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; 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. 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; 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. Reciprocal-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. 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; 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. Publication-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. 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; File_69 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); 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. 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; 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.

File_43 — Genealogical Bridge

Related Repository Files

File_69 genealogical-bridge reciprocal note: Final 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.

Machine Guard [FILE_43 FILE_54 FILE_69 GENEALOGICAL-BRIDGE ROUTING]: Final 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.

File_69 Matthean-microcosm reciprocal note: Final 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.

Machine Guard [FILE_43 FILE_54 FILE_69 MATTHEAN-MICROCOSM ROUTING]: Final 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.

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

0.2 File map

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

0.6 Range, arrow, and sign-convention register

0.7 Mirror, Key, and Residue protocol register

0.8 Dependency-state register

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:

Arithmetic verification ledger:

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.

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.

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 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-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.

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:

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

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:

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:

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:

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:

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:

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.

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:

Difference:

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:

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.

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:

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:

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:

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:

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:

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:

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.

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:

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.