File: File_46 Title: Harmonic Expansion Protocols — Expansion Operators on the 70-Year Genealogical Lattice Status: Final; Passes 0–2 complete under Project Procedures; prime-lattice section removed by author direction June 10 2026; marked Final by author June 10 2026; publication-clean verification current; deep-time overlay application bounded update applied Publication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive. Pressure-test status: Current; publication-clean verification complete after author-Final pass, prime-lattice section removal, and public-clean cleanup; focused check complete for the deep-time overlay application bounded update; no pre-existing argument-bearing content changed. Register Agreement status: Checked against State_Vocabulary_Register v1.18 and active companion controls; bounded deep-time overlay application addition (§6A; §7 scope record) only; no pre-existing arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries changed. Primary domain: Harmonic mechanics / expansion operators on the Matthew–Luke 70-year genealogical lattice Canonical source: Markdown Source-history identifiers: FILE_46: HARMONIC_EXPANSION_AND_PRIME_PROPAGATION.md; UUID PRIME_EXPANSION_ROSETTA_MIRROR; source status DEFINED (v10.1-compatible) Major operators: civil cross-axis span BC + AD − 1; Prophetic Ratio 70/69; Priestly Ratio 25/23; doubled base span 9660 = 2 × 4830; Danielic wave-set {490, 700, 1400, 4900, 7000} by File_44 / File_45 dependency; 6624 = 1656 × 4 = 23 × 288 = 96 × 69; twenty-of-years pair 7200 = 20 × 360 / 6720 = 20 × 336; 920 × 25/23 = 1000; double-expansion licensing 23² × 25/23 × 25/23 Major modal states: 70-year carrier display lattice (File_43); Enoch pivot state 4836 BC (File_45); figurative God bookend label state; Daniel 9 pattern-template state; non-lock +460 motif state; deep-time overlay application state; staged-Flood display state; Adam-field expansion state; twenty-of-years pair state; double-expansion licensing corollary state Related files: File_43 (primary genealogy-lattice locks); File_44 (cycle family / scaling-law controls); File_45 (Daniel-9 template, Danielic wave-set, Enoch pivot, statistical proof burden); File_22 (cumulative deep-time 14006 BC by dependency); File_54 (comparative Luke lattice, mediated through File_43); File_42 (source-history support only); File_16; File_17; File_18 (LXX cumulative overlay source-table); File_51b; File_56 (+460 rail); Restart Capsule v11.17; State Vocabulary Register v1.18; 490d Repository Style Guide v2.5; Project Procedures v3.3 Revision basis: author-supplied FILE_46 source; author direction of June 10 2026 removing the prime-lattice section; 490d Repository Style Guide v2.5; Restart Capsule v11.17; State Vocabulary Register v1.18; Project Procedures v3.3; File_43 Final Harmonized; File_45 Final post-final pressure tested; File_54 Final; File_00 Public-Clean precedent; Repository_Change_Archive (non-controlling history) Current refresh note: Public-clean trust-status equalization aligns active control pointers to 490d Repository Style Guide v2.5, Restart Capsule v11.17, State_Vocabulary_Register v1.18, and Project Procedures v3.3. Bounded deep-time overlay application (§6A) registered from the Regular / Cumulative page publication discussion record. Register Agreement status is recorded in the header; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries are changed. Detailed pass logs, pressure-test records where applicable, pointer-refresh history, and replacement-workflow notes are preserved in Repository_Change_Archive.

September 8 2026 bounded Lamech routing: former §6A.1–§6A.3 777-overlay executions move to Appendix A; stable headings route to them. §§1–6 and §6A.4–§6A.5 proof bodies are preserved. Registered at Register v1.53 §D.43 / Capsule v11.52 §10.30. Focused verification only; no new full pressure test or separate re-Finalization.

File_46 — Harmonic Expansion Protocols

0. File-function

File_46 defines the expansion operators that generate and lock spans within the Matthew–Luke 70-year genealogical lattice and its Danielic wave-set. The file is an operator register, not a static date list. All computations are stated as integers under the civil no-year-0 convention of the Restart Capsule.

Active state: 70-year carrier display lattice by File_43 dependency; Enoch pivot state 4836 BC by File_45 dependency; expansion-operator state (70/69; 25/23); actual chronology / local-state default.

Proof-burden rule: File_43 carries the genealogy-lattice locks (MattSpan_BirthHinge = 2800; MattSpan_Carrier = 2870; LukeSpan = 5320; LukeIntervals = 5250). File_45 carries the statistical proof burden for the wave-set and the Daniel-9 segmentation template. File_46 supplies operator mechanics; it does not re-prove and must not overwrite those locks.

Claim-status frame: Each span equation below is an arithmetic fact under its stated operator. Each lattice placement (which generation block an endpoint lands on) is a structural inference controlled by the File_43 display ledger. Calendar-theological framing is labeled where it appears.

0.1 Working state register

Machine Guard [CIVIL SPAN EXECUTION]: For all programmatic execution, enforce BC + AD − 1 = Total explicitly for spans crossing the epoch boundary. Do not use standard algebraic subtraction, such as AD − (−BC), across the boundary; it introduces a 1-year error. Treat BC and AD labels as absolute magnitudes when applying this rule.

Machine Guard [DISPLAY-LEDGER SPAN USE]: The File_43 genealogy ledger is display-table-only. Where this file uses a ledger boundary as a span endpoint, the local section restates its node-class. No span here redefines or overwrites MattSpan_BirthHinge, MattSpan_Carrier, LukeSpan, or LukeIntervals.

0.2 File map

1. Locked Constants

The constant labels L0–L4 are source-retained labels for the file's explicit integer chains.

L0. Civil span identity (no year 0)

For spans crossing from BC to AD:

BC + AD − 1 = Total

This is the repository's one cross-axis span formula. Same-side spans use ordinary subtraction.

L1. The 4830 base span

Active state: Enoch pivot state (File_45); solar same-side span.

4836 BC → 6 BC = 4836 − 6 = 4830

The 4830 span from the Enoch pivot to the 6 BC Christ-generation hinge is the base input to both expansion operators below.

State note: 4830 here is a solar same-side span value. It is not an Enochian-calendar constant; the Enochian calendar family (364; 1274 = 3.5 × 364) is a separate state controlled elsewhere.

L2. Prophetic Ratio (70/69)

Active state: Key-of-23 Prophetic Expansion state.

4830 × 70/69 = 4900

because 4830/69 = 70 and 70 × 70 = 4900.

Therefore:

4836 BC → AD 65 = 4900

since 4836 + 65 − 1 = 4900.

The source associates this operator with Jared (the Jared / Prophetic expansion); the association is developed in §4.2.

L3. Priestly Ratio (25/23)

Active state: Key-of-23 Priestly Expansion state.

4830 × 25/23 = 5250

because 4830/23 = 210 and 210 × 25 = 5250.

Therefore:

5256 BC → 6 BC = 5256 − 6 = 5250

The source associates this operator with Luke (the Luke / Priestly expansion); the association is developed in §4.2.

L4. Danielic wave-set

Active state: Danielic wave-set state by File_44 / File_45 dependency.

The cycle family used in the repository's statistical framework is:

C = {490, 700, 1400, 4900, 7000}

Dependency note: The wave-set is owned by File_44 (scaling-law controls) and tested by File_45 (exact-sweep statistics). It is recorded here as shared vocabulary only; this file does not re-derive or re-test it.

2. Generator Locks: Solomon and Christ

2.1 Solomon expansion (Priestly operator from deep time)

Active state: Priestly Ratio 25/23; cumulative deep-time anchor 14006 BC by File_22 dependency; Matthew-side display ledger (File_43 70-year carrier display; source wording: "Matthew shadow lattice").

Goal: generate 1756 BC, the end of Solomon's 70-year carrier (1826–1756 BC), by applying the Priestly operator to the deep-time → Abraham boundary span.

Lattice placement: 1756 BC is the end of Solomon's 70-year carrier (1826–1756 BC) in the File_43 display ledger.

Claim-status note: The span chain is arithmetic fact under the stated operator. The identification of the projected endpoint with the Solomon carrier boundary is structural inference controlled by the File_43 ledger. "Lock" in this file's source is a legacy label for these lattice placements; it is not the File_33 Value Lock or Ordinal Lock state.

2.2 Christ-generation generator (Prophetic operator from the Enoch pivot)

Active state: Prophetic Ratio 70/69; Enoch pivot state 4836 BC.

Goal: generate the AD 65 terminus of the Christ generation from the Enoch pivot.

Lattice placement: AD 65 is the end of the Christ generation (6 BC → AD 65) in the 70-year lattice framing of File_43.

3. The 9660 Dual Expansion: Adam and Noah/Shem

Define the doubled base span:

9660 = 2 × 4830

3.1 Prophetic track — Matthew-side Adam at 4206 BC

Active state: Prophetic Ratio 70/69; deep-time anchor 14006 BC; Matthew-side display ledger.

Lattice placement: 4206 BC opens the Matthew-side display bracket "Creation of Adam" (4206–4136 BC) in the File_43 ledger.

3.2 Priestly track — Noah/Shem hinge at 3506 BC

Active state: Priestly Ratio 25/23; deep-time anchor 14006 BC; Matthew-side display ledger.

Lattice placement: 3506 BC is the Noah/Shem hinge boundary — end of the Noah generation (3576–3506 BC), start of the Shem generation (3506–3436 BC) — on the Matthew side of the File_43 ledger.

4. The Rosetta Stone: 3-Calendar Resolution

Section-heading note: "Rosetta Stone" is retained as a legacy theorem label; its evidential role is supplied by the claim-status notes below.

4.1 One fixed solar span

4836 BC → 6 BC = 4830 solar years

4.2 Three translations of the same 4830 span

Node-class note: 4906 BC is the opening boundary of Luke's Jared generation, and 5256 BC is Luke's Adam-Creation ledger boundary (LukeIntervals lock endpoint), per File_43 and File_54. The correspondence of each expanded value to a lattice boundary is structural inference.

4.3 The 11th-Week correction (420 vs 490 resolved)

This section distinguishes calendar-conversion residue from Danielic week count.

Conversion residue (Priestly head vs solar pivot):

5256 − 4836 = 420

The 420 is the conversion delta that arises because Luke's head is expressed in Priestly units while the Enoch pivot is solar.

Luke's additional head generation:

Active state: figurative God bookend label state (File_43).

The 5326–5256 BC row of Luke's ledger — the "God" row — adds one more 70-year generation above the Priestly head:

5326 − 5256 = 70

Display-label note: The God entry is the author-resolved figurative Luke-derived bookend label of File_43. The 5326 BC boundary is an arithmetic lattice endpoint (the LukeSpan = 5320 lock endpoint); the label itself is not an arithmetic input and asserts no literal divine origination.

Therefore Luke's full step ahead of the Enoch pivot is:

420 + 70 = 490

Week counts on the 490-scale:

4836 BC → AD 65 = 4900 = 10 × 490
5326 BC → AD 65 = 5390 = 11 × 490
5390 − 4900 = 490

Conclusion: Luke's "11th week" is not 420 years; it is 490 years, composed as 420 conversion residue plus 70 head generation.

5. 2nd Cainan: Non-Lock Motif Only

Active state: non-lock +460 motif state (File_45).

This file does not use 2nd Cainan as an operative targeting lock. The motif is recorded only as an optional correspondence seen elsewhere:

460 (2nd Cainan) + 30 (Adam apparent age) = 490

Policy: The equality may be referenced as a thematic Danielic correspondence. It is not used in this file as a generator, anchor shift, or targeting operator.

Machine Guard [STATIC +460/+30 MOTIF]: The equation 460 + 30 = 490 is a static motif. Programmatic engines must not extract 460 or 30 from this section as dynamic variables, offsets, or generators in any other calculation within the lattice.

6. Jared → 2nd Cainan as Daniel-9 Front-Packet Analogue

Active state: Jared / 2nd Cainan Danielic front-packet state; Daniel 9 pattern-template state; Christ-generation bisection state — all by File_45 dependency.

Dependency note: The statistical and template proof burden for this section is carried by File_45. This section restates the lattice mapping only.

6.1 The explicit lattice interval

Using the 70-year lattice start-years of the File_43 ledger:

Jared start: 4906 BC
2nd Cainan start: 4416 BC
4906 − 4416 = 490 = 7 × 70

This is a full Danielic week of weeks — a 490-year packet — in lattice units.

6.2 Daniel-9 decomposition and the x10 echo

Daniel 9 is often schematized as:

49 + 434 + 3.5 + 3.5 = 490

Under x10 scaling:

490 + 4340 + 35 + 35 = 4900

Within the lattice:

The front packet is represented by the Jared → 2nd Cainan 490 — a structurally distinct first segment in "troubled times" terms, the Watcher-crisis horizon. The terminal halving is represented at the Christ boundary under the same x10 template, where the final week is bisected (6 BC → AD 30 → AD 65; see File_45).

Claim-status note: This section asserts structural isomorphism — a pattern-template mapping within the lattice. It does not claim that Daniel 9:25 is historically about Jared, and it opens no 434-year lock.

6A. Deep-time overlay application (dependency-controlled bounded addition)

Active states: main-chain cumulative comparison and Adam-field expansion; general double-expansion licensing. Deep-time 777 overlay, staged-Flood, and twenty-of-years executions are appendix-only.

Source record: the Regular / Cumulative page publication discussion. Main source-table values remain controlled by File_18 §6D. Its LXX 777 overlay is now in File_18 Appendix B.2; applications depending on it have moved from §6A.1–§6A.3 to this file's Appendix A. The unaffected §6A.4–§6A.5 use the main cumulative chain and MT comparisons. Narrative homes remain File_22, File_44, and File_51b; no comparison becomes an independent anchor.

Scope note: this section applies File_46 operators outside the Matthew–Luke lattice, on the LXX cumulative deep-time frame. The application is registered here because the operators are this file's; the lattice-local rulings of §§1–6 are unchanged.

Non-collapse guard [§5 vs deep-time +460]: §5's non-lock ruling for the 2nd Cainan is lattice-local to the Matthew–Luke carrier. The deep-time +460 states (File_56 rail; File_18 restored-Cainan tables; the 430-alignment of the leveled MT / LXX cumulatives) are load-bearing in their own frames and are not governed by §5. Do not collapse.

6A.1 The twenty-of-years pair — appendix route

The LXX 777-overlay application formerly executed here is preserved unchanged in Appendix A.1. It is not a main-chain Lamech derivation.

6A.2 The staged-Flood display — appendix route

The dependent staged-Flood example is preserved in Appendix A.2, with its overlay provenance and typological classification retained.

6A.3 Double-expansion licensing and the appendix example

A span divisible by 23² admits two successive integral 25/23 expansions. This operator fact remains in the main body. The particular LXX 777-overlay example formerly here, including its onward conversions, is retained in Appendix A.3 and is not independent main-chain evidence.

6A.4 The cross-track 2300 and the Jared span

8048 BC (Lamech Flood node, Moses member) → 5748 BC (Arphaxad Flood node, Aaron member) = 2300
10349 BC (Jared span head) → 5748 BC = 4601 = 2301 + 2300 = 4000 + 1 + 600

Member selections are author-declared: Jared's span head; Lamech's Moses member; Arphaxad's Aaron member. The +1 is the Flood-year inclusive device — Noah "in the 600th year… in the 601st" (Gen. 7:11; 8:13) — which warrants the head-member selection; Shem's 600 stands in for Noah's 600 in the stacked frame. Device recurrence: the SP regular's inclusive-600th −1 (File_18) is the same instrument seen from the other side. Claim-status: arithmetic fact (spans); textual datum (the device); structural inference (selection and substitution).

6A.5 The Adam-field expansion

Heads: 14896 / 14466 / 14436 / 14006 BC = 430 + 30 + 430
Apparent head 14926 BC: 30 + 400 + 30 + 30 + 400 + 30 = 920;   920 × 25/23 = 1000

The four Adam heads (each tradition with and without Cainan) span a field whose intermediate spans are 400 / 430 / 460 / 490 and whose whole is 920 = 460 + 460, expanding to 1000 — "a thousand years as a day" (2 Pet. 3:8; typological reading). Head-toggle: from 14926 BC to the MT Lamech seven-span edge (7156 BC) is 7770 = 777 × 10 (Shem's ±2 completing); from 14896 BC, 7740 = 430 × 18 = 1290 × 6; Lamech's own 777 continues to 6379 BC: 8547 = 777 × 11. The field occupies the nine generations Adam through Lamech, a third of the twenty-seven. Narrative classification remains with File_22 / File_44; File_46 registers the 920 → 1000 expansion and the field grammar. Claim-status: arithmetic fact throughout; structural inference (field reading); typological reading as labeled.

7. Content-Scope and Removal Record

Arithmetic-control note: Every retained equation in this file resolves to explicit integers under its stated operator.

Source-history note: The source draft recorded that earlier FILE_46 material containing placeholders, undefined units or endpoints, or non-deterministic content had been removed before this revision. That removal is source history; no placeholder content remains.

Removal record: The source's prime-lattice section (P8–P12 extensions, including the P11 Exodus/Exile/Decimal spans, the P12 container span, and the "Enochian Unit" constant label) was removed in this revision by author direction of June 10 2026, as tangential to the file's harmonic-expansion subject. The prime-quadruple grid remains controlled by File_32, File_33, and File_35; nothing in this file depends on it.

Scope-record addition (bounded): §6A retains the main-chain deep-time applications and stable routing headings. September 8 2026 relocates only the LXX 777-dependent executions to Appendix A. The Matthew–Luke lattice scope of §§1–6 and the main §6A.4–§6A.5 are unchanged; the §5 non-lock ruling remains lattice-local.

Appendix A. Preserved LXX 777-overlay applications

These examples use the appendix-only, row-local LXX 777 overlay, not the main 753 lifespan chain. Their equations are preserved from former §6A.1–§6A.3. File_18 Appendix B.2 controls the unchanged 8077–8070 BC envelope; its 8070 close is the source of the following applications. Neither the overlap nor these expansions propagate an extra 24 into the cumulative chronology. Main §6A.4–§6A.5 and MT 777 comparisons remain outside this relocation.

A.1 The twenty-of-years pair

8070 BC → 1446 BC = 6624 = 1656 × 4 = 23 × 288 = 96 × 69
6624 × 25/23 = 7200 = 20 × 360
6624 × 70/69 = 6720 = 20 × 336

The overlay's seven-year close to the Exodus expands to twenty years-of-years in each calendar — the same pair-structure as the five-of-years at 1656 (1800 = 5 × 360; 1680 = 5 × 336; File_17 §14; File_18 Lamech block). Claim-status: arithmetic fact; exact-ratio arithmetic fact.

A.2 The staged-Flood display

1446 + 7200 = 8646 BC;   1446 + 6720 = 8166 BC;   original close 8046 BC
8646 BC (+480) → 8166 BC (+120) → 8046 BC;   480 + 120 = 600

The two expansions stage Genesis 6:3 in deep time: Noah's 480th year, the 120-year countdown, the Flood at 600. Increments: 7200 − 6624 = 576; 576 + 24 = 600; 6720 − 6624 = 96; 96 + 24 = 120 — the 24 being the overlay quantum. Claim-status: arithmetic fact (spans and increments); display motif / structural inference (the staging); typological reading (the Gen. 6:3 identification).

A.3 Onward conversions and the double-expansion licensing corollary

8070 BC → 5494 BC = 2576 = 23 × 112;   × 25/23 = 2800
8070 BC → 3838 BC = 4232 = 23 × 23 × 8;   × 25/23 = 4600;   × 25/23 = 5000

Licensing corollary: a 23²-multiple admits two successive integral 25/23 expansions; the 4232 instance closes on 5000, ten times the 500 at which Noah begat Shem, Ham, and Japheth. Claim-status: arithmetic fact; exact-ratio arithmetic fact; the 500 resonance is a display motif.

Revision and archive note

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

Detailed revision history is preserved in the Repository_Change_Archive.

The source-history removal record in §7 is retained because it controls the absence of the removed prime-lattice section.

Inherited public-clean note: the earlier cleanup did not alter its source arithmetic or states. The September 8 amendment now changes the publication/proof hierarchy of the LXX 777 examples to appendix-only; their equations, endpoints, and stated interpretations are preserved.