | Peleg | Boaz |\n| 3086–3016 BC | Reu | Obed |\n| 3016–2946 BC | Serug | Jesse |\n| 2946–2876 BC | Nahor | David |\n| 2876–2806 BC | Terah | Nathan |\n| 2806–2736 BC | ABRAHAM | Mattatha |\n| 2736–2666 BC | Isaac | Menna |\n| 2666–2596 BC | Jacob | Melea |\n| 2596–2526 BC | Judah | Eliakim |\n| 2526–2456 BC | Perez | Jonam |\n| 2456–2386 BC | Hezron | Joseph |\n| 2386–2316 BC | Ram | Judah |\n| 2316–2246 BC | Amminadab | Simeon |\n| 2246–2176 BC | Nahshon (Aaron's brother-in-law) | Levi |\n| 2176–2106 BC | Salmon | Matthat |\n| 2106–2036 BC | Boaz | Jorim |\n| 2036–1966 BC | Obed | Eliezer |\n| 1966–1896 BC | Jesse | Joshua |\n| 1896–1826 BC | David | Er |\n| 1826–1756 BC | Solomon | Elmadam |\n| 1756–1686 BC | Rehoboam | Cosam |\n| 1686–1616 BC | Abijah | Addi |\n| 1616–1546 BC | Asa | Melki |\n| 1546–1476 BC | Jehoshaphat | Neri |\n| 1476–1406 BC | Joram | Shealtiel |\n| 1406–1336 BC | Uzziah | Zerubbabel |\n| 1336–1266 BC | Jotham | Rhesa |\n| 1266–1196 BC | Ahaz | Joanan |\n| 1196–1126 BC | Hezekiah | Joda |\n| 1126–1056 BC | Manasseh | Josech |\n| 1056–986 BC | Amon | Semein |\n| 986–916 BC | Josiah | Mattathias |\n| 916–846 BC | Jeconiah | Maath |\n| 846–776 BC | Shealtiel | Naggai |\n| 776–706 BC | Zerubbabel | Esli |\n| 706–636 BC | Abiud | Nahum |\n| 636–566 BC | Eliakim | Amos |\n| 566–496 BC | Azor | Mattathias |\n| 496–426 BC | Zadok | Joseph |\n| 426–356 BC | Achim | Jannai |\n| 356–286 BC | Eliud | Melki |\n| 286–216 BC | Eleazar | Levi |\n| 216–146 BC | Matthan | Matthat |\n| 146–76 BC | Jacob | Heli |\n| 76–6 BC | Joseph (husband of Mary) | Joseph |\n| 6 BC–AD 65 | Jesus Christ | Jesus |\n| AD 65–AD 135 | Final generation | Final generation |\n\nNote:\nThis ledger may be framed by an end-cap overlap concept, the double-generational knot, as literary / compositional warrant. It is not permitted to overwrite arithmetic locks or substitute spans: `2800` vs `2870`, `5250` vs `5320`, or `8050` vs `8750`.\n\n## 4. Jubilee Bridge: head-to-head\n\nActive state:\nLuke-head bracket; Matthean head-envelope marker; head-to-head Jubilee bridge.\n\nClaim-status: arithmetic fact for the equality; structural inference for Jubilee bridge framing.\n\nUsing the locked head-envelope markers:\n\n| Head bracket | Value |\n|---|---:|\n| Lukan head bracket, LukeSpan from `6 BC` | 5326 BC |\n| Matthean head bracket | 2876 BC |\n\nDifference:\n\n```markdown\n5326 − 2876 = 2450\n2450 = 5 × 490 = 50 × 49\n```\n\nArithmetic check:\n`5326 − 2876 = 2450`; `5 × 490 = 2450`; `50 × 49 = 2450`. Verified.\n\nLock:\nLuke-head ↔ Matthew-head = `2450`, or 50 Jubilees.\n\nArgument-control note:\nThe equality `2450 = 5 × 490 = 50 × 49` is arithmetic fact. Naming the relation a Jubilee bridge is structural inference based on the active head-bracket states and Jubilee grammar. It does not by itself prove direct Lukan or Matthean source-critical intent.\n\n## 5. MirrorVolume and Key-of-23 expansion\n\nActive state:\nMirrorVolume span-provenance state; ordinary Key-of-23 whole-year expansion state; Seal700 state; inactive Residue Protocol state.\n\n### 5.1 MirrorVolume definition\n\nActive state:\nGenealogical MirrorVolume state; hard span-provenance state.\n\nClaim-status: arithmetic fact for `5250 + 2800 = 8050`; source-retained structural label for MirrorVolume; hard span provenance.\n\nMirrorVolume uses `LukeIntervals = 5250` and `MattSpan_BirthHinge = 2800` only:\n\n```markdown\n8050 := 5250 + 2800\n```\n\nArithmetic check:\n`5250 + 2800 = 8050`. Verified.\n\nProhibition:\n`MattSpan_Carrier = 2870` must not be substituted into `8050`, `8750`, or Seal700.\n\nArgument-control note:\n`MirrorVolume` is a source-retained structural label for a verified span-provenance sum. The label does not open formal Mirror coordinate-completion, Protocol 1, Protocol 2, target-Mirror, or inverse-number reasoning in this file.\n\n### 5.2 Key-of-23 expansion and Seal700\n\nActive state:\nordinary Key-of-23 whole-year expansion; Seal700 generated state.\n\nClaim-status: exact-ratio arithmetic fact for the expansion; structural label for Seal700; non-Residue control.\n\n```markdown\n8050 × 25/23 = 8750\n8050 ÷ 23 = 350\n8750 − 8050 = 700 = 10 × 70\n```\n\nArithmetic check:\n`8050 ÷ 23 = 350`; `350 × 25 = 8750`; `8750 − 8050 = 700`; `10 × 70 = 700`. Verified as exact-ratio whole-year expansion.\n\nLock:\n`8050 → 8750` under `25/23`.\n\nLock:\nSeal700 = `700`, generated by the expansion.\n\nTerminology guard:\nThis is an ordinary Key-of-23 whole-year expansion. It is not the Residue Protocol unless a later section explicitly shifts into residue arithmetic.\n\nArgument-control note:\nSeal700 is a structural label for the verified difference `8750 − 8050 = 700`. It is not an additional genealogy span and is not an independent input into MirrorVolume.\n\n## 6. Double-generational knot\n\nActive state:\ndouble-generational knot compositional state; end-cap overlap / literary-framing state; non-arithmetic-input guard.\n\n### 6.1 Definition\n\nActive state:\ncompositional end-cap operator; display / literary-framing state.\n\nClaim-status: structural / compositional operator; author-clarified Job-only typological warrant; not an arithmetic input.\n\nThe system permits a double-generational knot as a compositional end-cap operator. By author clarification, the local warrant is Job-only: Job’s restoration pattern is read typologically as a doubled-life display, `140 = 2 × 70` restored toward `280 = 4 × 70`, with four generations as the visible restoration witness.\n\nLock:\nThe double-generational knot is a display / compositional operator only. It is not an arithmetic input.\n\nSource-control note:\nThe prior compound warrant phrase is narrowed by author decision to Job-only. The unclear secondary warrant is removed because the local source-control basis is unclear. The Job pattern remains a typological / compositional warrant, not an arithmetic input and not an independent chronology claim about Job unless a later source-control dependency opens that material.\n\n### 6.2 Hard guards\n\nThe knot may justify end-cap overlap as a literary framing device, but it must not overwrite or substitute:\n\n| Distinction | Guard |\n|---|---|\n| Matthew span states | `MattSpan_BirthHinge = 2800` vs `MattSpan_Carrier = 2870` |\n| Luke span states | `LukeIntervals = 5250` vs `LukeSpan = 5320` |\n| Volume states | MirrorVolume `8050` vs expanded volume `8750` |\n| Seal state | Seal700 `700` |\n\n### 6.3 God bookend, outer Luke rail, and Alpha-Omega 22-fold clarification\n\nActive state:\nAuthor-resolved figurative God bookend label; File_54 outer Luke rail / overlapped middle-generation dependency state; Alpha-Omega 22-fold bracket state; BJ / Jubilees 22-fold Creation-genealogy witness by File_53 dependency through File_54; Johannine typological / reception-history note; non-arithmetic-input guard.\n\nClaim-status: author-clarified theological note; structural inference by dependency; typological / Johannine note; reception-history note; shared-tradition evidence by dependency; not a local arithmetic driver.\n\nThe `God` display label is retained as a figurative Luke-derived bookend. It refers to Luke's terminal phrase `Adam, son of God` and to Christ the Son of God. The label assigns a display generation to the God-side bookend only in this figurative sense. It does not mean that God came into existence, nor does it create a literal pre-Adam chronology for God.\n\nDependency note:\n`File_54` supplies the outer Luke rail / overlapped middle-generation clarification. The relevant dependency-controlled structure is:\n\n```markdown\n5356 BC → AD 5355 = 10710 = 153 × 70\n10710 + 70 = 10780 = 154 × 70 = 22 × 490\n22 × 490 = 22 × 7 × 70\n```\n\nUnder this reading, the strict outer span preserves `153` actual 70-year generations. The overlapped central Christ-generation is then conceptually added back, producing a `153 + 1` structure. This explains the double-generational knot as a restored / doubled central-generation concept without changing the local `File_43` locks.\n\nAuthor-supplied display form:\n\n```markdown\n5356/5286 BC → 36 BC/AD 35 → AD 5285/5355\n```\n\nThis slash-display is retained as explanatory Mirror-display context only. It is not a new local arithmetic lock in `File_43`. The `AD 5285/5355` slash-pair is treated as the strict counterpart display for `5286/5356 BC`; it must not be collapsed into File_54's separate same-label eschatological display block `AD 5286–5356`.\n\nAlpha-Omega 22-fold note:\nThe `22 × 490` total may be read as a 22-fold jubilean Alpha-Omega bracket. In this display, the start, central Christ-generation, and terminal rail form a beginning / middle / end bracket around the `22 × 7 × 70` total. This fits the 22-letter Hebrew alphabet symbolic field and the BJ / Jubilees 22-fold Creation-genealogy witness, where `File_53` treats the 22 created works as corresponding to 22 covenantal heads from Adam to Jacob.\n\nRevelation reception-history note:\nThe Alpha-Omega passages in Revelation supply the threefold theological field for this display:\n\n| Revelation field | Display block | Function |\n|---|---|---|\n| Revelation 1:8: Alpha and Omega; who was | `5356–5286 BC` | Pre-Creation / before-this-Creation rail |\n| Revelation 1:8: who is | `36 BC–AD 35` | Central overlapped Christ-generation |\n| Revelation 1:8: who is to come | `AD 5286–5356` | New-Creation / eschatological rail |\n| Revelation 21:6 and 22:13 | full `22 × 490` bracket | Beginning and End; First and Last; Alpha and Omega |\n\nThe three Revelation Alpha-Omega passages are therefore used as typological / reception-history framing for the start / middle / end bracket. They do not prove direct Lukan, Johannine, or BJ authorial dependence. The arithmetic basis remains the dependency-controlled outer Luke rail and the overlapped middle generation.\n\nJohannine note:\nThe `153` structure may be read as a restrained Johannine typological resonance with John 21:11's `153` fish. This is a typological note only. It does not prove direct Johannine authorial dependence and does not carry the local arithmetic burden.\n\nMachine Guard [OUTER LUKE RAIL NON-IMPORT]:\nThe outer Luke rail, `153 + 1` structure, and Alpha-Omega `22 × 490` display clarify the bookend / double-generational-knot logic. They must not overwrite `LukeSpan = 5320`, `LukeIntervals = 5250`, `MattSpan_BirthHinge = 2800`, `MattSpan_Carrier = 2870`, MirrorVolume `8050`, expanded volume `8750`, or Seal700 `700`.\n\nMachine Guard [ALPHA-OMEGA 22-FOLD NON-DRIVER]:\nThe Alpha-Omega `22 × 490` note is theological / typological / reception-history framing. It is not a new local arithmetic operator, not a new Mirror protocol, not a substitute for File_43's genealogy locks, and not proof of direct textual dependence unless a later source-critical dependency explicitly opens that claim.\n\n## 7. Prohibited 30-year-straddling claims\n\nActive state:\nFile_32 / File_33 P2 namespace; P2 positive rails-window local Operator A; P2 negative-polarity / signed A-space local Operator B; non-straddling guard.\n\n### 7.1 Disallowed conflation\n\nClaim-status: argument-control correction; Machine Guard; dependency-controlled P2 operator separation.\n\nAny prior pattern that treated `36 BC ↔ 6 BC ↔ AD 25` as a single continuous operator is prohibited.\n\nMandatory correction:\n\n| Span | Correct state |\n|---|---|\n| `36 BC ↔ 6 BC` | P2 positive rails-window; local Operator A only |\n| `6 BC ↔ AD 25` | P2 negative-polarity / signed A-space bridge; local Operator B only |\n\nThese spans must not be chained as a single operator.\n\nArgument-control note:\nThe arithmetic fact that `36 BC → AD 25 = 60` under civil cross-axis counting is not an authorization to create a 60-year P2 composite or a 30-year straddling operator. The local argument depends on preserving the two separate verified 30-year states.\n\n### 7.2 Status of former composite patterns\n\nWhere older presentations used the composite straddling habit, those patterns are either:\n\n1. removed;\n2. reclassified as display motif only; or\n3. reframed under the double-generational knot as composition only.\n\n## 8. Cumulative cube lock\n\nActive state:\ndependency-controlled cumulative cube lock; capsule-authorized anchor state; not locally rederived.\n\nClaim-status: arithmetic fact for the verified values; dependency-controlled lock for local argument function.\n\nDeep-time cumulative anchor tether, as a lock only when already authorized by the capsule anchor set:\n\n```markdown\n14006 BC → 5256 BC = 8750 years = 125 × 70 = 5³ × 70\n```\n\nArithmetic check:\n`14006 − 5256 = 8750`; `125 × 70 = 8750`; `5³ × 70 = 8750`. Verified as same-side BC arithmetic. Dependency authorization remains governed by the capsule anchor set.\n\nLock:\n`14006 BC → 5256 BC = 8750 = 125 × 70`.\n\nArgument-control note:\nThe arithmetic is verified locally, but the claim remains dependency-controlled. `File_43` preserves this lock because it is already authorized by the capsule anchor set; it does not independently prove the cumulative system.\n\n## 9. Optional display motif — 40/70/100 triad\n\nActive state:\noptional 40/70/100 display motif; anti-overfitting guard; non-lock interpretive overlay.\n\nClaim-status: typological / display motif only; anti-overfitting guard.\n\nThe `40/70/100` triad can be presented as a display motif when explicitly tied to allowed brackets and the double-generational knot. It must not be used as a driver to re-derive locked spans.\n\nDisplay motif only; not a lock:\nAny triadic framing that relies on combining both rails and both ends simultaneously is compositional unless independently locked elsewhere.\n\nMachine Guard [ANTI-OVERFITTING]:\nThe values `30`, `40`, and `100` within the Davidic decomposition and the 40/70/100 triad are display motifs only. Do not extract these values for use as active arithmetic operators, offsets, or bridging variables. Do not dynamically combine them, such as by subtracting `30` from `70`, to calculate new spans or substitute them for locked spans. They are interpretive overlays only.\n\n## 10. File_44 harmonization control note\n\nThe File_44 terminology-harmonization cycle is retained as active dependency-control language only.\n\n| Area | Public-clean handling |\n|---|---|\n| File_32 / File_33 namespace | Active P2 terminology routes through the File_32 / File_33 Prime–Civil / Polarity Namespace. |\n| P2 Operator A/B labels | Retained only as local shorthand for the P2 split: Operator A names the P2 positive rails-window `6 BC / 36 BC`; Operator B names the P2 negative-polarity / signed A-space bridge `6 BC / AD 25`. |\n| File_42 relationship | Retained as geometry-first source-history support only; not reactivated as File_43's active P2 dependency route. |\n| File_44 reciprocal context | Retained as downstream / reciprocal scaling-law context only; not proof-bearing upstream. |\n| Coordinate Mirror | Secondary agreement where explicitly opened; not primary polarity generation. |\n| Arithmetic and anchors | No arithmetic, anchor, node-class, sign-convention, Mirror-protocol, theological-claim, or dependency-lock correction is made in this public-clean source. |\n\n## 13. Final Audit Notes\n\nAudit note:\nNo reopened harmonization correction required changing arithmetic, anchors, modal states, node-classes, sign conventions, operators, Mirror protocols, theological claims, or dependency locks.\n\nAudit note:\nThe File_32 / File_33 Prime–Civil / Polarity Namespace is a terminology and dependency-control layer in File_43. It does not add a new proof burden beyond the bounded P2 states already active.\n\nAudit note:\nP2 Operator A and P2 Operator B remain local File_43 shorthand only. Operator A names the P2 positive rails-window `6 BC / 36 BC`. Operator B names the P2 negative-polarity / signed A-space bridge `6 BC / AD 25`. These labels must not be exported to unrelated ratio expansions, scaling laws, Ordinal Authentication, Half-Step, target-Mirror states, or later prime-grid systems.\n\nAudit note:\nFile_42 remains geometry-first / source-history support only. It supports the P2 split and related geometry but does not replace the active File_32 / File_33 terminology route and does not revive the former skipped-prime active dependency label.\n\nAudit note:\nFile_44 remains downstream / reciprocal scaling-law context only. It may confirm File_43's display-vs-lock discipline and local-label export restraint, but it does not become proof-bearing upstream for File_43.\n\nAudit note:\nMirrorVolume remains a source-retained structural label for span provenance: `8050 = LukeIntervals 5250 + MattSpan_BirthHinge 2800`. It is not formal Mirror coordinate-completion, and `MattSpan_Carrier = 2870` remains excluded from MirrorVolume, `8750`, and Seal700.\n\nAudit note:\nThe genealogy ledger remains display-table-only. The figurative `God` bookend label remains a theological / display note and does not become an ontological chronology claim or arithmetic input.\n\nAudit note:\nThe double-generational knot, Job-only restoration warrant, Alpha-Omega `22 × 490` bracket, Revelation Alpha-Omega reception-history note, BJ / Jubilees 22-fold witness, and Johannine `153` resonance remain typological / reception-history / dependency-controlled explanatory material. None of these carries the local arithmetic burden.\n\nAudit note:\nThe cumulative cube lock remains dependency-controlled. Its arithmetic is verified, but File_43 does not promote it into an independent proof apart from capsule / upstream anchor authorization.\n\nAudit note:\nHenry B. Smith Jr.'s LXX Genesis 5 / 11 reconstruction witness remains inactive in the body. File_43 uses NT Luke / Matthew genealogical span mechanics and treats `Cainan (2nd)` only as a Luke-genealogy display label; it does not materially open LXX Genesis 5 / 11 reconstruction.\n\n## 14. Final Unresolved Issues and Dependency Notes\n\nNo finalization source blocker was identified. No argument-status, arithmetic, modal-state, or dependency-lock correction is required.\n\nThe current File_44 terminology-harmonization finalization remains focused pressure tested during trust-status equalization; this caution is preserved in the header rather than expanded as a pressure-test log.\n\nThe following items remain dependency-controlled rather than unresolved:\n\n| Issue | Handling |\n|---|---|\n| File_44 reciprocal registration | Resolved as downstream context only; keep it from becoming proof-bearing upstream. |\n| File_42 source-history support | Resolved as background support only; do not reactivate the former active skipped-prime dependency label. |\n| Cumulative cube lock authorization | Arithmetic and argument status are resolved; authorization remains dependency-controlled by the capsule anchor set. |\n| Outer Luke rail / `153 + 1` structure | Preserved as dependency-controlled explanatory material by `File_54`; keep guarded against overwriting File_43 locks. |\n| Alpha-Omega `22 × 490` bracket | Preserved as typological / reception-history framing by `File_54` / `File_53` dependency. |\n| Smith LXX source-reconstruction witness | Not active; revisit only if LXX Genesis 5 / 11 reconstruction becomes local to the argument. |\n\n## Revision and archive note\n\nThis public-clean Markdown source removes only archival amendment history, pass logs, pressure-test repetition, pointer-refresh records, and obsolete replacement-workflow notes.\n\nDetailed revision history is preserved in the `Repository_Change_Archive`.\n\nNo arithmetic, anchors, modal states, node-classes, sign conventions, operators, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries are changed.\n\nFinal pressure-test status is preserved in the file header. Detailed pressure-test records are archived rather than repeated in the public file body.\n", "evidenceLinks": [{"id": "d-9f0e41022cab59a4", "title": "File 53"}, {"id": "d-548a6d186972f534", "title": "File 15"}, {"id": "d-ed718a9e579978a9", "title": "File 00"}, {"id": "d-e415d58136a6e9bc", "title": "File 69"}, {"id": "d-1ff1914fa180de2a", "title": "File 54"}]}