File: File_72
Title: Regular MT–SP–LXX Genealogical Comparative Synthesis
Status: Final — author-authorized October 7 2026; consolidated source review complete; registration and publication pending Spot installation
Primary domain: Regular; Comparative; Calendar; Theological
Traditions: MT; SP; LXX; bounded BJ/Jubilees corroboration
Canonical source: Markdown; source rows, anchors, and generic operators retain their existing Repository owners
Primary anchors: MT Creation endpoint 4114 BC; Year-6 opening 4116 BC; G2 Flood start 2458 BC; fixed Arphaxad 2456 BC; Abram 2166 BC; Conquest 1406 BC
Related files: File_71 / Report I; Files 00/01/02/05/06/07/11/12/14/15/16/17/18/20/46/53/54/63/69; broader context pointers to Files 09/22/58–60/70 and Supplement A; Report III
Major operators: regular Cainan 130; Terah 60; selected SP +215 positional equalization; named ordinary Gear and SP local person-companion; generated anchored translation; exact ratios 25/23, 70/69, 300/299; separately declared calendar/scalar comparisons
Major modal states: Regular Actual Nisan; Cainan all OFF / all ON; native versus restored Cainan; Terah OFF with named ON comparisons; G2 primary default; explicit G1 elected-line module; SP inclusive counts and completed capacities; generated geometry; corporate-Adam projection
Revision basis: Original Report II, September 2 2026; shared overlap-and-correction audit and consolidated revision October 7 2026; author-authorized adapted workflow and Finalization October 7 2026; Style Guide v2.5; Procedures v3.5; Restart Capsule v11.56; State Vocabulary Register v1.57; File_18 September 18 SP amendment
Source review: 23 relevant public files checked and rechecked October 7 2026, byte-identical to the reviewed basis, plus the author-finalized local File_71 continuity source; the local File_71 installation remains separate from the live index
Registration and publication: Final source prepared; not yet installed or centrally registered; existing Repository controls and public files are unchanged
Publication targets: https://490d.com/source/490d-unified-chronology/File_72.Regular_MT_SP_LXX_Genealogical_Comparative_Synthesis.md; /file-72-regular-mt-sp-lxx-genealogical-comparative-synthesis/; File_71 then File_72 installation order, with File_71 publication separately pending

# Regular MT–SP–LXX Genealogical Comparative Synthesis

## 0. File-function and controls

This study resolves Report I's Creation–Noah comparison one begetting father at a time. Its principal contributions are the named Creation-week ladder, Kenan/Jared/Cainan relations, the leveled post-Flood countdown, the variant-slot inventory, and the relation of the raw SP remainder to the current primary Noah station. It retains the Enoch calendar, corporate-Adam, and biographical-matrix corroborations in appendices.

The arithmetic gives a compact, conditional account of the received field. Its proposed Creation pattern and providential organization remain positive interpretations. Current source bindings determine which event or station each calculation reaches; equal numbers do not identify events or establish an ancient transmission mechanism.

### 0.1 Working-state register

| Object or state | Active binding |
|---|---|
| Main comparison | Regular Actual Nisan, Terah OFF, Cainan OFF in all lanes, selected full-430 comparison plane. SP native dates are translated +215; native LXX Cainan is expunged by 130 for the leveled row. |
| Creation endpoint | Year-7 close: LXX 5364, SP 4414, MT 4114 BC. Year-6 opening is separately two earlier; Year-6 close is one earlier. |
| Cainan all ON | Native LXX is retained; MT/SP receive regular 130 insertion. Corresponding upstream Creation-through-Arphaxad stations move; Shelah onward remains fixed. |
| Main Noah / Flood | G2 primary biographies and Flood start. LXX/SP Noah 3708→2758 and Flood 3108; MT Noah 3058→2108 and Flood 2458 BC. SP primary death retains the source's inclusive/harmonic qualification. |
| SP local companion | Noah/Shem person-stations alone move −1. G2 Noah 3707→2757 BC is distinct from primary 3708→2758. Flood start→close 3108→3107 is independently the event-year interval. |
| Raw begetting inventory | Retain SP Lamech age 53 and raw running sum 707. The canonical-primary path uses 52 completed units and sum 706. Do not substitute one basis into the other's classification. |
| Selected post-Flood and Shem module | Explicit G1 / Arphaxad-bound Shem: LXX/SP 3206, MT 2556 BC. Matched G1 Noah gives 500; fixed Arphaxad gives the next 100. G2 biological Shem remains distinct. |
| Running total versus Cumulative | A running total here sums regular begetting ages. Repository Cumulative chronology stacks lifespans and remains outside this study's proof. |
| SP counts | Inclusive lifespan counts, completed-year subtraction, and equivalent capacities to Flood close are labelled separately. A capacity does not change the selected physical death. |
| Generated and projected geometry | Translated heads, formal Jared elision, calendar contractions, and the corporate Eve 930 projection are declared constructions. They do not replace source biographies. |
| Evidence | Exact arithmetic, structural interpretation, theology, and transmission hypotheses retain different claim statuses. The weighted Shelah/Cainan center remains provisional pending its full selection algorithm. |

### 0.2 File map

| Location | Function | Active state / role |
|---|---|---|
| §1 | Source inputs and theological reading | Regular comparison; source ownership |
| §2 | Creation-week ladder and Seth/Noah–Shem exchanges | Raw and primary rows; generated Keys |
| §3 | Kenan, Jared, Cainan, Terah | Half-gaps; explicitly opened operator rectangle |
| §4 | Post-Flood countdown and named inventories | All-OFF / all-ON leveling; G1 Shem; raw variant counts |
| §5 | Flood pivot and three 1656 roles | Raw 129; local primary closure; distinct Noah events |
| §6 | Compact carriers and evidence hierarchy | Conditional arithmetic and structural synthesis |
| Appendix A | SP calendar and historical count models | Current Enoch dates; inclusive and closing capacities |
| Appendix B | Day 13/14 and Corporate Adam | Year-6-derived envelopes; declared 930 projection |
| Appendix C | MT Shem and biographical matrix | Selected coherent G1; generated remainder sums |
| Appendix D | Source corrections and cumulative agenda | Current Lamech settlement; historical continuation |

### 0.3 Dependency and source map

| Source owner | Retained responsibility | Local use |
|---|---|---|
| [File_18](https://490d.com/source/490d-unified-chronology/File_18.Chronological_Data_Tables.md), §§2–4A and September 18 amendment | MT/SP/LXX source rows; restored/native Cainan; operative Lamech; current SP person/event stations | Every chronology row and biography binding |
| [File_71 / Report I](https://490d.com/source/490d-unified-chronology/File_71.Regular_MT_SP_LXX_Creation_Noah_Comparative_Engine.md) | Author-finalized local comparative parent; publication by Spot pending in the checked index | Inherited 190/405 field, 1250/650 gaps, half-gap hubs, and 1656 spine; the prospective URL is an installation target |
| Files 00/02/11/17/46 | Anchors, Noah/Shem/Flood ontology, ordinary Gear, and exact Key protocols | Named comparison states and generated span applications |
| Files 07/12/14 | Creation markers, calendar bodies, and boundary distinctions | Year-6 / Day-13 envelopes; 364/365 and 180/182 comparisons |
| Files 01/05/06/15/16/63 | Abrahamic and Conquest target roles; generation/scale distinctions | Held 1406 target and Cainan/Terah 2091 convergence |
| Files 20/53/54/69 | BJ/Jubilees, literal 49 versus completion 50, genealogy and Enoch/Cainan context | Bounded corroboration and claim-status discipline |
| Files 58–60 and Supplement A | Broader Atonement Weave | Context pointer for LXX 6+7=13; no complete parent proof is rederived here |
| Files 09/22/70 and Supplement A; Report III | Cumulative architecture and later comparative development | Historical research route in Appendix D; no cumulative date claim enters the Regular proof |

Current Register §D.43 governs the LXX Lamech source hierarchy; §D.44 governs relevant Shem/Terah/week distinctions. File_18's published September 18 SP amendment controls its current station and inclusive-count bindings; that source retains central-registration debt. This file recognizes the source amendment without treating that debt as closed.

### 0.4 Local non-collapse guards

Machine Guard [REPORT II ROW AND SOURCE OWNERSHIP]:
Local tables execute parent-controlled rows. Running begetting totals are Regular, not Cumulative lifespan chronology. File_71 is the finalized comparative parent, not a replacement raw-data controller. Its Final status alone does not establish public installation; publication state is recorded separately.

Machine Guard [REPORT II RAW AND PRIMARY SP]:
Retain textual 53 / raw sum 707 / difference 129 beside completed primary 52 / sum 706 / difference 130. Raw 22+1 classification and primary completed chronology use different bases. The local Noah/Shem −1 does not propagate to Enoch or Creation.

Machine Guard [REPORT II GEAR AND EVENT BINDINGS]:
G2 primary is the default. Name G1 or cross-Gear comparisons where selected. Keep Noah birth/death, Shem birth/death, fixed Arphaxad, and Flood start/close distinct. Shared civil labels do not merge events.

Machine Guard [REPORT II COUNT AND CAPACITY]:
SP inclusive lifespan counts and completed capacities to Flood close do not move selected deaths. Fixed G2 Enoch is 3892→3527 BC; the 180 half-calendar selects companion Noah, and the sixfold 420 selects Flood close.

Machine Guard [REPORT II PROJECTION AND SCALE]:
Derive Day-13/14 opening and close from the Year-6 envelope. The corporate Eve 930 is a theological projection. A scalar, calendar day, ordinary year, and year-of-years comparison require their declared scale and endpoint roles.

Machine Guard [REPORT II CLAIM STATUS]:
Retain positive structural and providential readings alongside exact conditional arithmetic. Correlated constructions are not independent witnesses. The weighted-center claim awaits a full algorithm; transmission and unique-generator hypotheses remain unproved.

## 1. Comparison states and source inputs

### 1.1 A genealogy resolved one named row at a time

File_71, developed from Report I, controls the wider comparative Creation–Noah engine: the Terah/Cainan `60|70|60` field, the full `405` lattice, Creation wrappers, the three endpoint roles of `1656`, the `1250/650` manuscript gaps, their `625/325` half-gaps, and the associated exact Keys and external comparisons. This study follows the regular begetting-age differences one father at a time from Adam through Abraham. Its contribution is the named-row sequence within that inherited field, rather than a second source table or generic Gear protocol.

The sequence joins a seven-generation Creation-week descent, a Kenan/Cainan center, Jared's Day-6 transfer, a post-Flood countdown, the LXX `6+7=13` and SP `3+7=10` inventories, and the raw `22+1=23` lane-slot diagnostic. It then relates their variant magnitudes to Noah's `950` years and the three `1656` endpoint roles. Appendix A preserves the Enoch/calendar comparisons, Appendix B develops the corporate-Adam `720/728` and Fall field, and Appendix C extends the selected G1 Shem/biography comparisons.

All chronology here is Regular. A **running total from Adam** sums regular begetting ages to a named birth node. It is not Repository Cumulative chronology, which stacks lifespans. The later cumulative continuation remains a separate research domain.

Unless stated otherwise, civil labels are BC in the Nisan comparison. The main date plane holds the selected `+215` position, with `+60 Terah` OFF and second Cainan OFF in all three lanes. The Creation/Adam endpoint row is:

$$
(5364,4414,4114)_{\mathrm{LXX,SP,MT}},
\qquad5364-4414=950,\qquad4414-4114=300,
\qquad950+300=1250.
$$

The first coordinate is theoretical LXX Cainan-OFF. Native LXX retains Cainan. Moving from native LXX to this row removes his `130`; returning to ON restores the native state. MT/SP ON inserts the corresponding regular `130` generation. It does not add another Cainan to native LXX.

The comparison admits **all OFF** or **all ON**. At the ON transition the corresponding upstream Creation-through-Arphaxad stations acquire the shared `+130`, while Shelah and the downstream regular suffix remain fixed under File_18's insertion rule. Thus the corresponding manuscript gaps remain leveled. The Adam-through-Moses name inventory changes from `26` to `27`; the genealogy's count and its date operator are different objects.

The inherited full variant field is:

$$
(60+70+60)+(25+60+70+60)=190+215=405.
$$

These tables select one fixed `+215` slice. Terah, restored Cainan, local Noah/Shem stations, and generated translations are opened only where named. File_18 supplies the ages, chronology rows, native/restored distinction, and current SP station bindings; Files 11/17/46 and File_71 retain generic Gear, Key and comparison authority.

### 1.2 The theological and providential reading

The study reads the received MT–SP–LXX comparison as a theological or providential cipher. The proposed architecture may involve deliberate scribal arrangement, inherited chronographic shaping, reciprocal adjustment among traditions, providential superintendence beyond a single human encoder, or a combination of these. It does not require one historical scribe to have consciously designed the whole field.

The repeated grammar is the study's positive structural proposal. Textual/source inputs, exact arithmetic, structural inference and theological interpretation retain distinct roles. A named-row fit does not by itself identify an ancient encoding process, establish statistical rarity, or prove that the genealogy is uniquely generated by these few scalars.

## 2. The Creation-week ladder

### 2.1 Seven begetters and the `3+3+1` pattern

The first seven begetting fathers are read as a seven-generation Creation week:

| Comparison day | Begetting father | Birth node reached |
|---|---|---|
| 1 | Adam | Seth |
| 2 | Seth | Enosh |
| 3 | Enosh | Kenan |
| 4 | Kenan | Mahalalel |
| 5 | Mahalalel | Jared |
| 6 | Jared | Enoch |
| 7 | Enoch | Methuselah |

The grouping is `3+3+1`. Methuselah is the eighth named patriarch and the first birth node after that completed block. These are genealogical comparison positions read through the Creation pattern, not a claim that seven ordinary generations elapsed in the literal Creation week. Jared's SP `62` occupies Day 6, and Enoch's Day 7 begetting completes the six LXX centenary differences at Methuselah's birth.

### 2.2 Complete Adam-to-Noah row field

The following table retains the raw begetting-age sum. Lane order is always **LXX / SP / MT**. A manuscript gap is calculated by subtracting the lane's running total from its held Creation endpoint, then comparing corresponding reached birth stations. Consequently a begetting-age difference can transfer a gap internally without reducing the outer LXX–MT gap.

| Position / begetter | Birth reached | Ages, LXX / SP / MT | Running total from Adam, LXX / SP / MT | LXX−SP | SP−MT | Outer gap | Row function |
|---|---|---|---|---:|---:|---:|---|
| Opening endpoint / Adam | Adam | — | 0 / 0 / 0 | 950 | 300 | 1250 | Opening field |
| Day 1 / Adam | Seth | 230 / 130 / 130 | 230 / 130 / 130 | 850 | 300 | 1150 | Outer contraction 100 |
| Day 2 / Seth | Enosh | 205 / 105 / 105 | 435 / 235 / 235 | 750 | 300 | 1050 | Outer contraction 100 |
| Day 3 / Enosh | Kenan | 190 / 90 / 90 | 625 / 325 / 325 | 650 | 300 | 950 | Day-4 threshold |
| Day 4 / Kenan | Mahalalel | 170 / 70 / 70 | 795 / 395 / 395 | 550 | 300 | 850 | Outer contraction 100 |
| Day 5 / Mahalalel | Jared | 165 / 65 / 65 | 960 / 460 / 460 | 450 | 300 | 750 | Jared threshold |
| Day 6 / Jared | Enoch | 162 / 62 / 162 | 1122 / 522 / 622 | 350 | 400 | 750 | Internal transfer 100 |
| Day 7 / Enoch | Methuselah | 165 / 65 / 65 | 1287 / 587 / 687 | 250 | 400 | 650 | Final LXX centenary |
| Week 2, Day 1 / Methuselah | Lamech | 187 / 67 / 187 | 1474 / 654 / 874 | 130 | 520 | 650 | SP internal transfer 120 |
| Week 2, Day 2 / Lamech, raw age 53 | Noah, raw SP companion station | 182 / 53 / 182 | 1656 / 707 / 1056 | 1 | 649 | 650 | Raw Lamech differential 129 |
| Same G2 primary comparison, SP completed count 52 | Noah, canonical primary stations | 182 / 52 completed / 182 | 1656 / 706 / 1056 | 0 | 650 | 650 | Current primary station closure |

The final two rows are adjacent station readings, not two replacements for the textual age. Raw SP `53` remains visible:

$$
182-53=129,\qquad4414-707=3707.
$$

File_18's current G2 primary path uses the 53rd counted year with `52` completed units from Lamech's station:

$$
182-52=130,\qquad4414-706=3708.
$$

The raw reached Noah labels are `3708 / 3707 / 3058 BC`; the primary comparison is `3708 / 3708 / 3058 BC`. The latter gives the co-registered LXX/SP biography of File_71. SP primary birth/death `3708→2758` and companion `3707→2757` each retain `950`. Primary Flood start `3108` and companion-matched Flood close `3107` each give the qualified `350` post-Flood interval with their matching death stations. Flood close is the event boundary, not a person-companion operator. The primary death retains File_18's inclusive/harmonic qualification.

The source's phase-completion display is retained as a comparison of integer compartments:

$$
(130,520)\xrightarrow{129}(1,649)\xrightarrow{1}(0,650).
$$

The last unit records the change from raw SP full-53 sum/station to the primary completed-52 sum/station. It does not change the textual `53`, independently add a calendar year to the ancestry, or move the upstream SP chain. The event-year and the adjacent Noah station must remain separately typed.

### 2.3 Odd-number descent, direct age locks and formal Jared elision

The opening and seven day-states give:

$$
(1250,1150,1050,950,850,750,750,650)
=50(25,23,21,19,17,15,15,13).
$$

The day grouping is `(23,21,19) | (17,15,15) | 13`. In the corresponding `3+3+1` operations, Days 1–3 reduce the outer gap by `100` each, Days 4–5 do the same, Day 6 transfers `100` internally, and Day 7 resumes the `100` outer contraction. Jared is active:

$$
(450,300)\longrightarrow(350,400),\qquad450+300=350+400=750.
$$

This is the generation-resolved form of File_71's outer `25:13` gap frame. Several day-values directly scale begetting ages:

$$
1150=5\times230,\quad1050=10\times105,\quad950=5\times190,
\quad850=5\times170,\quad650=10\times65.
$$

The duplicated `750=50×15` is the exception addressed by the two operator projections in §3.4.

If the equal adjacent `750` states are collapsed **for structural comparison**, the Jared-elided list is:

$$
(1250,1150,1050,950,850,750,650)=50(25,23,21,19,17,15,13).
$$

Its center and mean are `19×50=950`:

$$
25+23+21+19+17+15+13=133=7\times19,
\qquad\frac{1250+1150+1050+950+850+750+650}{7}=950.
$$

The complete seven-term odd-number ladder is therefore obtained by formally removing/restoring Jared's exceptional Day-6 slot. The report proposes a cipher-slot analogy to second Cainan; it does not assert that an extant Genesis manuscript omitted Jared.

### 2.4 Seth's `1150→1250` exchange

On this same Cainan-OFF plane, LXX Adam `5364→5134` uses `230`, while MT Adam `4114→3984` uses `130`. Both are source-derived regular birth rows under the stated offsets. The Seth gap is:

$$
5134-3984=1150=23\times50,
\qquad1150\frac{25}{23}=1250.
$$

The `100` expansion gain may be absorbed on either side in a **generated anchored comparison**:

| Held/source side | Generated moved Seth label, BC | Expanded Seth gap | Adam-to-generated-Seth span |
|---|---:|---|---|
| MT Seth 3984 held; LXX Adam 5364 held | LXX 5134→5234, earlier by 100 | 5234−3984=1250 | 5364−5234=130 |
| LXX Seth 5134 held; MT Adam 4114 held | MT 3984→3884, later by 100 | 5134−3884=1250 | 4114−3884=230 |

Thus the age magnitudes exchange geometrically, `(230_LXX,130_MT) ↔ (130_LXX,230_MT)`. The generated endpoints do not claim that a manuscript simultaneously states both ages.

The cross-diagonal and whole-pair translation are distinct executions:

$$
5364-3984=1380=23\times60,
\qquad(5364,5134)+100=(5464,5234).
$$

The translated LXX pair preserves its internal `230`, while `5234−3984=1250`. Between the translated Adam head and the **untranslated** Seth station, `5464−5134=330`. This generated envelope matches second Cainan's `330` remaining years after Shelah; it is not the internal lifespan of the translated pair.

### 2.5 The same `1150` at the Noah–Shem close

The post-Flood table uses the G1 Arphaxad-bound Shem stations: MT `2556 BC` and co-registered Cainan-OFF LXX/SP `3206 BC`. At the held Conquest target `1406 BC`:

$$
2556-1406=1150,\qquad3206-1406=1800=650+1150.
$$

With the matched G1 co-registered Noah birth `3706 BC`, the mixed-manuscript comparison is:

$$
3706\rightarrow2556\rightarrow1406\ \mathrm{BC}=1150+1150=2300.
$$

The `3706→2556` segment is LXX/SP Noah versus MT Shem, not a same-person or same-manuscript biography. The Priestly expansion of `1150` again gives `1250`. Holding Conquest and MT Shem death `1956 BC`, generate the earlier head `2656=2556+100`:

$$
2656-1406=1250,\qquad2656\rightarrow2556\rightarrow1956=100+600=700.
$$

The original Shem lifespan remains `2556−1956=600`; the generated head does not make it `700`. The report reads this recurrence as an opening/closing correspondence: `1150+1150=2300`, `1150+650=1800`, and the separately generated `100+600=700` repeat the Day-One Key exchange near the Noah–Shem close.

## 3. Kenan, Jared, Cainan and Terah

### 3.1 Kenan's variant row and chronological half-gap magnitudes

The incoming LXX age at Kenan's birth is Enosh's `190=130+60`, the total width of the elementary Cainan/Terah field. This does not confuse it with Kenan's own outgoing LXX age `170`. Kenan, Hebrew **קֵינָן**, is paired by name and by the repository's comparison with second Cainan.

At Kenan the partition is `650|300`, total `950`:

$$
(650,300,950)=5(130,60,190).
$$

The actual regular running totals at this named node are `625 / 325 / 325`. File_71's half-gap magnitudes therefore occur here as begetting-age sums:

$$
625=\frac{1250}{2}=25^2,\qquad325=\frac{650}{2}=25\times13,
\qquad950=625+325=650+300.
$$

Their relation is the central exchange:

$$
(625,325)+(25,-25)=(650,300).
$$

This locates the `625/325` geometry at the Day-4 threshold in the named genealogy. The running sums and gap partition are complementary descriptions of the same declared row; their equality is not a second independent chronology witness.

### 3.2 Jared's flanks and the `460→500` threshold

Days 5 and 7 carry the same age vector `165 / 65 / 65`, flanking Jared's `162 / 62 / 162`. The two flanks reproduce second Cainan's regular biography:

$$
65+65=130,\qquad165+165=330,\qquad130+330=460.
$$

| Orientation | 130 | 330 | Total |
|---|---|---|---:|
| Second Cainan biography | Birth→Shelah | Shelah→death | 460 |
| Jared-flank comparison | 65+65 | 165+165 | 460 |

At Jared's birth the running totals are `960 / 460 / 460`. The MT/SP `460=130+330` is the Cainan/Watcher comparison unit; the extra LXX `500` is its Priestly expansion:

$$
460=23\times20,\qquad460\frac{25}{23}=500,
\qquad960=460+500=460+460\frac{25}{23}.
$$

The report's proposed reading is Cainan's anatomy rotated through the Jared field, with one `460` unit accompanied by its expanded `500`. File_11 retains the broader Kenan/Cainan and Watcher context; this local row does not import its cumulative scale as a regular duration.

### 3.3 Jared's non-mod-5 slot

Within the seven Creation-day begetters, Jared alone has ages not divisible by `5`. Removing his interval from the Methuselah running totals produces a second formal elision:

$$
(1287,587,687)-(162,62,162)=(1125,525,525)=25(45,21,21).
$$

Thus `1125=45×25` and `525=21×25`. Jared's retention both duplicates the outer `750` state and interrupts these mod-25 running totals; his formal elision restores both regularities. This supports the proposed removable/restorable Day-6 cipher-slot interpretation. It remains a comparison operation, not an attested missing patriarch or a replacement source genealogy.

### 3.4 The two operator projections of `750`

The unshifted Day-6 Enoch row is `350|400=750`. Open the report's asymmetrical comparison operators explicitly:

| Projection | Operation on outer gap | Internal partition | Begetting-age lock |
|---|---|---|---|
| LXX/SP Terah ON; MT held | 750+60=810 | 350 ∣ 460; 400+60=460 | 810=5×162 |
| MT restored Cainan ON; LXX/SP held | 750−130=620 | 350 ∣ 270 | 620=10×62 |
| Both operators open | 750+60−130=680 | Complete comparison rectangle | Audit corner, not the preferred one-operator interpretation |

The four scalar corners, sorted, are:

$$
620,680,750,810,\qquad60|70|60.
$$

The positive historical/theological proposal selects the two one-operator projections `620 ←130← 750 →60→ 810`, rather than taking `680` as its primary convergence. Opening this rectangle is a separately declared mixed-variant comparison; it does not change the leveled OFF/ON tables in §§2/4.

### 3.5 `750` as a scale crossover

The same scalar has two factorizations and an exact Priestly origin:

$$
750=50\times15=30\times25,
\qquad690\frac{25}{23}=750.
$$

The report reads the duplicated `15` as a responsive crossover among the `50`-unit manuscript ladder, the `30`-unit Priestly `720/30` rail, Jared's `162/62` pair, and the Terah/Cainan `60/130` operators. The scalar correspondence does not authorize an undeclared calendar-state change or merge the distinct units of the larger Priestly comparison.

### 3.6 Cainan and Terah at `2091 BC`

The regular restored-Cainan MT biography, on the held `+215` plane with Terah OFF, is:

$$
2551_{\mathrm{Cainan}}\rightarrow2421_{\mathrm{Shelah}}\rightarrow2091_{\mathrm{Cainan\ death}}\ \mathrm{BC}
=130+330=460.
$$

The selected Terah-ON biography is:

$$
2296_{\mathrm{Terah}}\rightarrow2166_{\mathrm{Abram}}\rightarrow2091_{\mathrm{Terah\ death/call}}\ \mathrm{BC}
=130+75=205,
\qquad130=70+60.
$$

The first uses MT restored Cainan `+130`; the second is the LXX/SP Terah `+60` comparison used in §3.4. SP's `205` here is the explicitly opened **architectural/Ideal** lifespan, not its official textual `145`. File_18 retains both the official SP `145` and the admitted `+60`/`205` architecture. On this date plane, the official SP path `2236→2091` uses `145`; the selected architectural path `2296→2091` uses `205`. Neither replaces the other.

The distinct paths therefore meet at the same civil label:

$$
\mathrm{Terah\ death}_{\mathrm{LXX/SP},\,+60}
=\mathrm{Cainan\ death}_{\mathrm{MT},\,+130}
=2091\ \mathrm{BC}.
$$

File_01 controls Abram's ordinary `2166→2091→1991` birth/call/death biography; `2166−2091=75` gives the call/departure hinge used here. Agreement at `2091` is a cross-state comparison, not a claim that Cainan and Terah were one event or that a lane must execute both operators together.

The source report gives this convergence a theological setting: second Cainan's reception-history association with Watcher-derived astral knowledge and Terah's idolatrous Mesopotamian world stand at opposite ends of the post-Flood corridor from which Abram is called. That significance is retained as a theological/reception-history reading, rather than an arithmetic proof of transmission.

Their remaining years also recover the full variant weave:

$$
330+75=405=190+25+190,
\qquad165+165=330,\qquad750=10\times75,
\qquad405=(165+165)+75.
$$

This is a secondary exact comparison of the two biographies' remainders, subordinate to the simpler operator-ownership convergence.

## 4. The leveled post-Flood countdown and inventories

### 4.1 The common Cainan-OFF table

The primary post-Flood table removes native LXX Cainan and inserts none into MT/SP. It holds the same `+215` position and Terah OFF. Its Shem row is explicitly **G1 / Arphaxad-bound**: co-registered LXX/SP `3206`, MT `2556`. Fixed Arphaxad is `3106 / 3106 / 2456` under these held variants.

Matched G1 primary Noah births `3706 / 3706 / 3056` give the round `500` relation to these Shem births. G2 primary Noah `3708 / 3708 / 3058` instead gives `502` to these G1 stations. The G2 biological Shem row is `3208 / 3208 / 2558`, with its own matched `500`; it lies `102` before fixed Arphaxad. These are named endpoint bindings, not competing corrections of one birth. The SP local companion remains a distinct −1 person-station option.

| Birth reached | Parent's ages, leveled LXX / SP / MT | Birth BC, leveled LXX / SP / MT | LXX−SP | SP−MT | Gap ÷ 50 |
|---|---|---|---:|---:|---:|
| Shem, G1 Arphaxad-bound | Matched G1 Noah→Shem 500; G2 Noah→this G1 Shem 502 | 3206 / 3206 / 2556 | 0 | 650 | 13 |
| Arphaxad, fixed suffix | Shem 100 / 100 / 100 | 3106 / 3106 / 2456 | 0 | 650 | 13 |
| Shelah | Arphaxad 135 / 135 / 35 | 2971 / 2971 / 2421 | 0 | 550 | 11 |
| Eber | Shelah 130 / 130 / 30 | 2841 / 2841 / 2391 | 0 | 450 | 9 |
| Peleg | Eber 134 / 134 / 34 | 2707 / 2707 / 2357 | 0 | 350 | 7 |
| Reu | Peleg 130 / 130 / 30 | 2577 / 2577 / 2327 | 0 | 250 | 5 |
| Serug | Reu 132 / 132 / 32 | 2445 / 2445 / 2295 | 0 | 150 | 3 |
| Nahor | Serug 130 / 130 / 30 | 2315 / 2315 / 2265 | 0 | 50 | 1 |
| Terah | Nahor 79 / 79 / 29 | 2236 / 2236 / 2236 | 0 | 0 | 0 |
| Abraham | Terah 70 / 70 / 70 | 2166 / 2166 / 2166 | 0 | 0 | 0 |

The native-LXX-ON versus MT-OFF gap `130+650=780` at Shem/Arphaxad belongs to a different, mixed-Cainan comparison. It is not the gap in this all-OFF table. An all-ON comparison preserves the corresponding `650` because MT/SP receive the same upstream `130` already native to LXX; Shelah onward remains fixed.

### 4.2 Seven gaps close through six centuries and a half-century

Shem's common `100` carries the `650` gap unchanged to Arphaxad. The seven positive gap states then count down:

$$
(650,550,450,350,250,150,50)=50(13,11,9,7,5,3,1).
$$

Their coefficient and scalar sums are:

$$
13+11+9+7+5+3+1=49,
\qquad650+550+450+350+250+150+50=50\times49=2450.
$$

This sums successive manuscript-gap **states**; `2450` is not elapsed time along one genealogy. The qualified Jubilee association retains File_20's literal `49` cycle versus `50` completion/macro vocabulary.

The closing differences are fully specified by the table:

$$
135-35=130-30=134-34=130-30=132-32=130-30=100,
\qquad79-29=50.
$$

Thus each non-MT lane contributes `6×100+50=650`. Nahor is one named father but contributes half of a centenary differential unit. The repeated equality notation records six distinct parent rows; it does not collapse six persons into one.

### 4.3 Named count and the provisional weighted center

The Cainan-OFF inventory has `26` names from Adam through Moses; all-ON has `27`. The study separately proposes a **centenary-weighted** convention in which Nahor's `50` counts as half the ordinary `100` differential unit. The seven post-Flood differing fathers therefore carry `6+1/2=6.5` such units.

Under that proposed convention the source designates Shelah as the privileged center with Cainan OFF, and second Cainan as the center with Cainan ON. This positive weighted-center reading is retained; it is not asserted to be the ordinary median of equally weighted names.

Dependency note [WEIGHTED GENERATION CENTER]: The source supplies the `50/100` weighting rationale and the Shelah/Cainan center designations, but not a complete reproducible algorithm assigning weights/positions across all `26/27` names and selecting the center. The `6.5` differential-unit total is exact; it does not alone derive either named center. The centering result remains provisional under that author-defined convention until its full weighting and selection rule are supplied.

### 4.4 LXX and SP variant inventories

The differing fathers relative to MT are:

| Lane and epoch | Named fathers | Signed age differences | Count | Magnitude |
|---|---|---|---:|---:|
| LXX before Noah | Adam, Seth, Enosh, Kenan, Mahalalel, Enoch | Six +100 | 6 | 600 |
| LXX after Flood, Cainan-leveled | Arphaxad, Shelah, Eber, Peleg, Reu, Serug, Nahor | Six +100; final +50 | 7 | 650 |
| SP before Noah, raw ages | Jared, Methuselah, Lamech | −100, −120, −129 | 3 | 349 |
| SP after Flood, Cainan-leveled | Arphaxad, Shelah, Eber, Peleg, Reu, Serug, Nahor | Six +100; final +50 | 7 | 650 |

For LXX:

$$
6+7=13,\qquad600+650=1250,
\qquad600=12\times50,\qquad650=13\times50,
\qquad1250=50(12+13)=50\times25.
$$

The report reads `6+7=13` as an expression of the project's Atonement Weave. Files 58–60 and File_70 Supplement A retain that broader theological context; this local lane count does not re-prove their complete arguments.

For SP, the raw three walkbacks are:

$$
62-162=-100,\qquad67-187=-120,\qquad53-182=-129,
\qquad100+120+129=349.
$$

The named count `3+7=10` is read as a biblical completion pattern of `3`, `7` and `10`. Raw absolute volume and signed net are different measures:

$$
349+650=999,\qquad-349+650=301.
$$

The separately declared one-unit primary-station closure gives:

$$
1+129+120+100=350,\qquad999+1=1000,
\qquad-350+650=300.
$$

Thus the integer volume closes `999→1000` and the signed displacement `301→300`. This retains the source's completion/perfection reading without calling `1000` a technical perfect number. The raw `129` and the source age `53` remain unchanged; closure selects the current completed primary path, not a universal phase operator.

### 4.5 Complementary pre-Flood lanes, shared post-Flood lanes

The nine begetting fathers Adam through Lamech are marked without overlap: six by the LXX lane and three by SP, `6+3=9`. After the Flood the two lanes co-register the same seven differences, giving `7+7=14` lane-slots. Therefore:

$$
9+14=23=13_{\mathrm{LXX}}+10_{\mathrm{SP}}.
$$

This is a count of non-MT **lane-slots**, not `23` distinct people or independent textual witnesses. The structural proposal is complementary allocation before Noah followed by a shared countdown afterward.

## 5. The Flood pivot and the three `1656` roles

### 5.1 Raw `22+1=23` and the signed pivot

All `13` LXX differing ages are divisible by `10`. Of the `10` SP differences, nine are divisible by `10`; raw `−129` is the exception. Hence the raw textual comparison has:

$$
22\ \mathrm{decadal\ values}+1\ \mathrm{nondecadal\ value}=23,
\qquad129=130-1.
$$

This diagnostic belongs to the raw age inventory. Replacing raw SP `53` with the completed `52` station count yields a different comparison in which `−130` is decadal; it must not silently be called the same `22+1` scan.

Written in genealogical direction relative to MT, the SP pre-Noah walkbacks and the shared post-Flood payload are:

$$
\ldots,-100,-120,-129\quad|\quad1\ \mathrm{Flood\ event\ year}\quad|\quad
+100,+100,+100,+100,+100,+100,+50.
$$

The source reads the sole residual unit beside the complete Flood event-year as a theological/structural pivot. The literal Flood start→close remains an event interval under File_18; the last begetting transition precedes Noah's birth, not the Flood in elapsed time. The display compresses the genealogical era around its Flood pivot rather than claiming those listed age differences are consecutive historical intervals around the ark.

### 5.2 The ten-term lifespan identity and `129+1` closure

When the negative SP walkbacks are read backward from the pivot, their magnitudes appear in reverse order. The full identity retains the six separate LXX centuries and the three separate SP fathers:

$$
(100+100+100+100+100+100)+1+(129+120+100)=950.
$$

Its term anatomy is `6+1+3=10`: nine begetting-father terms plus the central boundary unit. Only after that anatomy is visible is it abbreviated:

$$
600+1+349=950,\qquad1+129+120+100=350.
$$

At Lamech's birth the comparison compartments are `(130,520)`. Raw `129` leaves `(1,649)`; selecting the adjacent primary Noah station gives `(0,650)`, as specified in §2.2. Thus `1+129=130` is an exact integer/station closure. The source's biographical framing places the full Flood event-year at Noah `600→601`; this remains distinct from the SP adjacent person-station choice. Its positive interpretation associates the residual unit with that Flood year, but the event-year is neither counted twice nor authorized as an upstream calendar move. Matched Noah biographies keep `600+350=950`, and the source age remains `53`.

The post-Flood lanes supply the proposed unit correspondence:

$$
100+100+100+100+100+100+50=650=5\times130,
\qquad650+650=10\times130=1300.
$$

The source's explanatory hierarchy is therefore preserved: `600+1+349=950` locates the residual unit within the ten-term comparison; `650+650=10×130` relates its completion to the repeatedly displayed `130` magnitude. This is a structural reading of the selected lanes, not an independent proof that a Flood calendar caused the textual `129` or a license to round another age.

### 5.3 The sixfold parallels and opening/closing `130`

Before the pivot, `1+129=130`; afterward, each lane gives `650=5×130`. Together:

$$
130+650=6\times130=780.
$$

This scalar composite is distinct from §4.1's mixed-Cainan civil gap also labeled `780`. It compares a completed pre-pivot unit with one post-Flood lane payload.

The `1+5=6` anatomy parallels Shem's `100+500=6×100=600`, while Noah's first `600` years reverse that order as `500+100=600`. Under the matched G1 Noah/Shem and fixed-Arphaxad path, `500` is Noah→Shem and `100` Shem→the G1 Flood/Arphaxad station; G2 biological Shem and G1 elected-line endpoints remain separately named. Shem's own `100+500` lifespan partition uses his begetting age and remaining years.

$$
500|100\ \longleftrightarrow\ 100|500,
\qquad130|650=1(130)|5(130).
$$

The source interprets the closure at Noah's `600th`-year/Flood comparison as a sixfold resonance between biography and variant field. The two partitions use distinct units and roles; numerical analogy does not convert a manuscript differential into lived years.

The era's opening Adam→Seth age is `130` in MT/SP. Its raw closing differential and selected boundary unit recover `129+1=130`. Appendix B's separately developed corporate-Adam Fall→Flood comparison contributes `700+600=1300=10×130`, and the doubled post-Flood payload repeats `650+650=1300`. The full interpretive frame is:

$$
130\longrightarrow1300\longrightarrow1+129=130\longrightarrow650+650=1300.
$$

The Fall-side `700/600` comparison keeps the corporate-Adam state and endpoints declared in Appendix B. It is not inferred from this regular begetting table alone.

### 5.4 One MT base, three named `1656` endpoints

The common MT Adam→Noah birth sum is `1056`. The six LXX centuries add `600`, while MT retains Noah's ordinary pre-Flood age `600`. SP's primary comparison uses the completed genealogy `1056−350=706` and Noah's whole lifespan `950`:

$$
\begin{aligned}
\mathrm{LXX}:\quad&1056+600_{\mathrm{variant\ ages}}=1656_{\mathrm{Noah\ birth}},\\
\mathrm{MT}:\quad&1056+600_{\mathrm{Noah\ age}}=1656_{\mathrm{Flood\ start}},\\
\mathrm{SP\ primary}:\quad&1056-(1+129+120+100)+950
=1056-350+950=1656_{\mathrm{Noah\ death}}.
\end{aligned}
$$

On the current held OFF plane the source-bound stations are:

| Tradition and named endpoint | Creation endpoint → target, BC | Span |
|---|---|---:|
| LXX Cainan-OFF, G2 Noah birth | 5364 → 3708 | 1656 |
| MT, G2 Flood start | 4114 → 2458 | 1656 |
| SP, G2 primary Noah death | 4414 → 2758 | 1656 |

LXX's six-father payload and Noah's literal pre-Flood age have the same magnitude `600`, but different node classes. SP's completed walkback magnitude equals Noah's post-Flood remainder:

$$
950-350=600,\qquad600+350=950,
\qquad(6\times100)+1+(129+120+100)=950.
$$

The raw SP age-sum remains a separate adjacent path: `1056−349=707`, raw reached Noah `3707`, and matched companion death `2757`. Its Creation→companion-death span is `707+950=1657`. It does not supply the primary `1656` unless the source-bound primary station is explicitly selected. The integer/station completion preserves this distinction rather than emending the age.

The report's positive generational interpretation is that the selected variant magnitudes reproduce Noah's biography as `600|1|349 = 600|350 = 950`, and thereby explain the three different `1656` roles from one MT base. This is a conditional named-row explanation of File_71's spine. It retains the chronology's source inputs, the primary/companion choice, and the distinction between variant payload and biographical duration.

## 6. Comparative synthesis and evidence hierarchy

### 6.1 The compact carriers

The following register consolidates the original closing formulas. The named derivations retain the source rows, comparison states, and endpoint permissions; the register does not establish a second source chronology. File_71, the Final Repository edition of Report I, controls the preceding macro comparison. This study resolves its inherited Creation–Noah field generation by generation.

| Carrier | Retained compact relation | Meaning and operative destination |
|---|---|---|
| Creation-week ladder | `50(25,23,21,19,17,15,15,13)`; the elided ladder is centered on `950=50×19`. | §§2.1–2.3 retain the complete Adam-to-Noah named-row comparison and the seven-day reading. The repeated `15` marks Jared's Day-6 internal century-transfer slot; eliding it is a declared reduction, not deletion of Jared from the source genealogy. |
| Kenan hub | `(625,325,325)`; `625+325=650+300=950`; `650∣300∣950=5(130∣60∣190)`. | §3.1 retains the actual half-gap placement and its common `5×` variant grammar. |
| Jared branches | `750−130=620=10×62`; `750+60=810=5×162`; `810−620=190=130+60`. | §3.4 retains the two branches from the `750` scalar and their asymmetrically declared Cainan/Terah operations. |
| Post-Flood countdown | `650,550,450,350,250,150,50=50(13,11,9,7,5,3,1)`; total `2450=50×49`. | §§4.1–4.2 retain all seven named differences. The `49/50` vocabulary remains qualified by File_20's literal-cycle/completion distinction. |
| Lane-slot inventory | LXX `6+7=13`; SP `3+7=10`; `13+10=23=22+1`; equivalently `9+14=23`. | §§4.4–4.5 count nine unique pre-Flood fathers and fourteen doubled post-Flood slots. These are declared comparison slots, not twenty-three independent manuscripts or witnesses. |
| Ten-term Flood pivot | `6×100+1+(129+120+100)=950`; `6+1+3=10`; `600+1+349=950`. | §5.2 retains the six individual century terms, one Flood-year term, and three post-pivot terms. The selected field reconstructs the scalar `950`; this does not independently establish Noah's source lifespan or a historical transmission mechanism. |
| `129+1` closure | `182−53=129`; `1+129=130`; `650+650=10×130=1300`. | §§5.1–5.3 distinguish a raw begetting-number difference from the separately declared adjacent station/count completion. The closing year does not shift the preceding SP genealogy. |
| Triple-`1656` | LXX and MT: `1056+600=1656`; SP: `1056−350+950=1656`; Noah `600+350=950`. | §5.4 names the different targets: LXX Noah birth, MT Flood, and SP Noah death. A common span does not merge these events. |
| Corporate Adam/Fall projection | `1656+2−930=728=2×364`; `1656−6−930=720=2×360`. | B.4–B.5 retain the fixed-G2 target field and the declared Year-6/Day-13-close projection. The shared `930` is corporate-Adam interpretation, not a scriptural lifespan for Eve. |
| Selected MT Shem rail | `4116→2556→1956 BC=1560+600=2160`; `1560=12×130`; `2160=6×360=6(130+130+100)`. | C.1 retains MT Year-6 opening and the matched G1/elected-line Shem biography. The G2 biological station and fixed Arphaxad remain distinct. |
| Opening/closing biography matrix | Every combination of `700/800` with `450/500` gives `1150/1200/1250/1300=50(23/24/25/26)`; `1150+1300=1200+1250=2450=50×49`. | C.3–C.4 retain the ordered `2×2` matrix, the selected `500` Noah–Shem relation, and the Jubilee/square closures. Cross-corner equality follows from the additive row/column construction. |

The Creation coefficients above also yield the full scalar sequence `1250,1150,1050,950,850,750,750,650`; §§2.2–2.3 retain its order and the distinct Jared positions. The carrier table consolidates the repeated final ledger while its derivations remain active in the body and appendices.

### 6.2 Arithmetic, structure, and interpretation

The report's argument has three distinct burdens. Exact calculations establish the displayed relations under their declared inputs. Structural readings explain their organization. Theological or historical interpretations address meaning and proposed origin. The positive comparative interpretation remains; the three burdens are not interchangeable.

| Level | Retained argument | Evidential function |
|---|---|---|
| Primary arithmetic spine | The Adam-to-Noah table; full and elided Creation ladders; Kenan hubs; post-Flood odd countdown; lane-slot counts; raw `182−53=129`; ten-term `950`; three `1656` equations; projected `720/728`; selected MT `2160`; and the four-corner biography matrix. | Exact source computations or exact consequences of declared constructions. Generated projections retain their additional assumptions and node classes. |
| Strong structural readings | Seven begetting patriarchs as Creation days; `3+3+1`; Kenan as center of the `625/325` and `130/60/190` fields; Jared's internal century transfer; Day-5/Day-7 flanks recovering Cainan `130+330`; Cainan/Terah convergence at `2091 BC`; `22+1=23`; the one-year completion of `129`; ten terms corresponding to Adam–Noah's ten positions; and the corporate-Adam tri-manuscript invariant. | The original study's strong interpretation of the exact selected field. The day mapping, corporate reading, and proposed design are interpretations of its organization rather than additional raw textual ages. |
| Subordinate corroboration | Enoch `364/365` and `69/70`, Enochian `299→300`, qualified SP `180/182`, square/Jubilee and historical `653` count constructions, Genesis 9 backward-walking typology, and the weighted Shelah/Cainan center. | Appendices A–C and §4.3 explain or corroborate the simpler main spine. They do not carry its primary burden. |
| Transmission or providential interpretation | The proposed purposeful organization of the variant field, its theological/providential significance, and possible transmission explanations. | Positive readings retain their appropriate claim status. A historical claim that one identifiable scribe consciously encoded the entire field remains subordinate and unproved. Arithmetic compatibility does not identify an ancient author, scribe, or sequence of transmission. |

The subordinate calendar and square comparisons remain distinct: A.2 carries `299×300/299=300`; A.6 retains the historical SP Lamech `653` count geometry beside the current dated `654` midpoint, the `587/588` Adam-year counting comparison with only `588=12×49`, and `785→784` with `784=28²=16×49`. A.4 retains Methuselah's completed closing path `720=120+480+120` beside the primary `719` elapsed-year path. A.3 retains the qualified `180/182` comparison; C.2 retains Genesis 9's backward-walking typology. The weighted center at §4.3 remains an author-defined structural proposal where a complete weighting/center algorithm has not been supplied; it is not presented as a reproduced ordinary-median theorem.

Several conclusions share inputs. The two halves of a repeated rail, a normalization of the same scalar sequence, the four additive matrix corners, and their equal cross-corner sums are correlated consequences of the chosen construction. Their exact agreement supports the report's proposed organization without multiplying them into independent witnesses. The corporate `720/728` theorem is exact conditional on its `930` projection, held Gear, and three named Noah targets; it does not supply a literal Eve biography. The compact grammar remains a source-bound compression proposal, not a proved unique generator or minimum-description theorem.

### 6.3 The regular result and its scope

Report I organized the large Creation–Noah variant engine; this study follows that organization through the individual generations. In the declared comparison the LXX and SP differences distribute methodically around the MT: before the Flood their nonzero lanes partition the nine fathers, while after the Flood they co-register in the same seven-patriarch countdown. Their combined lane-slot inventory is `23`. The sole non-decadal term in the declared raw begetting-number difference inventory is `129=182−53`, one short of the `130` unit displayed by the doubled `650` countdown. The current SP primary-station path instead uses `52` completed years and yields `130=182−52`; it is not the same input inventory. The ten-term field closes at Noah's `950`, and the same selected variant payload carries `1656` to Noah birth, Flood, and Noah death in the three different traditions. The corporate-Adam `720/728` pair supplies the corresponding conditional calendar/Gear comparison.

The original reduced vocabulary is retained: `1,50,60,100,120,129/130,190,300,350,600,650,720/728,950,1000,1250,1300,1656`. These are roles in the declared field, not a list that independently fixes every source row, chronological anchor, or operator permission. The study's objective remains to explain the greatest amount of chronological complexity with a small arithmetic grammar. Report III develops the deferred cumulative investigation; Appendix D preserves the original research agenda and its state boundaries.

## Appendix A. SP calendar corroborations: current dates and historical count models

This appendix consolidates original Report II §§40–46. These corroborations explain why the Enoch–Noah one-unit completion belongs to the comparative argument; they do not replace its primary begetting-age proof. Dates below use the held full-430 comparison plane: native SP dates translated by `+215`, Terah `+60` OFF, second Cainan OFF, and a named Gear. `File_18` §3 and its September 18 amendment control the current SP source rows; Files 11/12/17 control Gear and calendar/ratio grammar; Files 20/53 retain the BJ/Jubilees corroboration and its theological reading.

### A.1. The Flood-death triad and Enoch's sixfold measures

Jared, Methuselah, and Lamech are the three SP-specific walkback fathers and the three whose selected deaths meet the G2 Flood start. Enoch is taken earlier. The raw Adam-year count ledger is retained:

$$
460+847=587+720=654+653=1307.
$$

Here `460/587/654` are the running birth positions and `847/720/653` are the retained lifespan counts. The current annual dates verify the same cap inclusively:

| Father | G2 birth BC | Selected death / Flood start BC | Retained inclusive count | Equivalent capacity to Flood close |
|---|---:|---:|---|---|
| Jared | 3954 | 3108 | `3954−3108+1=847` | `3954−3107=847` |
| Methuselah | 3827 | 3108 | `3827−3108+1=720` | `3827−3107=720` |
| Lamech | 3760 | 3108 | `3760−3108+1=653` | `3760−3107=653` |

The cap does not assign these fathers a lower companion birth, or move their selected deaths to the closing boundary. Consequently the SP `100+120+129` walkback is a Flood-death triad organized around Enoch.

With current fixed G2 Enoch taking at `3527 BC`, the sixfold `70` comparison selects Flood **close**, not start:

$$
3527-3107=420=6\times70,
\qquad3527-3108=419.
$$

The BJ/Jubilees Enoch accounting retained by `File_53` §14A is:

$$
70+294+1=365,\qquad294=6\times49.
$$

Within that unified accounting, `70` is the taking station, `294` the six Jubilees of service, and the last unit completes `365`. The positive corroboration is therefore `6×49 ↔ 6×70`, with the respective service-count and Flood-close endpoint classes stated. This is the report's calendrical and theological interpretation of the two checked sixfold measures. Historical SP date displays in File 53's corroborating section do not override File 18's current raw SP dates.

### A.2. Enoch's `364/365`, `299/300`, and MT `69/70` clutch

The source biography retains `365` years for Enoch; the Enochian calendar register retains `364` days. Their one-unit comparison is:

$$
364+1=365.
$$

Enoch begets Methuselah at `65`. The source biography and the separately generated one-unit contraction give:

$$
365-65=300,\qquad364-65=299,
\qquad299\times\frac{300}{299}=300.
$$

Current G2 coordinates support the uncontracted biography directly:

$$
3892-3527=365,\qquad3892-3827=65,\qquad3827-3527=300.
$$

Thus `299` is a contracted count/calendar comparison, not the age obtained from the fixed current taking date. The report reads Enoch as personifying the completion of exclusive `299` to `300`; calendar days, biographical years, and an exact-rational span remain separately declared units.

The MT provides the analogous hinge:

$$
3127-3058=69,\qquad69\times\frac{70}{69}=70,
\qquad3128-3058=70.
$$

These are MT G2 Enoch taking and Noah birth in the held plane. Keeping Noah `3058` and Enoch birth `3492` fixed while expanding the interval moves the **generated** taking boundary from `3127` to `3128`; the effective biography becomes:

$$
3492-3127=365,\qquad3492-3128=364.
$$

Both SP/BJ and MT therefore place Enoch at a `364/365` and `69/70` one-unit clutch. The generated MT boundary does not replace its source taking date.

### A.3. The qualified SP `180/182` half-calendar

Current SP Enoch remains fixed at `3892→3527 BC`. The adjacent person-station rail belongs only to Noah/Shem. It does not generate an upstream `3893→3528` Enoch companion. With G2 Noah primary/companion `3708/3707 BC`:

$$
3708-3527=181,\qquad3707-3527=180=\frac{360}{2}.
$$

Accordingly the report's `180` member selects G2 **companion Noah** against fixed G2 Enoch taking; it is not invariant across both Noah stations. The calendar counterpart remains:

$$
364=(90+1)\times4=360+4,
\qquad182=\frac{364}{2}=180+2.
$$

The local `+2` Gear comparison may hold the taking boundary and select the G3 companion Noah station:

$$
3709-3527=182.
$$

This is a qualified cross-Gear endpoint comparison, not a second coherent G2 biography. The original positive reading remains: the selected local two-year separation mediates Prophetic `180` and Enochian `182` at half-calendar scale.

### A.4. Methuselah's `720`: inclusive life and completed closing path

The source retains Methuselah's `720` inclusive lifespan count. Current G2 completed-year subtraction to his selected death / Flood start gives `719`:

$$
3827-3108=719,\qquad3827-3108+1=720,
\qquad3827-3107=720.
$$

The underlying age formula remains:

$$
67+53=120,\qquad600-120=480.
$$

It must be bound to the appropriate annual stations. The primary path reaches Flood start:

$$
3827\xrightarrow{119}3708\xrightarrow{480}3228
\xrightarrow{120}3108,\qquad119+480+120=719.
$$

The completed companion path reaches Flood close:

$$
3827\xrightarrow{120}3707\xrightarrow{480}3227
\xrightarrow{120}3107,\qquad120+480+120=720.
$$

The intermediate `3228/3227 BC` warning stations are generated by the selected `480+120` partitions. The closing path is an equivalent completed capacity calculation; Methuselah's selected death remains at `3108 BC` inclusively. These bindings preserve the original `120|480|120` corroboration without silently mixing Noah stations or event boundaries.

At the declared calendar/geometric level:

$$
720=360+360=2\times360.
$$

The two years-of-years correspond numerically to the SKL `360:1` dilation of a selected local two-year Gear interval. This is a cross-scale structural correspondence, with `2` ordinary years and `720` dilated years distinguished.

### A.5. The other one-unit witnesses

The original witnesses are retained together:

| Witness | Equation | Active class |
|---|---|---|
| Enoch calendar/body | `364+1=365` | Calendar/biographical correspondence |
| Methuselah at Enoch's taking | `299→300` | Generated contraction and exact-rational completion in A.2 |
| Lamech/Noah | `129+1=130` | Raw walkback remainder completed at the named hinge; not an emended begetting age |
| Noah's ordinal Flood year | `599+1=600` | Companion birth→Flood-start completed count and ordinal completion |
| SP walkback | `349+1=350` | Local count completion in the main comparison |
| Full SP absolute variant volume | `999+1=1000` | Absolute-variant count completion |

These remain distinct calendrical, ordinal, ratio, and comparative-count states. Their repeated one unit supports the report's Enoch–Noah hinge interpretation; it is not a universal operator for moving raw dates.

### A.6. Squares, Jubilees, and the historical `653` model

The source preserves the contracted/count geometry:

$$
785\rightarrow784,\qquad784=28^2=16\times49,
\qquad587\leftrightarrow588,\qquad588=12\times49.
$$

The first pair also has a current, explicitly counted rebinding:

$$
3892-3108+1=785,\qquad3892-3108=784.
$$

Here `785` is Enoch's inclusive capacity to Flood start, not his lifespan; `784` is completed subtraction. The `587↔588` line remains a historical Adam-year one-unit count comparison, not permission to change current Methuselah birth `3827 BC` or propagate an upstream companion.

The original equal-halves constructions remain exact as historical count models:

$$
653+653=1306,\qquad654+654=1308.
$$

The preferred current Creation→Flood-start interval is indeed `4414−3108=1306`, but its actual Lamech partitions are unequal:

$$
4414-3760=654,\qquad3760-3108=652,
\qquad654+652=1306.
$$

Therefore the historical `653+653` threshold model must not be attached to current Lamech's dates as a midpoint. Nor should the old description of `654+654` as a completed Flood boundary be used as a current date claim. The executable G2 equal-halves relation selects **fixed Arphaxad**, as controlled by File 18 §3.1.4:

$$
4414\rightarrow3760\rightarrow3106
=654+654=1308.
$$

Lamech's G2 birth is the midpoint from Creation to fixed Arphaxad. Separately, G1 Lamech death / G1 Flood start / fixed Arphaxad share `3106 BC` as distinct node classes; that coordinate convergence is not a midpoint. The square and Jubilee witnesses retain their positive role as secondary corroboration of the main one-unit argument.

## Appendix B. Day 13/14, Corporate Adam, and the doubled calendar closure

This appendix consolidates original §§47–54, including §§49A and 54A. It keeps Actual source chronology, declared Day/Year projections, literal biography, and theological interpretation distinct. Creation endpoints and Year-6 Adam states follow File 07; current person/event bindings follow File 18. Genesis 1:27 and 5:2 supply the corporate-name reading; File 20 controls BJ/Jubilees Fall/Flood corroboration.

### B.1. Day/Year 13 from the Year-6 envelope

The report reads the Creation week at two declared scales: seven literal days and seven figurative years. Adam occupies Day/Year 6; Eve is placed seven units later in the typological Day/Year-13 horizon, with the Fall read on that horizon. This is the report's Creation-side projection, not an assertion that Genesis explicitly gives Eve a numerical lifespan or a BC date.

The standard MT wrapper remains:

$$
4121\rightarrow4116\rightarrow4114\text{ BC}.
$$

Here `4116` is Year-6 opening, `4114` the Creation endpoint, and the closing Day-13 Eve/Fall projection is `4108`. The source-controlled Year-6 envelope supplies the opening/closing distinction for all three traditions:

| Tradition / Cainan state | Creation endpoint BC | Year-6 opening→close BC | Day-13 opening→close BC | Next Day-14 opening→close BC |
|---|---:|---|---|---|
| LXX, leveled Cainan OFF | 5364 | 5366→5365 | 5359→5358 | 5358→5357 |
| SP, Cainan OFF | 4414 | 4416→4415 | 4409→4408 | 4408→4407 |
| MT, Cainan OFF | 4114 | 4116→4115 | 4109→4108 | 4108→4107 |

Each Day-13 envelope subtracts `7` from the **Year-6 envelope**. Its closing member equivalently satisfies:

$$
\text{Creation endpoint}-6=\text{Day-13 close}.
$$

SP `4415` in this table is Year-6 close; it is not an upstream Creation-head companion to `4414`.

### B.2. SP Day-13/Day-14 `1300` rail

The SP Year-6-derived Day-13 and adjacent Day-14 envelopes preserve the original one-unit phase rail:

$$
(4416,4415)-7=(4409,4408),
\qquad(4409,4408)-1=(4408,4407).
$$

Their qualified landings are:

$$
4409-3109=4408-3108=1300,
$$

$$
4408-3108=4407-3107=1300.
$$

`3109 BC` is the conjectural Ark-preparation station corroborated by the BJ event translation in File 18 §3.1.1. The same coordinate independently labels G3 Flood **close**; the two events are not thereby identical. `3108→3107` is the G2 Flood start→close event span, independent of the SP Noah/Shem companion rail.

The one-unit slide preserves `1300` while changing the selected Day-13/Day-14 opening or close and the Ark-preparation / Flood-start / Flood-close landing. The report reads this as the Creation-side analogue of the Enoch `364/365` and Noah `600th/601st` phase states. Its theological and structural corroboration is retained with those endpoint qualifications.

### B.3. The Actual `1300/2600` family and MT death axis

Against the current G2 Flood start, SP Day-13 **close** gives:

$$
4414-6=4408,\qquad4408-3108=1300.
$$

The coherent G2 primary Noah station partitions that same interval:

$$
4408\rightarrow3708\rightarrow3108
=700+600=1300.
$$

Here `700` is the chronological segment from Day-13 close to primary Noah birth, and `600` is Noah's age to Flood start. This preserves the original §34 Fall→Noah→Flood relation routed from the main argument; this `700` is distinct from LXX Adam's `700`-year remainder after Seth in C.3.

File 20 §3B retains the BJ/Jubilees comparison `3849−2549=1300`, with Fall and Flood both assigned Month 2, Day 17. The source interprets that alignment as the Flood's reversal of the Fall and `1300=13×100` as an epochal rebellion measure. The SP numerical agreement is a corroborating structural/theological relation; by itself it does not establish the historical direction of literary dependence.

The leveled LXX Day-13 close is `950` earlier than SP's:

$$
5358-4408=950,\qquad5358-2758=2600=2\times1300.
$$

The second line selects LXX Cainan-OFF G2 Noah death. Thus SP projects one `1300` from Eve/Fall to Flood start, while leveled LXX projects two to Noah death. These are Actual chronology nodes joined to the declared Eve/Fall projection, not Rounded or inverse dates.

The MT selects a different death-axis relation:

$$
4108-2108=2000=2\times1000.
$$

Here `2108` is G2 Noah death. Holding the projected Fall member fixed and selecting G1 Noah death `2106` exposes the local two-year difference:

$$
4108-2106=2002.
$$

This named adjacent-Gear comparison does not replace the exact G2 `2000` member. The MT opens the Noah death axis and then the sixfold `360` Shem construction in Appendix C, complementing the SP/LXX `1300/2600` family.

### B.4. Corporate Adam and the fixed-G2 `1656` targets

Genesis 1:27 moves from singular **הָאָדָם** to plural **אֹתָם** in the male-and-female creation. Genesis 5:2 adds **וַיִּקְרָא אֶת־שְׁמָם אָדָם**, “He called their name Adam.” These texts support the report's typological treatment of Adam and Eve as corporate **אָדָם**. Genesis explicitly assigns Adam `930`; applying it to Eve is a **corporate-Adam chronological projection**, not a literal Eve lifespan datum.

Hold the report's leveled Cainan-OFF plane and the G2 primary Noah/event bindings. The Triple-`1656` has manuscript-specific targets:

| Tradition | Creation endpoint BC | Fixed-G2 target BC | Target event | Span |
|---|---:|---:|---|---:|
| LXX | 5364 | 3708 | Noah birth | 1656 |
| MT | 4114 | 2458 | Flood start | 1656 |
| SP | 4414 | 2758 | Primary Noah death | 1656 |

$$
5364-3708=4114-2458=4414-2758=1656.
$$

The event role changes by tradition; the Gear is held fixed. SP primary death retains File 18's inclusive/harmonic person-station qualification. The lower Noah companion is a separate state and is not substituted into this table.

### B.5. The tri-manuscript `720/728` theorem

The Day-13 closing projections are `6` later than the Creation endpoints, while Day-6/Year-6 openings are `2` earlier:

$$
1656-6=1650,\qquad1656+2=1658.
$$

Applying Adam's source `930` at the Year-6 opening produces the Day-6 Adam-death projection. Applying the same number at the Day-13 close produces the corporate-Adam Eve-death projection:

| Tradition | Day-6 opening BC | Adam-death projection BC | Day-13 close BC | Corporate Eve-death projection BC | Held G2 target BC |
|---|---:|---:|---:|---:|---:|
| LXX | 5366 | 4436 | 5358 | 4428 | 3708, Noah birth |
| MT | 4116 | 3186 | 4108 | 3178 | 2458, Flood start |
| SP | 4416 | 3486 | 4408 | 3478 | 2758, primary Noah death |

The full coordinate identities remain:

$$
5366-930=4436,\quad4116-930=3186,\quad4416-930=3486,
$$

$$
4436-3708=3186-2458=3486-2758=728=2\times364,
$$

$$
5358-930=4428,\quad4108-930=3178,\quad4408-930=3478,
$$

$$
4428-3708=3178-2458=3478-2758=720=2\times360.
$$

Hence the compact theorem is:

$$
1656+2-930=728=2\times364,
\qquad1656-6-930=720=2\times360,
$$

$$
728-720=8=2(364-360).
$$

All three manuscripts therefore project the same doubled calendar bodies onto their respective Noah birth–Flood–death targets. The original positive interpretation is a tri-manuscript corroboration of the local two-year Noah/Shem Gear: `2 → 720/728 = 2(360/364)`. This is a declared year-of-years/calendar-body correspondence; it neither changes the source biography nor equates its ordinary years with calendar days without the stated scaling.

### B.6. The MT local `730=2×365` extension

Hold the MT Day-6 Adam-death projection at `3186 BC`. Fixed Arphaxad is `2456 BC` and remains fixed when ordinary Flood Gear changes. The local comparisons are:

$$
3186-2456=730=2\times365,
$$

$$
3186-2458=728=2\times364,\qquad3178-2458=720=2\times360.
$$

Thus the MT opens:

$$
720/728/730=2(360/364/365).
$$

`2456 BC` independently co-registers with G1 Flood start; it is not a “Gear-1 Arphaxad” moved by the Gear operator. The G2 Flood-start→fixed-Arphaxad seam is:

$$
2458-2456=2.
$$

The report reads that local two-year seam through the doubled years-of-years calendar bodies. This remains a local extension of the three-tradition `720/728` theorem, with the held projection, G2 Flood start, fixed Arphaxad, and co-registered G1 Flood identified; it does not add a fourth manuscript target.

## Appendix C. MT Shem and the opening/closing biographical matrix

This appendix consolidates original §§55–60. File 18 supplies the Regular source biographies; File 11 supplies ordinary Gear. The selected MT Shem `2556→1956 BC` is G1 / Arphaxad-bound, not the main G2 Shem `2558→1958`. The Year-6 opening `4116` is held as the Creation-side input. Biographical decompositions, generated sums, and typological readings retain their separate roles.

### C.1. MT Year 6 to the selected G1 Shem biography

The controlled comparisons are:

$$
4116-1956=2160=6\times360,
$$

$$
4116-2556=1560=12\times130=6\times260,
$$

$$
2556-1956=600=6\times100,
\qquad2160=1560+600.
$$

Equivalently:

$$
6\times360=6\times260+6\times100=6(130+130+100).
$$

This selected MT Shem construction is the positive counterpart to the SP/LXX `1300/2600` family. The sixfold pattern is an exact comparison of held Year-6 and selected G1 Shem nodes, followed by the report's calendar/theological interpretation; it does not reassign G1 Shem to G2.

### C.2. The G1 Flood-centered reversal and Genesis 9

Select coherent MT G1 Noah `3056→2106`, G1 Shem `2556→1956`, and G1 Flood start `2456 BC`. Shem's Flood-centered biography gives:

$$
2556-2456=100,\qquad2456-1956=500,
\qquad100+500=600.
$$

Noah's first `600` reverses that order:

$$
3056-2556=500,\qquad2556-2456=100,
\qquad500+100=600.
$$

The hinge therefore displays:

$$
500\mid100\quad\longleftrightarrow\quad100\mid500.
$$

The report reads this narrative/arithmetic reversal alongside Genesis 9: Shem and Japheth walk backward to cover Noah, while Ham sees and reports his nakedness. The text explicitly supplies the backward walk of Shem and Japheth, not a forward walk by Ham. The manuscript forward/backward analogy is retained as typological/providential interpretation, not lexical proof.

### C.3. The four-corner biographical generator

The opening residuals follow directly from Adam's biography:

$$
930=130+800\quad\text{(MT/SP)},
\qquad930=230+700\quad\text{(LXX)}.
$$

The closing residuals select the full `500` Noah→Shem and `100` Shem→Arphaxad age bindings:

$$
950=500+450,\qquad600=100+500.
$$

For the selected MT G1 dates, these mean Noah `3056→2556→2106` and Shem `2556→2456→1956`. Fixed Arphaxad and G1 Flood start share `2456 BC` but remain different event classes. The same full-age decomposition may be selected coherently in the leveled LXX/SP G1 primary field; SP's adjacent person-station alternative does not overwrite it. The matrix uses the declared `450/500` residuals, rather than an unlabeled mixed-Gear Noah/Shem interval.

| Opening residual | Noah after Shem: 450 | Shem after Arphaxad: 500 |
|---|---:|---:|
| LXX Adam after Seth: 700 | 1150 | 1200 |
| MT/SP Adam after Seth: 800 | 1250 | 1300 |

$$
700+450=1150,\qquad700+500=1200,
$$

$$
800+450=1250,\qquad800+500=1300.
$$

Therefore:

$$
(1150,1200,1250,1300)=50(23,24,25,26).
$$

The ordinary biographical data regenerate the principal comparative blocks:

$$
1150=23\times50,\quad1200=2\times600,
\quad1250=25\times50,\quad1300=2\times650.
$$

These entries are sums of selected biography remainders; they are not four new elapsed chronological intervals. Their regeneration of the report's `23/24/25/26` field is retained as a strong structural checksum on the more elaborate manuscript analysis.

### C.4. Jubilee and square closure

The opposite matrix corners sum equally:

$$
1150+1300=1200+1250=2450=50\times49.
$$

The full matrix and its arithmetic center give:

$$
1150+1200+1250+1300=4900=10\times490,
$$

$$
\frac{2450}{2}=1225=35^2.
$$

The `49`, `490`, and square signatures strengthen the report's biographical checksum reading. The literal Jubilee count `49` remains distinct from the matrix's factor `50` and any completion/announcement idiom; generated corner sums and the center do not become primary source anchors.

## Appendix D. Source history and cumulative research agenda

### D.1 Original status and current Lamech settlement

The source is the September 2, 2026 report `Regular_MT-SP-LXX_Comparative_Genealogical_Engine_Report_II_20260902.md`. Its closing §§61–71 and final ledger repeat the core results now consolidated at §6.1 and in their operative derivations. Original §§72–74 supply the evidence hierarchy; §§75–80 record the then-current correction, the end of the Regular discussion, and the proposed cumulative continuation. Those discussion-status statements are historical provenance, not an active instruction to suspend this edition or the basis of this edition's author-authorized Final status.

Original §75 classified transmitted Lamech `188` as corruption-only and categorically restricted its numerical interpretation. Later File_18 §4A and current State Vocabulary Register §D.43 supersede that restriction in scope. The operative LXX main reconstruction uses restored begetting `182` with attested lifespan `753`; remainder `571=753−182` is calculated. The combined `182/753` biography is component-wise reconstructed: no surviving joint attestation has been identified in the reviewed sources, while `753` itself is attested and its preferred-original status is the author's textual/structural judgment.

Transmitted `188` remains non-operative. A possible Key-of-23 gain-transfer/conflation origin may nevertheless be examined as an author-favored but unproved structural/transmission hypothesis. It is not an admitted main-chain begetting-age variant, and its generated comparisons do not prove an identifiable scribal mechanism or preserve the unchanged `1656` birth chain. LXX use of `777` is an MT-derived, non-propagating appendix overlay; MT's own `777` remains unchanged. This study inherits that current source hierarchy without replacing the begetting paths already based on `182`.

The original correction-preparation and separate-registration statements remain part of the dated source record. The Lamech settlement is now controlled by File_18 §4A/Register §D.43; the later File_18 September 18 SP amendment retains its separately recorded central-registration debt. These histories must not be merged into a claim that every current source amendment or this study's local conventions have already been centrally registered.

### D.2 State boundaries retained from the original restart

| Boundary | Current handling |
|---|---|
| Regular versus cumulative Cainan | Regular insertion `+130` and cumulative lifespan insertion `+460` remain different operations. Native LXX Cainan is not inserted a second time. |
| Regular versus cumulative chronology | Regular begetting-age running totals and cumulative lifespan stacking retain their own input rows, endpoint ontology, and controlling sources. |
| Creation and Fall node classes | Creation endpoint, Year-6/Adam node, and Day-13 Eve/Fall node remain distinct. A Day-label relation does not erase opening/closing boundaries or turn a corporate `930` projection into a literal Eve lifespan. |
| Noah/Shem event roles | Noah birth, Flood start/close, Noah death, Shem birth/death and fixed Arphaxad are separately named. Common civil labels do not establish event identity. |
| SP adjacent companion and Flood year | The local person-companion belongs to Noah/Shem; it does not shift the preceding genealogy. Flood start→close is independently the event-year span. The integer closure `129+1=130` does not authorize an upstream ripple. |
| Regular and cumulative Gear | Ordinary local regular `±2` comparisons remain distinct from cumulative propagated Gear/envelope states. A cross-Gear diagonal is not a matched single-Gear biography. |
| Prior regular findings | The controlled Regular comparison is the baseline for cumulative comparison. A new system's display does not silently redefine its parent source data; a genuine inconsistency must be identified and explicitly corrected under its controller. |

### D.3 The durable cumulative agenda

The original §§77–80 identified seven research subjects. They remain a source-controlled agenda rather than next-chat commands:

1. The full cumulative lifespan chronology.
2. The cumulative Creation labels `14006/14004 BC` and their related envelopes, preserving the selected member and phase roles.
3. Cumulative Noah, Shem, and Arphaxad node classes.
4. Cumulative restored Cainan `+460`, distinct from Regular `+130`.
5. The source states of cumulative `12558/12600/12740` and their relation to the Regular findings.
6. Cumulative Enoch and Cainan hinge proposals.
7. The complete cumulative-to-Regular comparison with `1250/650`, `600+350`, `720/728`, and the Triple-`1656` field.

| Reading route | Retained responsibility |
|---|---|
| File_71 / Report I and File_72 / Report II | Regular macro and generation-level comparison baselines. |
| Current File_18 | Raw Regular/cumulative input rows, current Lamech source hierarchy, phase/member labels, and Noah/Shem/Flood bindings. |
| Files 09/22 | Cumulative architecture and MT harmonic partition under their declared states. |
| File_70 and Supplement A | Cumulative/Regular interface where those parent-defined constructions are needed. |
| Files 53/20 | BJ, Cainan/Enoch and Jubilee source arguments with their inherited claim and calendar controls. |
| File_11 | Three-Gear distinctions and admitted transport/diagonal permissions. |
| Report III | The later comparative cumulative study that develops the deferred research programme. |

The original starting question survives: how do the cumulative MT, SP, and LXX Creation and Noah/Shem nodes reproduce, enlarge, or rotate the Regular relations `1250=950+300`, `650=950−300`, `600+1+349=950`, Triple-`1656`, and projected `720/728`? The objective is a small grammar with high explanatory reach. Whether one grammar can generate those systems after their source rows, node classes and anchors have been declared remains a research question; the historical agenda is not a unique-generator theorem.

## Revision Log

October 7 2026 — The author authorized Finalization of the reviewed Report II if no outright canonical contradiction was found. The fresh source and index check found no such contradiction and confirmed File_72 was unassigned. This edition assigns the stable File_72 identity and records Final source status. Its registration and public installation are prepared for Spot and remain pending; File_71 is the finalized local comparative parent whose separate installation precedes this file.

The Finalization changes only identity, status, dated revision lineage, source-recheck and publication wording, including stable publication wording in the source-ownership guard. The reviewed argument, every displayed mathematical block, table values, all six REPORT II guard labels and their state/ownership boundaries, weighted-center provisional status, and the existing research qualifications are retained. The published File_18 SP amendment's separate central-registration debt remains pending. This bounded Finalization does not claim a new full-file or full-repository pressure test.