File: File_43
Title: Genealogical Bridge
Entity: Genealogical Bridge (Matthew / Luke)
Classification: Theological Lattice / Genealogical Harmonics
UUID: GEN_BRIDGE_LUKE_MATT_SPLIT
Status: 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
Pressure-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.
Register 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.
Publication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive.
Source status: DEFINED (Harmonized with v10.1 capsule protocol)
Primary domain: NT Genealogical; Theological; Comparative; Structural
Traditions: NT / Luke; NT / Matthew; Davidic typological framing by dependency
Canonical source: Markdown
Primary 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
Dependency-controlled explanatory anchors: 5356/5286 BC; 36 BC/AD 35; AD 5285/5355; AD 5355; 10710; 10780; 153; 154; 22 × 490; 22 × 7 × 70
Related 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
Major 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`
Major 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
Major 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
Revision 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).
Current 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.

# File_43 — Genealogical Bridge

## Related Repository Files

| File | Function for `File_43` |
|---|---|
| `File_00` | Foundational source-map discipline, arithmetic-control / argument-control layering, Machine Guard style, and civil / Mirror / inverse firewalling. |
| `File_13` | Christological and Luke/Matthew dependency controls where broader Christological anchors are opened. |
| `File_15` | Generational-unit controls for the 70-year Jacobean carrier and optional 40/70/100 display motif. |
| `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. |
| `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. |
| `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. |
| `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. |
| `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. |
| `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. |
| `Restart Capsule v11.15` | Repository-wide anchors, operators, modal states, and File_54 dependency controls. |
| `490d Repository Style Guide v2.5` | Source formatting, terminology, modal-state control, claim-status labels, no-comma numbers, and cross-axis span discipline. |
| `Project Procedures v3.2` | Project workflow controls, authorial-direction protocol, audit-note discipline, Context Economy, Novelty Verification Rule, and canonical Markdown / derived-format boundary. |
| `State Vocabulary Register v1.17` | Current per-file modal-state vocabulary, convention entries, and Machine Guards. |

## 0. File-function

`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.

The file enforces four primary non-collapse rules:

1. `LukeSpan` and `LukeIntervals` remain distinct.
2. `MattSpan_BirthHinge` and `MattSpan_Carrier` remain distinct.
3. The P2 rails-window operator remains distinct from the P2 A-space bridge operator.
4. No `30`-year straddling operator is permitted.

This 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.

This 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`.

Terminology-control rule:
Where 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.

This 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.

Publication-cleanup note:
This 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.

Argument-control rule:
Arithmetic 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.

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

## 0.1 Working state register

| State | Value or anchor | Node-class / function | Handling in `File_43` |
|---|---:|---|---|
| Locked generational carrier | 70 years | Jacobean carrier unit | Active unit for Luke and Matthew displays. |
| LukeSpan names-span state | 5320 = 76 × 70 | names-span | Adam → Christ as names; not the interval count. |
| LukeIntervals interval-count state | 5250 = 75 × 70 | interval count | Intervals between 76 names; active MirrorVolume input. |
| Luke `6 BC` birth-hinge bracket | 6 BC → 5326 BC | birth-hinge projection | Uses LukeSpan from the Christ-side hinge. |
| 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. |
| MattSpan_BirthHinge state | 2800 = 40 × 70 | Abraham → 6 BC bracket | Active MirrorVolume input. |
| Matthean head-envelope marker | 2876 BC | envelope marker | `2806 BC + 70`; not a distinct span lock. |
| MattSpan_Carrier state | 2870 = 41 × 70 | Abraham → AD 65 carrier | Carrier bracket; not a MirrorVolume input. |
| Display genealogy ledger | 5326 BC → AD 135 | display table | Mechanized 70-year ledger; non-lock. |
| 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. |
| Jubilee bridge state | 2450 = 5 × 490 = 50 × 49 | head-to-head bridge | Luke head bracket to Matthean head bracket. |
| MirrorVolume state | 8050 = 5250 + 2800 | hard span-provenance volume | Uses LukeIntervals and MattSpan_BirthHinge only. |
| Key-of-23 expansion state | 8050 × 25/23 = 8750 | exact expansion | Ordinary Key-of-23 whole-year expansion; not Residue Protocol. |
| Seal700 state | 700 = 8750 − 8050 = 10 × 70 | expansion seal | Generated by the `25/23` expansion. |
| Double-generational knot | compositional end-cap operator | display / literary framing | Not an arithmetic input. |
| 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. |
| 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. |
| 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. |
| 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. |
| Optional 40/70/100 triad | 40; 70; 100 | display motif | Non-lock; not a driver for deriving spans. |
| 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. |
| 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. |
| 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. |
| Anti-straddling guard | 36 BC ↔ 6 BC; 6 BC ↔ AD 25 | P2 operator split | Operator A and Operator B must not be chained. |

## 0.2 File map

| Section | Function | Active state / operator |
|---|---|---|
| §0 | File-function and state controls | file-level modal states and dependency boundaries |
| §0.9 | Records final arithmetic-control verification | same-side spans; cross-axis spans; exact ratios; ledger rows |
| §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 |
| §0.12 | Confirms harmonized modal-state boundaries | File_32 / File_33 namespace; File_42 source-history support; File_44 reciprocal context |
| §0.13 | Confirms harmonized arithmetic controls | no arithmetic correction; operator preservation |
| §0.14 | Confirms harmonized argument status | proof-burden separation; claim-status calibration; non-driver guards |
| §1 | Defines the 70-year unit and Davidic display motif | Jacobean carrier; display-only `30 + 40` motif |
| §2 | Separates LukeSpan from LukeIntervals | LukeSpan; LukeIntervals; P2 rail bracket |
| §3 | Separates MattSpan_BirthHinge from MattSpan_Carrier | Matthew dual-bracket protocol; display table |
| §4 | Establishes the Luke / Matthew head-to-head Jubilee bridge | 2450 = 5 × 490 = 50 × 49 |
| §5 | Defines MirrorVolume, Key-of-23 expansion, and Seal700 | 8050; 8750; 700; `25/23` |
| §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 |
| §7 | Prohibits 30-year straddling | File_32 / File_33 P2 namespace; local Operator A / Operator B separation |
| §8 | Preserves the cumulative cube lock | dependency-controlled `8750` cube lock |
| §9 | Restricts the 40/70/100 triad | display motif only; anti-overfitting guard |
| 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 |

## 0.3 Machine Guards

Machine Guard [SPAN SPLIT]:
Do not use `LukeSpan` where the file requires `LukeIntervals`. Do not use `LukeIntervals` where the file requires `LukeSpan`.

Machine Guard [MATTHEW SPLIT]:
Bare `Matthew span` is disallowed. Specify either `MattSpan_BirthHinge = 2800` or `MattSpan_Carrier = 2870`.

Machine Guard [P2 NON-STRADDLING]:
Do 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.

Machine Guard [DISPLAY TABLE ONLY]:
The genealogy ledger is a mechanized 70-year display table. It must not overwrite LukeSpan, LukeIntervals, MattSpan_BirthHinge, MattSpan_Carrier, MirrorVolume, Expanded volume, or Seal700.

Machine Guard [MIRRORVOLUME PROVENANCE]:
MirrorVolume `8050` uses `LukeIntervals = 5250` and `MattSpan_BirthHinge = 2800` only. `MattSpan_Carrier = 2870` must not be substituted into `8050`, `8750`, or Seal700.

Machine Guard [P2 FILE_32 / FILE_33 ROUTE]:
The 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.

Machine Guard [P2 LOCAL-LABEL RESTRAINT]:
`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.

Machine Guard [FILE_42 SOURCE-HISTORY NON-REACTIVATION]:
`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.

Machine Guard [FILE_44 RECIPROCAL NON-IMPORT]:
`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`.

Machine Guard [GOD BOOKEND LABEL]:
The 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.

Machine Guard [JOB-ONLY WARRANT]:
The 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.

Machine Guard [FILE_54 NON-IMPORT]:
`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.

## 0.4 Modal-state processing rules

Active state:
`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.

1. `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.
2. A shared value, date-label, span, range, theological phrase, or genealogy name does not create identity unless state, node-class, tradition, and operator agree.
3. `LukeSpan = 5320` is a names-span state. `LukeIntervals = 5250` is an interval-count state. They must not be substituted for one another.
4. `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`.
5. `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.
6. `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.
7. `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.
8. 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.
9. 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.
10. 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.
11. 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.
12. The cumulative cube lock is dependency-controlled. Its arithmetic is verified locally; its authorization remains governed by the capsule anchor set.
13. `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.
14. `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.
15. 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.

## 0.5 Node-class and display-state register

| Date / value / display | Node-class | Active state | Do not collapse with |
|---|---|---|---|
| `70 years` | generational carrier unit | Jacobean carrier state | Davidic `30 + 40` display decomposition |
| `30 + 40` | display decomposition | Davidic display motif | arithmetic driver; span derivation operator |
| `LukeSpan = 5320` | names-span | Luke names-span state | `LukeIntervals = 5250`; display ledger row count |
| `LukeIntervals = 5250` | interval count | Luke interval-count state | `LukeSpan = 5320`; Matthew spans |
| `6 BC` | Christ-side birth hinge | Luke / Matthew birth-hinge state | `36 BC` rail; `AD 25` A-space target; table row terminal by itself |
| `36 BC` | P2 positive rail bracket | Luke alternate positive rails-window state | `6 BC`; `AD 25`; continuous straddling operator |
| `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 |
| `5326 BC` | Lukan head bracket | LukeSpan from `6 BC` | `5286 BC`; `5256 BC`; Matthean head bracket |
| `5286 BC` | Lukan rail bracket | LukeIntervals from `36 BC` rail | `5326 BC`; `5256 BC`; Rounded Scaffold states in `File_54` |
| `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 |
| `2806 BC` | Abraham anchor | MattSpan_BirthHinge endpoint | `2876 BC` head-envelope marker; MattSpan_Carrier target |
| `2876 BC` | head-envelope marker | Matthean head bracket | independent span lock; `2806 BC` Abraham anchor |
| `AD 65` | carrier target / ledger terminal | MattSpan_Carrier target and display-table row endpoint | MirrorVolume input; `6 BC` birth hinge |
| `AD 135` | display-table terminal | final-generation display row | span lock; Passion / Christological anchor |
| `2450` | head-to-head bridge value | Jubilee bridge state | MirrorVolume; Key-of-23 expansion; display ledger row count |
| `8050` | span-provenance volume | Genealogical MirrorVolume state | Protocol Mirror; expanded volume `8750`; MattSpan_Carrier substitution |
| `8750` | expanded volume / cumulative cube value | Key-of-23 expanded volume and dependency-controlled cumulative cube lock | MirrorVolume `8050`; Seal700 `700` |
| `700` | expansion seal | Seal700 state | independent genealogy span; display motif |
| `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 |
| `God` in Matthew-side display row | figurative Luke-derived bookend label | author-resolved display / theological state | literal divine origination; Matthean textual datum; arithmetic input |
| `14006 BC` | cumulative anchor by dependency | cumulative cube lock state | local Luke / Matthew genealogy origin |
| `Cainan (2nd)` | genealogy label | Luke-genealogy display label | local LXX Genesis 5 / 11 source-reconstruction proof |

## 0.6 Range, arrow, and sign-convention register

| Form | Local function | Guard |
|---|---|---|
| `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. |
| `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. |
| `AD 65–AD 135` | AD-side display-table row | Display-table-only; not a new span lock. |
| `→` | bracket / projection relation | Not a Mirror operator unless a local section opens a Mirror protocol. |
| `↔` | relation marker for bridge, window, or lock | State must be named: rails-window, A-space bridge, Jubilee bridge, or other local state. |
| `=` | asserted equality or definition | Verified or retained under final arithmetic-control notes; do not silently correct in later use. |
| `:=` | definition marker | Preserved for MirrorVolume definition. |
| slash-pairs | none active in `File_43` source | Do not introduce slash-pair logic from `File_13` or calendar files. |
| calendar suffixes | none active in `File_43` source | Do not add `n` / `t` suffixes unless a later dependency explicitly opens calendar-state refinement. |
| no-year-0 rule | active only where stated | Explicit in `MattSpan_Carrier`; final arithmetic-control checks preserve cross-axis arithmetic. |

## 0.7 Mirror, Key, and Residue protocol register

| Term / protocol | Local classification | Handling in `File_43` |
|---|---|---|
| MirrorVolume | span-provenance volume label | Preserved as source terminology for `8050 = 5250 + 2800`; not treated as formal Mirror coordinate-completion. |
| Expanded volume | exact-ratio output state | `8750` under the ordinary Key-of-23 whole-year expansion. |
| Seal700 | expansion-residue seal in ordinary whole-year arithmetic | `700`; generated only after the `25/23` expansion. |
| Formal Mirror coordinate-completion | inactive locally | Not opened in this file except by dependency vocabulary; ordinary civil spans remain distinct. |
| P2 positive rails-window | active by bounded File_32 / File_33 dependency | `36 BC ↔ 6 BC`; local Operator A only. |
| P2 negative-polarity / signed A-space bridge | active by bounded File_32 / File_33 dependency | `6 BC ↔ AD 25`; local Operator B only. |
| Residue Protocol | inactive | Do not import residue arithmetic into §5. |
| Cumulative cube lock | dependency-controlled | Preserved only where capsule authorization is already active. |

## 0.8 Dependency-state register

| Dependency state | Local handling | Harmonization control |
|---|---|---|
| `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. |
| `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. |
| `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. |
| `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. |
| `File_13` Christological dependency | Parallel / downstream Christological matrix using File_43 locks | Confirms that File_43 terms remain distinct where Christological states are opened. |
| `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. |
| `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. |
| `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. |
| 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. |

## 0.9 Arithmetic-control register

Active state:
harmonization 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.

Arithmetic-control scope:
This 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.

Arithmetic operators active in this file:

| Operator | Local use | Control |
|---|---|---|
| Same-side BC projection | project backward from a BC hinge by addition | Example: `6 BC + 5320 = 5326 BC`. |
| Same-side BC span | subtract later BC from earlier BC | Example: `5326 − 2876 = 2450`. |
| Same-side AD span | subtract earlier AD from later AD | Example: `AD 135 − AD 65 = 70`. |
| Civil cross-axis span | `BC + AD − 1` | Example: `2806 BC → AD 65 = 2806 + 65 − 1 = 2870`. |
| Exact-ratio expansion | multiply by stated ratio | Example: `8050 × 25/23 = 8750`. |
| 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. |

Arithmetic verification ledger:

| Item | Calculation | Arithmetic-control status |
|---|---|---|
| Davidic display decomposition | `30 + 40 = 70` | verified; display motif only |
| LukeSpan | `76 × 70 = 5320` | verified |
| LukeIntervals | `75 × 70 = 5250` | verified |
| Luke birth-hinge projection | `6 BC + 5320 = 5326 BC` | verified as same-side BC projection |
| Luke P2 rail projection | `36 BC + 5250 = 5286 BC` | verified as same-side BC projection |
| MattSpan_BirthHinge | `40 × 70 = 2800` | verified |
| Matthew birth-hinge projection | `6 BC + 2800 = 2806 BC` | verified as same-side BC projection |
| Matthean head-envelope marker | `2806 BC + 70 = 2876 BC` | verified as same-side BC projection |
| MattSpan_Carrier | `41 × 70 = 2870` | verified |
| Matthean carrier cross-axis span | `2806 BC → AD 65 = 2806 + 65 − 1 = 2870` | verified under no-year-0 rule |
| Matthean carrier component check | `2806 BC → 1 BC = 2805`; `1 BC → AD 65 = 65`; `2805 + 65 = 2870` | verified |
| P2 rails-window span | `36 BC − 6 BC = 30` | verified; Operator A only |
| P2 A-space bridge span | `6 BC → AD 25 = 6 + 25 − 1 = 30` | verified; Operator B only |
| Prohibited composite P2 chain | `36 BC → AD 25 = 36 + 25 − 1 = 60` | arithmetic fact only; not an allowed single operator in this file |
| Luke-head / Matthew-head bridge | `5326 − 2876 = 2450` | verified |
| Jubilee bridge | `2450 = 5 × 490 = 50 × 49` | verified |
| MirrorVolume | `5250 + 2800 = 8050` | verified; uses locked inputs only |
| Key-of-23 divisor | `8050 ÷ 23 = 350` | verified |
| Key-of-23 expansion | `8050 × 25/23 = 8750` | verified as exact-ratio whole-year expansion |
| Seal700 | `8750 − 8050 = 700 = 10 × 70` | verified |
| Cumulative cube same-side span | `14006 BC → 5256 BC = 14006 − 5256 = 8750` | verified; dependency-controlled lock |
| Cumulative cube factorization | `125 × 70 = 8750`; `5³ × 70 = 8750` | verified |
| Display ledger row width | all 78 displayed rows span 70 years under their local same-side or cross-axis rule | verified; display-table-only |
| Ledger primary terminal check | `5326 BC → AD 65 = 5326 + 65 − 1 = 5390 = 77 × 70` | verified as display-ledger check only |
| Ledger final-generation terminal check | `5326 BC → AD 135 = 5326 + 135 − 1 = 5460 = 78 × 70` | verified as display-ledger check only |

Arithmetic result:
No arithmetic correction is required. All checked calculations compute as written when the active operator and state are preserved.

Machine Guard [ARITHMETIC NON-COLLAPSE]:
A 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.


## 0.10 Argument-control and claim-status register

Active state:
final argument-control state; claim-status control; proof-burden separation; dependency-boundary restraint.

Argument-control scope:
This 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.

Argument-control rule:
The file's proof sequence is layered:

1. NT / Luke and NT / Matthew genealogy structures supply the local genealogy-count frame by dependency.
2. The 70-year carrier supplies the local generational measuring unit by `File_15` dependency and source usage.
3. Arithmetic facts verify products, projections, cross-axis spans, exact-ratio expansion, and ledger-row widths.
4. Structural inferences name the verified structures as `LukeSpan`, `LukeIntervals`, `MattSpan_BirthHinge`, `MattSpan_Carrier`, Jubilee bridge, MirrorVolume, Seal700, double-generational knot, and cumulative cube lock.
5. Typological, theological, or compositional language may explain why the structures matter, but it does not replace arithmetic verification or dependency control.

No 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.

| Claim / term | Claim-status in `File_43` | Argument handling |
|---|---|---|
| 70-year carrier | dependency-controlled generational unit; arithmetic base | Active local measuring unit; not rederived here. |
| Davidic `30 + 40` decomposition | typological / display motif | May frame the carrier compositionally; cannot derive or alter locked spans. |
| `LukeSpan = 5320` | arithmetic fact once the 76-name frame and 70-year carrier are active | Names-span label; not interchangeable with `LukeIntervals`. |
| `LukeIntervals = 5250` | arithmetic fact once the 75-interval frame and 70-year carrier are active | Interval-count label; active MirrorVolume input. |
| 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. |
| `MattSpan_BirthHinge = 2800` | arithmetic fact and structural birth-hinge label | Active MirrorVolume input. |
| `MattSpan_Carrier = 2870` | arithmetic fact and structural carrier label | Valid Matthew carrier bracket; excluded from MirrorVolume. |
| Matthean head bracket `2876 BC` | arithmetic fact and structural head-envelope marker | Envelope marker only; not a third Matthew span. |
| Genealogy ledger | display-table-only | Mechanized 70-year display; not a textual chronology and not a span source. |
| `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. |
| Jubilee bridge `2450` | arithmetic fact for equality; structural inference for Jubilee framing | The arithmetic is verified; the Jubilee label is interpretive / structural. |
| MirrorVolume `8050` | arithmetic fact plus source-retained structural label | Span-provenance volume only; not a local formal Mirror protocol. |
| Key-of-23 expansion `8050 × 25/23 = 8750` | exact-ratio arithmetic fact; structural expansion state | Ordinary whole-year expansion; not Residue Protocol. |
| Seal700 | arithmetic fact plus structural seal label | Generated by expansion difference; not an independent span input. |
| 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. |
| 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. |
| P2 non-straddling correction | Machine Guard and argument-control result | Separate verified 30-year operators remain separate; no continuous straddling operator. |
| Cumulative cube lock | arithmetic fact; dependency-controlled claim | Preserved only under capsule authorization; not locally rederived. |
| `Cainan (2nd)` in ledger | Luke-genealogy display label | Does not locally open LXX Genesis 5 / 11 source reconstruction. |

Machine Guard [ARGUMENT BURDEN]:
Arithmetic 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.

## 0.11 Author-decision integration register

Active state:
final author-decision state; dependency-label cleanup; resolved display label; narrowed compositional warrant; File_54 explanatory dependency.

| Decision area | Integrated state | Guard |
|---|---|---|
| Former skipped-prime dependency label | Removed from active dependencies | Active P2 routing now uses bounded `File_32` controls only. |
| `God` display label | Author-resolved figurative Luke-derived bookend label | Does not imply divine origination or literal chronology for God. |
| Prior compound warrant phrase | Narrowed to Job-only warrant | The unclear secondary warrant was removed because its local source-control basis is unclear. |
| Job restoration warrant | Typological / compositional doubled-restoration note | Not an arithmetic input and not a local chronology proof about Job. |
| 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. |
| 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. |
| Johannine `153` note | Typological resonance only | Does not prove Johannine authorial dependence. |
| 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. |
| 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. |

Integration rule:
These 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.

## 0.12 Harmonization modal-state confirmation register

Active state:
File_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.

Modal-state scope:
This 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.

| Modal-state field | Harmonization resolution | Boundary preserved |
|---|---|---|
| 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. |
| P2 positive rails-window | `6 BC / 36 BC`; local Operator A where shorthand is retained. | `36 BC` is the positive rail, not AD 25. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| MirrorVolume | Span-provenance label for `8050 = 5250 + 2800`. | Not formal Mirror coordinate-completion and not formed with `MattSpan_Carrier = 2870`. |
| 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. |
| Cumulative cube lock | Arithmetic verified by source-history; authorization remains dependency-controlled. | Not promoted into an independent File_43 proof. |
| 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. |

Modal-state result:
No modal-state correction is required beyond confirming and recording these boundaries.
## 0.13 Harmonization arithmetic confirmation register

Active state:
File_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.

Arithmetic-control scope:
This 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.

| Arithmetic field | Recheck | Arithmetic-control result | Boundary preserved |
|---|---|---|---|
| Davidic display decomposition | `30 + 40 = 70` | verified | display motif only |
| LukeSpan | `76 × 70 = 5320` | verified | names-span state only |
| LukeIntervals | `75 × 70 = 5250` | verified | interval-count state only |
| Luke birth-hinge projection | `6 BC + 5320 = 5326 BC` | verified | same-side BC projection |
| Luke P2 rail projection | `36 BC + 5250 = 5286 BC` | verified | P2 positive rails-window / local Operator A only |
| MattSpan_BirthHinge | `40 × 70 = 2800`; `6 BC + 2800 = 2806 BC` | verified | birth-hinge input to MirrorVolume |
| Matthean head-envelope marker | `2806 BC + 70 = 2876 BC` | verified | envelope marker, not a third span lock |
| MattSpan_Carrier | `41 × 70 = 2870`; `2806 + 65 − 1 = 2870` | verified | valid carrier bracket; excluded from MirrorVolume |
| P2 positive rails-window | `36 − 6 = 30` | verified | local Operator A only |
| P2 negative-polarity / signed A-space bridge | `6 + 25 − 1 = 30` | verified | local Operator B only |
| Prohibited P2 composite chain | `36 + 25 − 1 = 60` | verified as arithmetic fact only | not a single P2 operator |
| Luke-head / Matthew-head bridge | `5326 − 2876 = 2450` | verified | Jubilee bridge structural inference |
| Jubilee bridge factorization | `2450 = 5 × 490 = 50 × 49` | verified | arithmetic fact plus structural inference |
| MirrorVolume | `5250 + 2800 = 8050` | verified | span provenance only; no `2870` substitution |
| Key-of-23 expansion | `8050 ÷ 23 = 350`; `350 × 25 = 8750` | verified | ordinary whole-year expansion; not Residue Protocol |
| Seal700 | `8750 − 8050 = 700 = 10 × 70` | verified | generated seal, not independent input |
| Cumulative cube lock | `14006 − 5256 = 8750`; `125 × 70 = 8750`; `5³ × 70 = 8750` | verified | dependency-controlled lock |
| Display-ledger row widths | all 78 displayed rows span `70` years under their local same-side or cross-axis rule | verified | display-table-only |
| Ledger primary terminal check | `5326 BC → AD 65 = 5326 + 65 − 1 = 5390 = 77 × 70` | verified | display-ledger check only |
| Ledger final-generation terminal check | `5326 BC → AD 135 = 5326 + 135 − 1 = 5460 = 78 × 70` | verified | display-ledger check only |
| 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 |

Arithmetic-control result:
No 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.


## 0.14 Harmonization argument-status confirmation register

Active state:
File_44 terminology harmonization argument-control confirmation; claim-status calibration state; File_32 / File_33 terminology restraint; File_44 reciprocal context boundary; proof-burden separation.

Argument-control scope:
This 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.

Argument-control result:
The 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.

| Claim field | Claim-status classification | Guard |
|---|---|---|
| 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. |
| P2 local Operator A | local shorthand for P2 positive rails-window | Equivalent local label for `6 BC / 36 BC`; not a general repository operator. |
| 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. |
| 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. |
| 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. |
| File_44 | downstream / reciprocal context | Confirms scaling-law and display-vs-lock discipline; not proof-bearing upstream for File_43. |
| LukeSpan and LukeIntervals | arithmetic facts with structural labels | `LukeSpan = 5320` and `LukeIntervals = 5250` remain distinct; only `LukeIntervals` enters MirrorVolume. |
| MattSpan_BirthHinge and MattSpan_Carrier | arithmetic facts with structural labels | `MattSpan_BirthHinge = 2800` enters MirrorVolume; `MattSpan_Carrier = 2870` remains valid but excluded. |
| MirrorVolume | arithmetic fact plus source-retained structural label | Span-provenance volume only; not formal Mirror coordinate-completion. |
| Key-of-23 expansion | exact-ratio arithmetic fact | Whole-year expansion; not Residue Protocol. |
| Seal700 | arithmetic fact plus structural seal label | Generated by expansion difference; not an independent genealogy span input. |
| Genealogy ledger | display-table-only | Mechanized display of 70-year rows; not a textual chronology and not a proof source. |
| Figurative `God` bookend label | author-clarified theological / display note | Luke-derived bookend label only; not ontological chronology and not arithmetic input. |
| Jubilee bridge | arithmetic fact plus structural inference | `2450 = 5 × 490 = 50 × 49` computes; Jubilee framing is structural. |
| Double-generational knot | structural / compositional operator | May frame overlap and doubled-restoration typology; not arithmetic input. |
| Job-only restoration warrant | typological framing | Supports the doubled-restoration analogy only; not a local chronology proof about Job. |
| 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. |
| 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. |
| Cumulative cube lock | arithmetic fact; dependency-controlled claim | Arithmetic remains verified; authorization remains dependent on upstream capsule / anchor controls. |
| Smith LXX source-reconstruction witness | inactive in File_43 | Not added because LXX Genesis 5 / 11 reconstruction is not locally opened. |

Machine Guard [PASS 4 PROOF BURDEN]:
Do 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.

Argument result:
No claim-status correction requires arithmetic, anchor, modal-state, node-class, sign-convention, operator, Mirror-protocol, theological-claim, or dependency-lock revision.

## 1. Locked unit and Davidic display motif

Active state:
Jacobean 70-year carrier; Davidic `30 + 40` display motif; non-lock interpretive framing.

Claim-status: arithmetic fact for `30 + 40 = 70`; typological / display motif for the Davidic decomposition.

The locked generational carrier unit is 70 years. This file treats the 70-year unit as the Jacobean standard.

Display motif:
The 70-year generational carrier may be read compositionally as `30 + 40`, reflecting the Davidic template:

| Component | Value | Function |
|---|---:|---|
| David accession hinge | 30 years | display component |
| David reign length | 40 years | display component |
| Davidic decomposition | 70 := 30 + 40 | interpretive framing only |

Guard:
This decomposition is a compositional display motif only. It must not overwrite or substitute for any arithmetic locks:

| Lock | Required distinction |
|---|---|
| Luke side | `LukeSpan = 5320` vs `LukeIntervals = 5250` |
| Matthew side | `MattSpan_BirthHinge = 2800` vs `MattSpan_Carrier = 2870` |
| MirrorVolume | `8050` and expansion to `8750` remain bound to their locked inputs |
| Seal700 | `700` remains generated by the locked expansion |
| P2 operator protocol | `36 BC ↔ 6 BC` and `6 BC ↔ AD 25` must not be chained |

The decomposition may be cited as literary framing, including end-cap overlap or double-generational-knot warrant, but never as an arithmetic driver.

## 2. Luke — two distinct numbers

Active state:
NT / Luke genealogy; 70-year carrier; mandatory split between names-span and interval-count states.

### 2.1 LukeSpan: names-span state

Active state:
Luke names-span state; Adam → Christ as names.

Claim-status: arithmetic fact for `76 × 70 = 5320`; structural genealogy-span label for `LukeSpan`.

`LukeSpan = 5320 = 76 × 70`.

This is the names-span state: Adam → Christ as names.

Lock:
`LukeSpan = 5320`.

### 2.2 LukeIntervals: interval-count state

Active state:
Luke interval-count state; intervals between 76 names.

Claim-status: arithmetic fact for `75 × 70 = 5250`; structural interval-count label for `LukeIntervals`.

`LukeIntervals = 5250 = 75 × 70`.

This is the interval-count state: the intervals between 76 names.

Lock:
`LukeIntervals = 5250`.

### 2.3 Luke-side BC projection brackets

Active state:
Luke birth-hinge bracket; Luke P2 rails-window bracket; same-side BC projection display.

Claim-status: arithmetic fact; dependency-controlled P2 rail-state guard.

Using the locked birth hinge `6 BC` as the Christ-side bracket:

```markdown
6 BC + 5320 = 5326 BC
```

Arithmetic check:
`6 + 5320 = 5326`. Verified as same-side BC projection.

Lock:
`LukeSpan` bracket from `6 BC` → `5326 BC`.

Using the quad-window mate `36 BC` as an alternate Christ-side rail bracket, explicitly mapped to civil BC for display:

```markdown
36 BC + 5250 = 5286 BC
```

Arithmetic check:
`36 + 5250 = 5286`. Verified as same-side BC projection.

Lock:
`LukeIntervals` bracket from `36 BC` → `5286 BC`.

Guard:
The 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.

## 3. Matthew — explicit dual-bracketed requirement

Active state:
NT / Matthew genealogy; birth-hinge bracket; head-envelope marker; carrier bracket; display-table-only ledger.

### 3.1 MattSpan_BirthHinge

Active state:
Matthean Abraham → `6 BC` birth-hinge bracket.

Claim-status: arithmetic fact for `40 × 70 = 2800`; structural birth-hinge label for `MattSpan_BirthHinge`.

`MattSpan_BirthHinge = 2800 = 40 × 70`.

This is the Abraham → `6 BC` bracket.

From the birth hinge `6 BC`:

```markdown
6 BC + 2800 = 2806 BC
```

Arithmetic check:
`6 + 2800 = 2806`. Verified as same-side BC projection.

Lock:
`MattSpan_BirthHinge` bracket: Abraham anchor = `2806 BC`.

### 3.2 Matthean head bracket

Active state:
Matthean head-envelope marker; 42-name presentation envelope.

Claim-status: arithmetic fact for `2806 + 70 = 2876`; structural marker for the head-envelope function.

To express the head-envelope marker for the 42-name presentation, as an envelope only and not as a distinct span lock:

```markdown
2806 BC + 70 = 2876 BC
```

Arithmetic check:
`2806 + 70 = 2876`. Verified as same-side BC projection.

Lock:
Matthean head bracket = `2876 BC`.

### 3.3 MattSpan_Carrier

Active state:
Matthean Abraham → `AD 65` carrier bracket; civil cross-axis no-year-0 state.

Claim-status: arithmetic fact for `41 × 70 = 2870`; structural carrier-bracket label for `MattSpan_Carrier`.

`MattSpan_Carrier = 2870 = 41 × 70`.

This is the Abraham → `AD 65` bracket, with no year 0.

Civil arithmetic check:

```markdown
2806 BC → 1 BC = 2805 years
1 BC → AD 65 = 65 years
2805 + 65 = 2870
```

Arithmetic check:
Equivalent civil cross-axis check: `2806 + 65 − 1 = 2870`. Verified under the no-year-0 rule.

Lock:
`MattSpan_Carrier`: `2806 BC → AD 65 = 2870`.

Guard:
Bare `Matthew span` is disallowed. All references must specify `MattSpan_BirthHinge = 2800` or `MattSpan_Carrier = 2870`.

### 3.4 Genealogy chart

Active state:
display-table-only genealogy ledger; 70-year carrier display; non-lock schematic placement state.

Status: display table only.

Claim-status: display-table-only; author-resolved figurative God bookend label state; no literal divine-origin chronology claim.

This 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`.

Display-label audit state:
The 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.

| Primary 70-year generation | Matthew's genealogy | Luke's genealogy |
|---|---|---|
| 5326–5256 BC |  | God |
| 5256–5186 BC |  | Creation of Adam |
| 5186–5116 BC |  | Seth |
| 5116–5046 BC |  | Enosh |
| 5046–4976 BC |  | Kenan |
| 4976–4906 BC |  | Mahalalel |
| 4906–4836 BC |  | Jared |
| 4836–4766 BC |  | Enoch |
| 4766–4696 BC |  | Methuselah |
| 4696–4626 BC |  | Lamech |
| 4626–4556 BC |  | Noah |
| 4556–4486 BC |  | Shem |
| 4486–4416 BC |  | FLOOD & Arphaxad |
| 4416–4346 BC |  | Cainan (2nd) |
| 4346–4276 BC |  | Shelah |
| 4276–4206 BC | God | Eber |
| 4206–4136 BC | Creation of Adam | Peleg |
| 4136–4066 BC | Seth | Reu |
| 4066–3996 BC | Enosh | Serug |
| 3996–3926 BC | Kenan | Nahor |
| 3926–3856 BC | Mahalalel | Terah |
| 3856–3786 BC | Jared | Abraham |
| 3786–3716 BC | Enoch | Isaac |
| 3716–3646 BC | Methuselah | Jacob |
| 3646–3576 BC | Lamech | Judah |
| 3576–3506 BC | Noah | Perez |
| 3506–3436 BC | Shem | Hezron |
| 3436–3366 BC | FLOOD & Arphaxad | Ram |
| 3366–3296 BC | Cainan (2nd) | Amminadab |
| 3296–3226 BC | Shelah | Nahshon (Aaron's brother-in-law) |
| 3226–3156 BC | Eber | Salmon |
| 3156–3086 BC | Peleg | Boaz |
| 3086–3016 BC | Reu | Obed |
| 3016–2946 BC | Serug | Jesse |
| 2946–2876 BC | Nahor | David |
| 2876–2806 BC | Terah | Nathan |
| 2806–2736 BC | ABRAHAM | Mattatha |
| 2736–2666 BC | Isaac | Menna |
| 2666–2596 BC | Jacob | Melea |
| 2596–2526 BC | Judah | Eliakim |
| 2526–2456 BC | Perez | Jonam |
| 2456–2386 BC | Hezron | Joseph |
| 2386–2316 BC | Ram | Judah |
| 2316–2246 BC | Amminadab | Simeon |
| 2246–2176 BC | Nahshon (Aaron's brother-in-law) | Levi |
| 2176–2106 BC | Salmon | Matthat |
| 2106–2036 BC | Boaz | Jorim |
| 2036–1966 BC | Obed | Eliezer |
| 1966–1896 BC | Jesse | Joshua |
| 1896–1826 BC | David | Er |
| 1826–1756 BC | Solomon | Elmadam |
| 1756–1686 BC | Rehoboam | Cosam |
| 1686–1616 BC | Abijah | Addi |
| 1616–1546 BC | Asa | Melki |
| 1546–1476 BC | Jehoshaphat | Neri |
| 1476–1406 BC | Joram | Shealtiel |
| 1406–1336 BC | Uzziah | Zerubbabel |
| 1336–1266 BC | Jotham | Rhesa |
| 1266–1196 BC | Ahaz | Joanan |
| 1196–1126 BC | Hezekiah | Joda |
| 1126–1056 BC | Manasseh | Josech |
| 1056–986 BC | Amon | Semein |
| 986–916 BC | Josiah | Mattathias |
| 916–846 BC | Jeconiah | Maath |
| 846–776 BC | Shealtiel | Naggai |
| 776–706 BC | Zerubbabel | Esli |
| 706–636 BC | Abiud | Nahum |
| 636–566 BC | Eliakim | Amos |
| 566–496 BC | Azor | Mattathias |
| 496–426 BC | Zadok | Joseph |
| 426–356 BC | Achim | Jannai |
| 356–286 BC | Eliud | Melki |
| 286–216 BC | Eleazar | Levi |
| 216–146 BC | Matthan | Matthat |
| 146–76 BC | Jacob | Heli |
| 76–6 BC | Joseph (husband of Mary) | Joseph |
| 6 BC–AD 65 | Jesus Christ | Jesus |
| AD 65–AD 135 | Final generation | Final generation |

Note:
This 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`.

## 4. Jubilee Bridge: head-to-head

Active state:
Luke-head bracket; Matthean head-envelope marker; head-to-head Jubilee bridge.

Claim-status: arithmetic fact for the equality; structural inference for Jubilee bridge framing.

Using the locked head-envelope markers:

| Head bracket | Value |
|---|---:|
| Lukan head bracket, LukeSpan from `6 BC` | 5326 BC |
| Matthean head bracket | 2876 BC |

Difference:

```markdown
5326 − 2876 = 2450
2450 = 5 × 490 = 50 × 49
```

Arithmetic check:
`5326 − 2876 = 2450`; `5 × 490 = 2450`; `50 × 49 = 2450`. Verified.

Lock:
Luke-head ↔ Matthew-head = `2450`, or 50 Jubilees.

Argument-control note:
The 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.

## 5. MirrorVolume and Key-of-23 expansion

Active state:
MirrorVolume span-provenance state; ordinary Key-of-23 whole-year expansion state; Seal700 state; inactive Residue Protocol state.

### 5.1 MirrorVolume definition

Active state:
Genealogical MirrorVolume state; hard span-provenance state.

Claim-status: arithmetic fact for `5250 + 2800 = 8050`; source-retained structural label for MirrorVolume; hard span provenance.

MirrorVolume uses `LukeIntervals = 5250` and `MattSpan_BirthHinge = 2800` only:

```markdown
8050 := 5250 + 2800
```

Arithmetic check:
`5250 + 2800 = 8050`. Verified.

Prohibition:
`MattSpan_Carrier = 2870` must not be substituted into `8050`, `8750`, or Seal700.

Argument-control note:
`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.

### 5.2 Key-of-23 expansion and Seal700

Active state:
ordinary Key-of-23 whole-year expansion; Seal700 generated state.

Claim-status: exact-ratio arithmetic fact for the expansion; structural label for Seal700; non-Residue control.

```markdown
8050 × 25/23 = 8750
8050 ÷ 23 = 350
8750 − 8050 = 700 = 10 × 70
```

Arithmetic check:
`8050 ÷ 23 = 350`; `350 × 25 = 8750`; `8750 − 8050 = 700`; `10 × 70 = 700`. Verified as exact-ratio whole-year expansion.

Lock:
`8050 → 8750` under `25/23`.

Lock:
Seal700 = `700`, generated by the expansion.

Terminology guard:
This is an ordinary Key-of-23 whole-year expansion. It is not the Residue Protocol unless a later section explicitly shifts into residue arithmetic.

Argument-control note:
Seal700 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.

## 6. Double-generational knot

Active state:
double-generational knot compositional state; end-cap overlap / literary-framing state; non-arithmetic-input guard.

### 6.1 Definition

Active state:
compositional end-cap operator; display / literary-framing state.

Claim-status: structural / compositional operator; author-clarified Job-only typological warrant; not an arithmetic input.

The 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.

Lock:
The double-generational knot is a display / compositional operator only. It is not an arithmetic input.

Source-control note:
The 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.

### 6.2 Hard guards

The knot may justify end-cap overlap as a literary framing device, but it must not overwrite or substitute:

| Distinction | Guard |
|---|---|
| Matthew span states | `MattSpan_BirthHinge = 2800` vs `MattSpan_Carrier = 2870` |
| Luke span states | `LukeIntervals = 5250` vs `LukeSpan = 5320` |
| Volume states | MirrorVolume `8050` vs expanded volume `8750` |
| Seal state | Seal700 `700` |

### 6.3 God bookend, outer Luke rail, and Alpha-Omega 22-fold clarification

Active state:
Author-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.

Claim-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.

The `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.

Dependency note:
`File_54` supplies the outer Luke rail / overlapped middle-generation clarification. The relevant dependency-controlled structure is:

```markdown
5356 BC → AD 5355 = 10710 = 153 × 70
10710 + 70 = 10780 = 154 × 70 = 22 × 490
22 × 490 = 22 × 7 × 70
```

Under 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.

Author-supplied display form:

```markdown
5356/5286 BC → 36 BC/AD 35 → AD 5285/5355
```

This 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`.

Alpha-Omega 22-fold note:
The `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.

Revelation reception-history note:
The Alpha-Omega passages in Revelation supply the threefold theological field for this display:

| Revelation field | Display block | Function |
|---|---|---|
| Revelation 1:8: Alpha and Omega; who was | `5356–5286 BC` | Pre-Creation / before-this-Creation rail |
| Revelation 1:8: who is | `36 BC–AD 35` | Central overlapped Christ-generation |
| Revelation 1:8: who is to come | `AD 5286–5356` | New-Creation / eschatological rail |
| Revelation 21:6 and 22:13 | full `22 × 490` bracket | Beginning and End; First and Last; Alpha and Omega |

The 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.

Johannine note:
The `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.

Machine Guard [OUTER LUKE RAIL NON-IMPORT]:
The 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`.

Machine Guard [ALPHA-OMEGA 22-FOLD NON-DRIVER]:
The 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.

## 7. Prohibited 30-year-straddling claims

Active state:
File_32 / File_33 P2 namespace; P2 positive rails-window local Operator A; P2 negative-polarity / signed A-space local Operator B; non-straddling guard.

### 7.1 Disallowed conflation

Claim-status: argument-control correction; Machine Guard; dependency-controlled P2 operator separation.

Any prior pattern that treated `36 BC ↔ 6 BC ↔ AD 25` as a single continuous operator is prohibited.

Mandatory correction:

| Span | Correct state |
|---|---|
| `36 BC ↔ 6 BC` | P2 positive rails-window; local Operator A only |
| `6 BC ↔ AD 25` | P2 negative-polarity / signed A-space bridge; local Operator B only |

These spans must not be chained as a single operator.

Argument-control note:
The 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.

### 7.2 Status of former composite patterns

Where older presentations used the composite straddling habit, those patterns are either:

1. removed;
2. reclassified as display motif only; or
3. reframed under the double-generational knot as composition only.

## 8. Cumulative cube lock

Active state:
dependency-controlled cumulative cube lock; capsule-authorized anchor state; not locally rederived.

Claim-status: arithmetic fact for the verified values; dependency-controlled lock for local argument function.

Deep-time cumulative anchor tether, as a lock only when already authorized by the capsule anchor set:

```markdown
14006 BC → 5256 BC = 8750 years = 125 × 70 = 5³ × 70
```

Arithmetic check:
`14006 − 5256 = 8750`; `125 × 70 = 8750`; `5³ × 70 = 8750`. Verified as same-side BC arithmetic. Dependency authorization remains governed by the capsule anchor set.

Lock:
`14006 BC → 5256 BC = 8750 = 125 × 70`.

Argument-control note:
The 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.

## 9. Optional display motif — 40/70/100 triad

Active state:
optional 40/70/100 display motif; anti-overfitting guard; non-lock interpretive overlay.

Claim-status: typological / display motif only; anti-overfitting guard.

The `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.

Display motif only; not a lock:
Any triadic framing that relies on combining both rails and both ends simultaneously is compositional unless independently locked elsewhere.

Machine Guard [ANTI-OVERFITTING]:
The 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.

## 10. File_44 harmonization control note

The File_44 terminology-harmonization cycle is retained as active dependency-control language only.

| Area | Public-clean handling |
|---|---|
| File_32 / File_33 namespace | Active P2 terminology routes through the File_32 / File_33 Prime–Civil / Polarity Namespace. |
| 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`. |
| File_42 relationship | Retained as geometry-first source-history support only; not reactivated as File_43's active P2 dependency route. |
| File_44 reciprocal context | Retained as downstream / reciprocal scaling-law context only; not proof-bearing upstream. |
| Coordinate Mirror | Secondary agreement where explicitly opened; not primary polarity generation. |
| 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. |

## 13. Final Audit Notes

Audit note:
No reopened harmonization correction required changing arithmetic, anchors, modal states, node-classes, sign conventions, operators, Mirror protocols, theological claims, or dependency locks.

Audit note:
The 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.

Audit note:
P2 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.

Audit note:
File_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.

Audit note:
File_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.

Audit note:
MirrorVolume 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.

Audit note:
The 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.

Audit note:
The 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.

Audit note:
The 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.

Audit note:
Henry 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.

## 14. Final Unresolved Issues and Dependency Notes

No finalization source blocker was identified. No argument-status, arithmetic, modal-state, or dependency-lock correction is required.

The 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.

The following items remain dependency-controlled rather than unresolved:

| Issue | Handling |
|---|---|
| File_44 reciprocal registration | Resolved as downstream context only; keep it from becoming proof-bearing upstream. |
| File_42 source-history support | Resolved as background support only; do not reactivate the former active skipped-prime dependency label. |
| Cumulative cube lock authorization | Arithmetic and argument status are resolved; authorization remains dependency-controlled by the capsule anchor set. |
| Outer Luke rail / `153 + 1` structure | Preserved as dependency-controlled explanatory material by `File_54`; keep guarded against overwriting File_43 locks. |
| Alpha-Omega `22 × 490` bracket | Preserved as typological / reception-history framing by `File_54` / `File_53` dependency. |
| Smith LXX source-reconstruction witness | Not active; revisit only if LXX Genesis 5 / 11 reconstruction becomes local to the argument. |

## Revision and archive note

This public-clean Markdown source removes only archival amendment history, pass logs, pressure-test repetition, pointer-refresh records, and obsolete replacement-workflow notes.

Detailed revision history is preserved in the `Repository_Change_Archive`.

No 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.

Final pressure-test status is preserved in the file header. Detailed pressure-test records are archived rather than repeated in the public file body.