File: File_71
Title: Regular MT–SP–LXX Creation-to-Noah Comparative Engine
Status: Final
Finalization date: October 7 2026, by explicit author instruction
Pressure-test status: Not requested; source verification and focused Finalization checks complete
Register Agreement status: Inherited source-state controls retained; File_71 local-guard registration prepared for Spot, pending installation
Publication status: Final canonical source prepared for installation by Spot
Primary domain: Regular; Comparative; Methodological; Cumulative bridge and external corroboration in appendices
Traditions: MT; SP; LXX; selected SKL/Berossus comparisons; qualified Jubilee vocabulary
Canonical source: Markdown; source tables and operators remain controlled by existing Repository files
Primary anchors: MT Creation week 4121–4114 BC; MT Year-6 opening 4116 BC; G2 Flood start 2458 BC; fixed Arphaxad 2456 BC; Abram 2166 BC; Exodus 1446 BC; Conquest/Moses death 1406 BC; bounded targets 6 BC and 536 BC
Related files: Files 00/01/02/05/06/07/09/11/12/13/14/16/17/18/20/21/22/24/34/46/53/54/60/63/68/69/70 and File_70 Supplement A; Reports II–V as supporting comparative studies
Major operators: +60 Terah; regular Cainan +130; selected 215-position change; ordinary Gear and qualified cross-Gear comparison; midpoint; declared tuple translation; localized +30 Apparent Age; 25/23; 70/69; 300/299; distinct 10×/100×/360:1 scales; civil cross-axis count BC + AD − 1
Major modal states: Regular Actual Nisan; Terah OFF/ON; native/restored/expunged Cainan comparison; selected full-430 position plane; SP primary and local person-companion; Year-1/Year-6/Year-7 marker classes; generated geometry; author-designated Covenant state; Actual cumulative week-head preview
Revision basis: Original Report I, August 31 2026; October 7 source-preservation and arithmetic verification; author-invoked 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
Verification scope: Complete source-preservation/change-class audit of the substantive revision; all 84 source units and 549 source display occurrences reviewed; all 129 pre-Finalization changed ranges classified; eight Finalization edits logged and checked; 397 exact arithmetic checks passed; three source-preservation restorations applied; no unresolved editorial decision

# Regular MT–SP–LXX Creation-to-Noah Comparative Engine

## 0. File-function and controls

This study organizes the inherited Regular MT, SP, and LXX inputs into a comparative Creation–Noah field. Its main contribution is the relation among the `190/405` variant weave, the `1250/650` manuscript gaps, and the `625/325` half-gap geometry. The same declared field supports bounded Key-of-23 applications to the Exodus and Conquest, with secondary square, SKL/Berossus, Pillar, and cumulative comparisons in the appendices.

The working objective is to compress the selected field into a small set of geometric relations and candidate master equations. Source-retained chronologies, comparative variants, generated coordinates, exact identities, structural inferences, and theological interpretations remain distinct. The raw data and generic operators retain their existing owners.

Genesis 7:6 places the Flood when Noah was 600 years old; Genesis 9:28–29 gives 350 years after the Flood and a lifespan of 950. These source values provide the biographical backbone of the comparison. Genesis 5:32 and 11:10 supply the two Noah–Shem relations that must be named when different Gear endpoints are compared.

### 0.1 File map

| Location | Function | Active state |
|---|---|---|
| §1 | Variant rail and Creation wrappers | T/C states; selected 215-position planes; distinct Creation markers |
| §2 | Noah tables, Triple-1656, manuscript gaps, and biographical anatomy | Regular G2 primary; qualified G1/G3 comparisons |
| §3 | Half-gap hub, generated centers, and Gear/Key closure | Generated midpoint coordinates; named adjacent Gear |
| §4 | Creation/Egypt congruence and anchored applications | Actual Regular markers; declared translations; exact ratios |
| §5 | Candidate compression and evidence hierarchy | Working synthesis; source inputs remain explicit |
| Appendix A | Secondary squares and Abrahamic comparisons | Generated fields; G1 Noah death; author-designated Covenant |
| Appendix B | SKL/Berossus/Pillar scale corroboration | Source-bound external states; separate scales; civil axis |
| Appendix C | Actual cumulative preview and correction provenance | Week-head endpoints; regular/cumulative firewall |

### 0.2 Working-state register

All unsuffixed civil year labels in the local Regular tables are BC and use the declared Nisan comparison. A tuple's members are ordered by their stated roles, not interchangeable slash alternatives.

| State or object | Binding |
|---|---|
| Ordinary MT | No +60 Terah or restored Cainan by default; 430 years in Egypt; normal anchors remain visible |
| First comparison plane | SP is translated +215 from its native source position; LXX Cainan-OFF is the lower comparison base. This is a positional equalization, not a claim that each text states the same Egyptian sojourn. |
| Terah T | 60, OFF/ON explicitly opened; adding to a wrapper translates all its members together |
| Cainan C | 130 in Regular space. Native LXX ON is not a second insertion; MT/SP ON are restored comparison states. |
| Second position plane | The first four-state field is translated −215, producing the second wing of the 405 rail. This opening does not replace ordinary MT precedence. |
| Main Noah biographies | G2 primary birth → Flood start → death, with 600+350=950; SP uses current primary stations |
| SP companion | −1 belongs locally to Noah/Shem person-stations. Flood close is independently the event's end; no upstream companion ripple is used. |
| Fixed Arphaxad | Held under ordinary Gear at fixed other variant settings; MT baseline 2456 BC |
| Creation wrapper | (Year-1 opening, Year-6 opening, Year-7 close) = (E+7,E+2,E); Year-7 start/rest is separately E+1 |
| Apparent Age | Localized Adam/Creation +30; a whole-tuple translation is separately declared |
| Midpoints and translated geometry | Generated unless an independent parent controls an event role at the same label |
| External scales | 10× decimal, 100× square dilation, and 360:1 macro scale are separate executions |
| Actual cumulative preview | Shem/Flood week-head coordinates 5436/4836; no Regular Gear is assigned to the cumulative week |

### 0.3 Dependency and source map

| Controller | Retained authority | 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 rows, Noah/Shem/Flood bindings, fixed Arphaxad, native versus restored Cainan, Lamech hierarchy | Selected Creation and Noah tables |
| Files 00/02/11 | Primary anchors, Gear topology, Flood/SKL and node-class discipline | Named local and cross-Gear constructions |
| Files 07/14 | Creation markers and controlled boundary chains | Wrapper, 400/430 diagonal, double-1656 boundary chain |
| File_13 | Christological hinge and Incarnation-node classifications | §4.2 typological reading of 6→1 BC |
| Files 01/05/06/16/60/63 | Abrahamic chronology, Egypt/Affliction, Covenant and related source roles | Historical target field and Appendix A |
| Files 17/46 | Exact expansion protocols and precessional vocabulary | Priestly, Prophetic, and Enochian applications |
| Files 21/24/34 and Supplement A | External chronology, square-chain source provenance, scale/phase/Pillar states | Appendix-only corroboration; full derivations remain parent-owned |
| Files 09/22 | Actual cumulative architecture, week anatomy, harmonic bridge | Appendix C and route to Report III |
| Files 20/53 | Literal Jubilee and completion distinctions; BJ source arguments | Qualified 49/50 comparison |
| Files 51a/54 | Rounded/controller and claim-status exemplars | State classification; century-clean Actual spans are not Rounded execution |

Current Register §D.43 controls the LXX Lamech settlement; §D.44 controls the relevant Shem/Terah/week distinctions. File_18's September 18 SP amendment is published and author-authorized; its header records central Register/Capsule registration as pending. This file recognizes that source decision without closing the registration debt.

The operative LXX combined biography is restored begetting 182 with attested lifespan 753 and calculated remainder 571. LXX 777 remains an appendix overlay; MT 777 is unchanged. This study's active Creation/Noah birth paths do not execute the obsolete LXX 777 lifespan.

### 0.4 Local non-collapse guards

Machine Guard [REPORT I SOURCE AND COMPARISON OWNERSHIP]:
Use the parent-controlled source rows, anchors, and exact operators. Local comparison tables repeat selected executions; they do not replace native states or create a second raw-data controller.

Machine Guard [REPORT I CREATION MARKERS]:
Preserve Year-1 opening, Year-6 opening, Year-7 start/rest, and Year-7 close as separate node classes. The same-marker 405, cross-marker 400, and boundary +1 constructions require named endpoints.

Machine Guard [REPORT I NOAH SHEM AND FLOOD]:
Name the active Gear and primary/companion station beside every qualified comparison. The main G2 primary biography is distinct from cross-Gear 598 constructions. SP person-companion −1 and Flood start→close are separate; Arphaxad remains fixed under ordinary Gear.

Machine Guard [REPORT I GENERATED GEOMETRY]:
Midpoints, translated tuples, and generated boundary nodes remain generated. Agreement with a sourced civil label does not merge events, variants, or traditions.

Machine Guard [REPORT I SCALE AND AXIS]:
Local 2, decimal 20, and macro 720 belong to distinct scales. Civil cross-axis spans use BC+AD−1 with no year zero. A civil span alone does not open inverse-number or Mirror operators.

Machine Guard [REPORT I COMPRESSION STATUS]:
The master formulas compress a declared source-bound field. Retain the provisional minimum-grammar hypothesis and its open questions; do not present it as a proved unique generator, independent witness count, or ancient transmission theorem.

## 1. The variant rail and Creation field

### 1.1 The 190 rail and 25 hub

Define T=60 and C=130. The four offsets are 0,60,130,190. In descending BC order their adjacent intervals are 60,70,60; the middle 70 is generated by C−T, not a third independent variant.

$$
C-T=70,\qquad V=T+(C-T)+T=190.
$$

Open the second 215-position plane only after this first rail is defined. With S=215,

$$
h=S-V=25,\qquad W=2V+h=405=215+215-25.
$$

Thus the two overlapping conceptual 215 wings give the full interval weave:

$$
60\mid70\mid60\mid25\mid60\mid70\mid60=405.
$$

### 1.2 Creation wrappers on the first plane

For Year-7 close E, the wrapper is (E+7,E+2,E). Every member in the following table is BC; column members are Year-1 opening / Year-6 opening / Year-7 close. Year-7 start/rest E+1 is not printed as a fourth tuple member.

| Offset | MT wrapper | SP wrapper, +215 comparison | LXX wrapper, declared Cainan state |
|---|---|---|---|
| T+C=190 | 4311 / 4306 / 4304 | 4611 / 4606 / 4604 | 5561 / 5556 / 5554 |
| C=130 | 4251 / 4246 / 4244 | 4551 / 4546 / 4544 | 5501 / 5496 / 5494 |
| T=60 | 4181 / 4176 / 4174 | 4481 / 4476 / 4474 | 5431 / 5426 / 5424 |
| 0 | 4121 / 4116 / 4114 | 4421 / 4416 / 4414 | 5371 / 5366 / 5364 |

There are 3×4=12 tradition-state wrappers, each retaining three marker roles. In LXX, the C and T+C rows contain native Cainan; the 0 and T rows expunge it for comparison. MT/SP C and T+C rows are restored comparison states.

### 1.3 Opening the full 405 field

The original four-state rail and its −215 translated companion form eight positions. The selected marker differs by tradition:

| Tradition and selected marker | Ordered BC labels |
|---|---|
| MT Year-7 closes | 4304, 4244, 4174, 4114, 4089, 4029, 3959, 3899 |
| LXX Year-7 closes | 5554, 5494, 5424, 5364, 5339, 5279, 5209, 5149 |
| SP Year-1 openings | 4611, 4551, 4481, 4421, 4396, 4336, 4266, 4206 |

Each row has intervals 60|70|60|25|60|70|60. The SP final wrapper is native 4206–4199 BC. The lowest theoretical LXX close 5149 BC is the endpoint of this full comparison field; it is not the formally designated ordinary LXX Regular-Minimum.

## 2. Noah and the manuscript geometry

### 2.1 Eight unique G2 biography rows

Table members are Noah birth / Flood start / Noah death, all BC, in the same first comparison plane as §1.2.

| Offset | MT G2 primary | Co-registered SP G2 primary / LXX matched comparison |
|---|---|---|
| T+C | 3248 / 2648 / 2298 | 3898 / 3298 / 2948 |
| C | 3188 / 2588 / 2238 | 3838 / 3238 / 2888 |
| T | 3118 / 2518 / 2168 | 3768 / 3168 / 2818 |
| 0 | 3058 / 2458 / 2108 | 3708 / 3108 / 2758 |

SP native G2 primary 3493→2893→2543 BC, translated +215, gives the bottom shared row. The native LXX Cainan-ON G2 tuple (3623,3023,2673) reaches that same row by +215−130=(+85): (3623,3023,2673)+85=(3708,3108,2758). Removing the native Cainan for this comparison is distinct from restoring it in the C and T+C rows. The table uses the primary person-station and Flood start, replacing the older ambiguous “SP-inclusive” caption. The primary Noah death retains File_18 §3.2.1's inclusive/harmonic qualification. The adjacent companion is a separate state: native Noah 3492→2542 and Flood close 2892. At T+C, fixed SP/LXX Arphaxad is 3296 BC, while MT Arphaxad is 2646 BC; ordinary Gear changes do not move these stations.

For either primary biography,

$$
\text{birth to Flood}=600,\qquad\text{Flood to death}=350,\qquad600+350=950.
$$

SP and LXX share coordinates under this declared comparison, so 12 Creation wrappers contract to 2×4=8 unique Noah rows. This is coordinate co-registration, not textual identity. Their 650 offset from MT translates all three members; it does not enlarge the lifespan.

### 2.2 Triple-1656 with three endpoint roles

At T+C:

| Tradition | Named endpoints, BC | Span |
|---|---|---:|
| LXX | Year-7 close 5554 → Noah birth 3898 | 1656 |
| MT | Year-7 close 4304 → Flood start 2648 | 1656 |
| SP | Year-7 close 4604 → Noah death 2948, primary +215 state | 1656 |

A common offset applied to both endpoints preserves each span. The repeated scalar belongs to three different chronological roles, not three identical events.

### 2.3 The 1250/650 pair

At Creation, LXX→SP→MT gives 5554→4604→4304 BC and gaps 950+300=1250. At Flood start, the common LXX/SP 3298 versus MT 2648 gives 650=950−300.

$$
G_C=1250=950+300,\qquad G_N=650=950-300,
$$

$$
\frac{G_C+G_N}{2}=950,\qquad\frac{G_C-G_N}{2}=300,\qquad G_C-G_N=600.
$$

The mean is Noah's lifespan, the half-difference is the SP–MT Creation displacement, and the contraction is his age at the Flood. These are exact comparisons of the selected field.

### 2.4 Six-point field and repeated source magnitudes

The T+C field is 3898→3298→3248→2948→2648→2298 BC. Its adjacent intervals are 600|50|300|300|350 and its total is 1600=950+650=40².

| Repeated span | Endpoint examples, BC | Relation to the variant grammar |
|---|---|---|
| 650 | 3898−3248; 3298−2648; 2948−2298 | 5×130 |
| 600 | 3898−3298; 3248−2648 | 10×60 |
| 350 | 3298−2948; 2648−2298 | 5×70; the first also equals 50+300 |
| 300 | 3248−2948; 2948−2648 | 5×60 |
| 950 | 3898−2948; 3248−2298 | 5×190=300+350+300 |

The structural inference is that the larger field reproduces the smaller variant magnitudes in a common scale. The source lifespan 950 is retained as an input; these equalities do not independently derive it.

### 2.5 Noah and the Atonement comparison

The subfield 3298→3248→2948→2648→2298 BC gives 50|300|300|350. Regrouping yields a role-swapped palindrome:

$$
\text{Noah}:300+350+300=5(60+70+60)=950,
$$

$$
\text{Atonement comparison}:350+300+350=5(70+60+70)=1000.
$$

The difference is 1000−950=50=5×10, matching 3298→3248. Two 650 intervals, 3298→2648 and 2948→2298, overlap on the central 300:

$$
650+650-300=1000,\qquad350+350+650+650=2000=2\times1000.
$$

“Atonement” is the study's theological/literary designation for this geometric comparison; the arithmetic does not date an additional event. The 1000 is 10³, a decimal cube or millennial whole, not a technical perfect number.

### 2.6 Jared and the 1196 hinge

The MT/SP directed 1656 spine decomposes as 460+1196=23(20+52)=23×72. The Priestly Key acts on the full spans:

$$
\frac{25}{23}(460,1196,1656)=(500,1300,1800)
=(500,2\times650,3\times600).
$$

In the selected LXX T+C field, Year-7 close 5554→Jared 4594→Noah birth 3898 gives 960+696=1656. Noah G2 primary 3898→Shem G2 primary 3398 adds 500; hence 4594−3398=696+500=1196. The front-loaded difference 960−460=500 is balanced by the Noah-to-Shem primary relation.

The adjacent 3396 BC Shem station is the G1/Arphaxad-bound comparison tied to Genesis 11:10, with fixed Arphaxad 3296 BC. It is not an unexplained correction of 3398, nor the same endpoint role. Keep the G2 and G1 bindings visible.

### 2.7 Qualified 598 diagonals

Noah G2 birth→G3 Flood and Shem G1 birth→G2 death supply separately named 598 diagonals. For example, MT 3058→2460 and 2556→1958 BC give 598, while matched Noah birth→Flood and matched Shem lifespan intervals each retain 600; Noah's full lifespan remains 950.

$$
1196=598+598,\qquad598=2\times299=26\times23,
$$

$$
598\frac{300}{299}=600,\qquad598\frac{25}{23}=650,
$$

$$
1196\frac{300}{299}=1200=2\times600,\qquad
1196\frac{25}{23}=1300=2\times650.
$$

The Three-Gear topology is simultaneous, not a series of repairs. Ordinary G1/G2/G3 offsets +0/+2/+4 are distinct from a Shem-centered −2/0/+2 display and the external −720/0/+720 macro wheel. Apparent Mode +30 is orthogonal.

### 2.8 Adam–Seth and Cainan share a magnitude

At the Year-6 markers, 5556−4306=1250. Applying Adam's source begetting age 130 to the figurative Year-6 Adam marker 4306 generates a Seth projection at 4176 BC, so 5556−4176=1380=1250+130=3×460.

This 4176 is a generated Year-6-based projection, not the raw source-table Seth birth. File_18 §2.1.3 gives raw MT Seth 3769 in the minimum plane; +215+60+130 gives 4174 in the selected variant. The 4176 label separately occurs as the Cainan-OFF MT Year-6 opening, 4306−130. The projected Seth marker and altered Creation marker remain distinct node classes under File_07 §1/§3.1. Equality of translation magnitudes is the retained comparison.

## 3. Half-gap hub and generated centers

### 3.1 The 25-hub table

Let A=1250/2=625 and B=650/2=325. Applying the same h=25 to both rows gives:

| Object | −25 | Center | +25 |
|---|---:|---:|---:|
| Creation half-gap | 600 | 625 | 650 |
| Noah half-gap | 300 | 325 | 350 |
| Sum | 900 | 950 | 1000 |

The sums advance in 50=2×25 steps: 900=18×50, 950=19×50, 1000=20×50. The left sum is half the expanded 1800; the center is Noah's lifespan; the right is the Atonement comparison. The equivalent normalized rows are 25(24,25,26) and 25(12,13,14).

### 3.2 Recovering the variant magnitudes

$$
\frac{A-B}{5}=60,\quad\frac{3B-A}{5}=70,\quad
\frac{A+B}{5}=190,\quad\frac{2B}{5}=130.
$$

The generated half-gap field is therefore fitted to the selected variant grammar. This is the retained structural inference; it is not a proof that every possible center or genealogy is uniquely generated.

### 3.3 Creation and Noah-death midpoint pairs

The hub centers and explicit tuple translations are generated BC geometry; their selected endpoints retain their parent-controlled source/state roles. The selected LXX Cainan-OFF and MT Year-7 closes 5364/4114 have midpoint 4739. Translating the entire tuple −25 produces 5339→4714→4089, with the same 625+625 anatomy.

| Field | Source/generated tuple, BC | Anatomy |
|---|---|---|
| Creation | 5364 → 4739 → 4114 | 625+625 |
| Creation translated −25 | 5339 → 4714 → 4089 | 625+625 |
| G2 Noah deaths | 2758 → 2433 → 2108 | 325+325 |
| G2 death tuple translated −25 | 2733 → 2408 → 2083 | 325+325 |

Thus the hub pairs are Creation 4739/4714 and Noah-death 2433/2408. These are paired geometric outputs, not alternative transmitted event dates.

### 3.4 Same-Gear and adjacent-Gear center separation

The G2 death-midpoint pair gives:

$$
4739-2433=4714-2408=2306=1656+650.
$$

The G3 death endpoints 2760/2110 have generated mean (2760+2110)/2=2435. Their −25 translated pair 2735/2085 has mean 2410. Using this G3 death-midpoint pair 2435/2410 instead gives:

$$
4739-2435=4714-2410=2304=1656+648=48^2,
\qquad648=650-2.
$$

The moved object is the Noah-death midpoint rail, correcting the original “Flood-center” label. Same-Gear 2306 is not 48². The generated Creation midpoint is held while the named death Gear changes; this is not a free movement of arbitrary endpoints.

### 3.5 Gear, Key gain, and Jubilee closure

The Priestly expansion 1656→1800 gains 144=12²=2×72. Therefore:

$$
2306+144=2450,
$$

$$
1656+(650-2)+(1800-1656)+2
=1656+648+144+2
=48^2+12^2+2
=2450=50\times49.
$$

The 2 restores the explicitly reduced Gear comparison. This is a scalar/geometric closure, not a new lifespan or historical date. The literal Jubilee cycle remains 49; its 50 completion/announcement idiom is separately controlled by File_20.

## 4. Anchored applications

### 4.1 The 405→400→430 geometry

Year-1 opening and Year-6 opening differ by five years. A full 405 same-marker span therefore contains a 400 cross-marker diagonal; localized Apparent Age +30 makes 430:

$$
405-5=400,\qquad405-5+30=430=215+215.
$$

The three congruent fields are:

| Field | Earlier → middle → later BC labels | Anatomy |
|---|---|---|
| MT selected Creation geometry | 4336 → 4306 → 3906 | 30+400=430 |
| SP selected Creation geometry | 4636 → 4606 → 4206 | 30+400=430 |
| MT Egypt/Affliction target | 1876 → 1846 → 1446 | 30+400=430 |

The first two use distinct variant/marker states plus localized Apparent Age; they are not one ordinary person's biography. The MT target retains 430 Egypt and its distinct 400 Affliction state under Files 05/16.

The SP tuple translates uniformly by 2760:

$$
(4636,4606,4206)-2760=(1876,1846,1446),
\qquad2760=2\times1380=6\times460=120\times23.
$$

Each component difference is 2760; the operation is a declared tuple translation, not an upstream source-date correction.

### 4.2 Century-clean spans to 6 BC

Actual selected Creation labels 4606,4306,4206,3906 BC yield 4600,4300,4200,3900 years to 6 BC. “Century-clean” describes the resulting spans; no mod-5 Rounded Scaffold is executed.

Retaining the 405 same-marker rail 4306→3901 BC and the five-year target difference 6→1 BC gives corresponding vertical spans 4300 and 3900. The productive five-year difference remains a relation between named markers and targets.

Typological note: These century-clean spans are read against the 6 BC Christological hinge and the five-year 6→1 BC Incarnation comparison. File_13 §7.4 controls the conception-anchor, traditional birth datum, and covenant-node distinctions within that field.

### 4.3 Marker-specific Key landings and outer comparisons

| Selected marker | BC source → BC target | Exact span |
|---|---|---|
| LXX Year-7 close | 5494 → 1446 | 4048=23×176 |
| SP Year-1 opening | 4206 → 1446 | 2760=23×120 |
| MT Year-7 close | 4114 → 1446 | 2668=23×116 |

The repeated two-state Key hits are related to C+S=130+215=345=15×23. This marker preference is a structural observation within the selected eight-state field and the held 1446/1406 BC targets. It is not exclusive: MT Year-6 opening 4091−1446=2645=23×115 and LXX Year-1 opening 5431−1406=4025=23×175 also give exact Key spans. The proposed preference remains bounded to the named comparison, without a probability or authorial-intent conclusion from the hit pattern alone.

For maximum MT close 4304 BC and lowest theoretical LXX close 5149 BC:

$$
4304-1406=2898=18\times7\times23=69\times42,
$$

$$
5149-1446=3703=7\times23^2=\frac{25921}{7},
\qquad25921=(7\times23)^2=25920+1.
$$

The raw closest separation is 5149−4304=845, while the differently targeted spans differ by 3703−2898=805=5×7×23. Their 40 difference is Exodus→Conquest:

$$
845=805+40=5(7\times23)+40,\qquad1446-1406=40.
$$

The schematic Great-Year scalar 25920 is retained beside 25921; the one-unit relation does not identify precise physical astronomy.

### 4.4 Lowest comparison weeks and the 3750 field

| Named week | BC head → close | Relation |
|---|---|---|
| Lowest theoretical LXX full-field Creation | 5156 → 5149 | Comparison state; not ordinary LXX minimum |
| MT Minimum Creation | 3906 → 3899 | −215 comparison plane |
| SP Normal / G2 native Creation | 4206 → 4199 | Current preferred SP wrapper |
| Conquest → land-rest close | 1406 → 1399 | Distinct target-week class; rest onset 1400, close 1399 under File_06 |

At corresponding heads and closes, LXX→MT is 1250 and MT→Conquest/rest is 2500=50²=2×1250; the complete width is 3750=3×1250. SP divides the first arm as 950+300:

$$
5156-4206=950,\quad4206-3906=300,\quad3906-1406=2500,
$$

$$
3750=950+300+2500=1250+2500.
$$

Holding SP Year-1 opening 4206 BC, the Prophetic Key transfers the target from Exodus to Conquest:

$$
4206-1446=2760=69\times40,
$$

$$
2760\frac{70}{69}=2800=70\times40=4206-1406.
$$

The gain is 40 with the source held; no new Creation date is inferred.

### 4.5 Boundary completion and double-1656

The outer LXX–MT same-marker widths are 1250−405=845, 1250, and 1250+405=1655. The largest close-to-close difference 5554−3899=1655 becomes 1656 only when the earlier node is the LXX maximum Year-7 start/rest at 5555 BC.

$$
1656=1250+405+1,
$$

$$
5555\rightarrow3899\rightarrow2243\ \text{BC}
=1656+1656=3312.
$$

The endpoints are LXX maximum Year-7 start/rest; MT minimum Year-7 close; and MT Minimum-Regular Flood. File_14 controls this boundary chain. It is distinct from the three-tradition Triple-1656 roles of §2.2.

$$
3312\frac{25}{23}=3600=60^2,
\qquad2(1250+405+1)\frac{25}{23}=60^2.
$$

The +1 is a named boundary relation, not another free chronological variant.

### 4.6 Schematic precessional-day register

Under the repository's schematic Great-Year convention, 25920=360×72. Let d_p=72 years. Then:

$$
1656=23d_p,\quad1800=25d_p,\quad648=9d_p,\quad144=2d_p.
$$

The Priestly expansion converts 23 to 25 precessional-day units. Its 144 gain is analogous in form to a local two-year Gear difference, but the units remain distinct. Files 12/17/21/34 retain the relevant source and scale discipline.

$$
1250+190=1440=20\times72=2886-1446.
$$

The 2886 BC endpoint is the independently source-controlled selected SKL rail described in Appendix B, not a new biblical Flood date.

### 4.7 Generated 144 transfer around the MT Flood

With sourced MT G2 Flood 2458 BC and Exodus 1446 BC, the span is 1012=23×44. Define a generated earlier endpoint 2602=2458+144. It gives 2602−1446=1156=34² and 2602−1406=1196=23×52:

$$
1012\overset{+144}{\longrightarrow}1156
\overset{+40}{\longrightarrow}1196,
\qquad144+40=184=23\times8.
$$

$$
34^2-12^2=1012=23\times44.
$$

The 144 is borrowed as the declared gain from 1656→1800; it is not the gain of expanding 1012, whose Priestly expansion would be 1100. Define another generated endpoint 4258=2602+1656. Its two paths are:

$$
4258-1406=1656+1196=23(72+52)=23\times124=2852,
$$

$$
4258-1406=1800+1012+40=2852.
$$

Here 4258−2458=1800, and the exact transfer identity is:

$$
1800-1656=1196-(1012+40)=144=12^2=2\times72.
$$

These generated nodes are path geometry, not replacement Creation/Flood anchors. The original study treats this as a fine-resolution consistency checksum within the declared gain-transfer construction, subordinate to the simpler candidate formulas. The two paths recombine its held anchors and borrowed 144; they are not independent determinations of 2602 or 4258.

### 4.8 Translating the Noah-side 400|5 rail

Appendix B identifies the generated 3096→2906→2881→2691 BC field and its central 25. The selected 400|5 subrail translates as:

$$
3096\rightarrow2696\rightarrow2691\ \text{BC}=400+5,
$$

$$
(3096,2696,2691)-1250=(1846,1446,1441).
$$

Each component is translated by 1250. The target has the same 400|5 anatomy; 1446 BC remains the Exodus and 1441 BC is a generated five-year companion, not another historical Exodus date.

### 4.9 Additive and Prophetic 345→350

$$
130+215=345,\qquad345+5=350,\qquad345\frac{70}{69}=350.
$$

Addition of a declared five-year term and Prophetic expansion are parallel completions of the scalar. Their shared output compares to Noah's 350 post-Flood years; it does not identify the two operators or authorize either as a free source-date adjustment.

## 5. Candidate compression and claim ledger

### 5.1 One working formula set

The source study's six master candidates and anchor conversion are consolidated here. They remain working descriptions of the selected field.

| Candidate | Compact form | Role |
|---|---|---|
| A — manuscript field | V=60+(130−60)+60=190; h=215−V=25; (G_C,G_N,W)=(5(V+60),5(V−60),2V+h)=(1250,650,405) | Source-bound comparative gaps and variant width |
| B — hub | (625,325)+k(25,25), k=−1,0,+1 | Pairs (600,300), (625,325), (650,350); sums 900,950,1000 |
| C — Priestly resolution | (460,1196,1656)=23(20,52,72) → (500,1300,1800) under 25/23 | Exact complete-span expansion |
| D — Gear/Jubilee closure | 1656+648+144+2=48²+12²+2=2450=50×49 | Named Gear reduction/restoration and scalar completion |
| E — boundary closure | 2(1250+405+1)×25/23=3600=60² | Controlled Year-7 boundary chain |
| F — anchor conversion | (4206−1446)×70/69=4206−1406 | Held SP Year-1 opening; gain 40 |

The normalized manuscript formula is also retained:

$$
5[(60+70+60)\pm60]=950\pm300=(1250,650),
$$

$$
50[(6+7+6)\pm6]=50(25,13)=(1250,650).
$$

Thus 1250=25×50, 650=13×50, and 950=19×50. A comparison with biblical Jubilee 49/50 vocabulary remains qualified by File_20's literal-cycle/completion distinction.

The provisional compact seed is (T,C,S,g,p)=(60,130,215,2,72), where g=2 is the selected local Gear difference and p=72 years is the schematic precessional-day unit. It gives 70,190,25,405 through the stated equations. The scale 5 is selected from source Noah 950 against V=190; source anchors, row order, event types, and the permission for each diagonal remain additional inputs. The formula set conditionally compresses this declared field. Minimum-grammar status remains a working hypothesis; this notation does not prove minimality or reconstruct the source chronology from the five scalars alone.

### 5.2 Working verbal synthesis

The 60 Terah and 130 Cainan alternatives generate the 60|70|60 rail. The selected 215-position change exceeds that rail by 25, giving 190|25|190=405. Source Noah 950 and the 300 Creation displacement fit the common 5× display, yielding Creation/Noah gaps 1250/650. Their half-gaps 625/325, acted on by the same 25, recover the 600/650 and 300/350 blocks and the 900/950/1000 sequence. The 1656 spine expands to 1800, while the named 650−2 comparison supplies 648 and the 48² field. The 144 expansion gain and restored 2 close at 2450=50×49. Selected decimal, macro-scale, and Pillar constructions provide external corroboration; held-anchor Prophetic expansion carries the SP Creation span from Exodus to Conquest.

This remains a working comparative synthesis. Exact identities under stated inputs, structural inference, proposed intentional architecture, and theological/literary significance retain their different claim levels.

### 5.3 Evidence hierarchy and open question

The source report's strongest spine is the variant weave, manuscript gaps, 460+1196=1656 decomposition, and the exact 598/600/650 completions. The hub and square/boundary constructions provide geometric corroboration. Appendix B contains scale corroboration, with distinct input/scale states and the original qualifications preserved. The historical anchor field remains 1446/1406 BC; generated labels do not replace it.

Many equations share the same inputs. Recovering 60/70/130/190 from half-gaps already fitted to them is an inverse expression of that fit; equal midpoint separations after a uniform translation express one affine invariance. The overlapping square windows share their terms, and a decimal or square dilation repeats the chosen scalar relation at another scale. These connections support the report's proposed structural organization, but their repetitions are not independent witness counts.

| Claim level | Retained content | Evidential role |
|---|---|---|
| Textual/source datum | Noah 600+350=950; inherited chronology rows and held historical anchors | Declared inputs, under their source controllers |
| Arithmetic fact | Variant weave, manuscript gaps, exact Keys, halves, and named endpoint spans | Exact under the stated inputs and operations |
| Structural inference | Common scaled grammar, fitted hubs, qualified Gear closure, and marker preference | Proposed organization of the selected comparative field |
| Proposed intentional architecture | The small operation set repeatedly describes larger values | Working interpretation; no proved unique generator, minimality theorem, or probability result |
| Theological/literary reading | Atonement comparison, promised-seed midpoint, and qualified Jubilee vocabulary | Preserved significance with its textual context; distinct from arithmetic proof |
| External corroboration | Selected SKL/Berossus/Pillar correspondences | Appendix comparisons under declared source and scale states; shared inputs limit independence |

The external source traditions are distinct, while the selected overlays reuse biblical targets, comparison shifts, and scale factors. Their exact agreement is retained as corroboration of the proposed architecture without treating every projected or rescaled output as an independent historical witness. The main comparative argument remains the declared variant/manuscript spine; the appendices do not carry its primary burden.

The strongest open question is what a compact generator can reconstruct after the source rows, event roles, and held anchors have been declared, and what information it necessarily leaves as input. The cumulative continuation is now developed in Report III; Appendix C retains this report's original limited preview and routes further study there.

## Appendix A. Secondary geometry and Abrahamic comparisons

This appendix retains the secondary constructions of the original Report I §§32–39. Their equations are exact within the declared states. The square patterns and Abrahamic landings function as geometric corroboration of the main comparison; they do not independently generate the manuscript source data. `File_18` §§2–4 controls the regular chronology, `File_11` and `File_02` control Gear use, and `State_Vocabulary_Register` §D.44 preserves the distinction between biological/default Gear-2 and selected Gear-1 stations.

### A.1 The square-center kernel

The inputs are the Priestly-expanded span `1800`, the Creation manuscript gap `1250`, and the qualified cross-Gear gap `648 = 650 − 2`. Their halves are:

| Input | Half | Square form |
|---:|---:|---:|
| `1800` | `900` | `30²` |
| `1250` | `625` | `25² = 5⁴` |
| `648` | `324` | `18²` |

Therefore:

$$
900+625+324=1849=43^2,
\qquad
\frac{1800+1250+648}{2}=43^2,
\qquad
1800+1250+648=2\times43^2.
$$

These are scalar half-spans. Halving a qualified cross-Gear distance does not itself supply a new historical midpoint event.

The source SKL comparison is controlled specifically by `File_24.Kish_Dynasty_Cipher_En_Tarah_Ana_23_Kings.md` §5.1. It records Enmebaragesi `900`, Aga of Kish `625`, and Mesh-ki-ang-gasher `324`, with the same sum `1849 = 43²`. The first two rulers close the Kish list; the third opens the Uruk/E-anna succession and is not a twenty-fourth Kish king. This is a corroborative interface with the source's terminal square-chain clue, under that file's conjectural cipher and claim-status controls.

Restoring the full `650` gap changes the third half-span from `324` to `325`:

$$
\frac{650}{2}=325,
\qquad
625+325=950,
\qquad
900+325=1225=35^2.
$$

The reduced and full states consequently have different closures:

$$
625+900+324=43^2,
\qquad
625+325=950,
\qquad
900+325=35^2.
$$

The companion sums must remain precise:

$$
625+324=949,
\qquad
900+324=1224.
$$

Appending the second `625` produces the ordered scalar field:

$$
625\mid900\mid324\mid625.
$$

Its two overlapping windows are:

$$
625+900+324=1849=43^2,
\qquad
900+324+625=1849=43^2.
$$

Their shared middle is `900 + 324 = 1224`. Original provenance: Report I §§32–34. `File_46.Harmonic_Expansion_Protocols.md` controls the exact Priestly operator that produces `1656 × 25/23 = 1800`; the present construction applies inherited span values.

### A.2 The Covenant, Ishmael, and Isaac comparisons

Hold the report's equalized `+215` position plane, with Terah `+60` and restored second Cainan `+130` OFF for the Noah death pair used here. The selected Gear-1 endpoints are LXX Cainan-OFF/SP primary Noah death `2756 BC` and MT Noah death `2106 BC`. They are the Gear-1 counterparts of the main Gear-2 death pair `2758/2108 BC`; both complete Noah biographies remain `950` years. For SP, “primary” has the inclusive/harmonic qualification of current `File_18` §3.2.1; its lower companion remains a separate person-station.

The generated midpoint is `2431 BC`:

$$
2756-2106=650,
\qquad
\frac{2756+2106}{2}=2431,
\qquad
2431-2106=325.
$$

The Covenant-of-Pieces coordinate `2081 BC` is author-designated in `File_63.Scale_Neutral_480_483_490_Carrier.md` §7.9, as the `+215` counterpart of the `1866 BC` MT-Minimum Covenant state. Its status is a repository chronology designation; Genesis 15 does not explicitly supply that BC date. With this coordinate held:

$$
2106-2081=25,
\qquad
2431\rightarrow2106\rightarrow2081
=325+25=350.
$$

Thus:

$$
\frac{650}{2}+25=350.
$$

The companion scalar comparison uses the cross-Gear `648` half-span and the one-year Covenant-to-Ishmael movement:

$$
\frac{648}{2}=324,
\qquad
2081-2080=1,
\qquad
324+(25+1)=324+26=350.
$$

The `2080 BC` Ishmael birth coordinate belongs to the ordinary full-430 comparison, controlled by `File_60.Levitical_Covenant_Spine_161_299_Key_of_23_Reconciliation.md` §0.4 and its §2.2 MT-Minimum ledger translated by `+215`. It is not the cumulative Jacob coordinate that shares `2080`. The half-gap `324` is retained here as a scalar: it is not the `325` midpoint half of the matched Gear-1 `2756→2106` pair.

The resulting equality is:

$$
\frac{650}{2}+25
=\frac{648}{2}+25+1
=350.
$$

The one-year Covenant-to-Ishmael movement compensates arithmetically for the reduction of the half-gap from `325` to `324`. Original provenance: Report I §§35–36.

Isaac's ordinary MT birth `2066 BC` lies at the midpoint of the generated endpoint field `2691→1441 BC`:

$$
2691-2066=625,
\qquad
2066-1441=625,
\qquad
2691\rightarrow2066\rightarrow1441=625+625=1250.
$$

The historical Isaac coordinate remains source-controlled. `2691 BC` and `1441 BC` are generated comparison endpoints; the latter is `1446 − 5`, a target companion to the Exodus, not a new historical Exodus date. Their construction is retained in original Report I §§56–57, and the Isaac midpoint comparison in §37. `File_01.Abraham_Gen20_Fractal_Pivot.md` retains the ordinary Abraham/Isaac chronology; `File_18` §2.3 gives the MT-Minimum Isaac birth `1851 BC`, whose `+215` counterpart is `2066 BC`.

Isaac as the promised seed in the Genesis 15 promise context associated with the 400-year prediction gives the midpoint a theological/literary interpretation. That interpretation is distinct from the exact endpoint arithmetic and does not derive either generated endpoint independently.

### A.3 The Covenant hub and the `405 | 45 | 405` field

The upper rail is a declared comparison of selected source states:

$$
2296\rightarrow2236\rightarrow2166\rightarrow2106
=60\mid70\mid60=190.
$$

`2296 BC` and `2236 BC` are the Terah `+60` and base birth coordinates; `2166 BC` is ordinary Abraham birth; `2106 BC` is the selected MT Gear-1 Noah-death coordinate used above. The first two are alternative Terah biography states, and this display is not four consecutive events of one biography or four biological sibling births. `File_60` controls the Terah states; `State_Vocabulary_Register` §D.44.1 retains their current scope and distinctions.

The `25` hub reaches the held author-designated Covenant coordinate:

$$
2106-2081=25.
$$

The lower rail is the uniform `−215` comparison translation of the upper rail:

$$
(2296,2236,2166,2106)-215
=(2081,2021,1951,1891).
$$

Its internal anatomy remains:

$$
2081\rightarrow2021\rightarrow1951\rightarrow1891
=60\mid70\mid60=190.
$$

Here `2021 BC` is the Terah base birth in the minimum plane, `1951 BC` is the adjusted Abraham birth, and `1891 BC` is the corresponding Gear-1 Noah death in that plane. The translated `2081 BC` comparison label co-registers with the author-designated Covenant `2081 BC`; shared labels do not merge their node classes. The lower rail does not replace the unshifted ordinary chronology.

The combined field is therefore:

$$
2296\rightarrow2236\rightarrow2166\rightarrow2106
\rightarrow2081\rightarrow2021\rightarrow1951\rightarrow1891,
$$

$$
60\mid70\mid60\mid25\mid60\mid70\mid60=405,
\qquad
2296-1891=405.
$$

The next bridge to the Affliction display is:

$$
1891-1846=45,
\qquad
1846-1446=400,
\qquad
1446-1441=5,
\qquad
1846-1441=405.
$$

`1846 BC` is the declared `400`-year Affliction comparison head to the held `1446 BC` Exodus, controlled by `File_05.Exodus_Target_Fulcrum_Anchor.md` / `File_16.1876_BC_Nexus.md`. It is distinct from the ordinary `1876 BC` Egypt-entry coordinate. `1441 BC` remains generated.

The outer envelope is:

$$
2296\rightarrow1891\rightarrow1846\rightarrow1441
=405+45+405=855.
$$

The two overlapping spans are:

$$
2296-1846=450=405+45,
\qquad
1891-1441=450=45+405.
$$

Thus `405 | 45 | 405` has a central `45` overlap shared by two equal `450` spans. Its literal flanking arms are `405`, not `450`. Original provenance: Report I §§38–39. The arithmetic is a comparison across declared states; the proposed Abrahamic significance retains its corroborative weight.


## Appendix B. SKL, Berossus, and Pillar corroboration

The regular comparison has several exact counterparts in the repository's Sumerian King List (SKL), Berossus, and Temple-Time Pillar fields. This appendix preserves those finite comparisons. File_34 controls the full SKL/Berossus derivation, computational anchors, and phase chains; File_21 controls the SKL application states and Projective Pillar labels; File_70 Supplement A §8.9 controls the distinction between source `24510` and generated `24500`.

The equations are arithmetic facts within those declared states. Their correspondence with the regular manuscript geometry is structural corroboration. They do not supply an independent derivation of the biblical chronology or establish an ancient writer's execution of every comparison.

### B.1. Source coordinates and scale distinctions

The SKL whole-year source states are:

| State | Duration of the 23 kings | Physical terminal, BC | `+30` terminal, BC | Physical Flood, BC |
|---|---:|---:|---:|---:|
| SKL Short | `17980` | `2906` | `2936` | `20886` |
| SKL Long | `24510` | `2856` | `2886` | `27366` |

Thus `20886−2906=17980` and `27366−2856=24510`. The duration difference and the terminal difference combine as:

$$
24510-17980=6530,\qquad2906-2856=50,
$$

$$
27366-20886=6530-50=6480.
$$

The comparisons below sometimes cross these source positions. For example, `20886→2886 BC` joins the Short physical Flood to the Long `+30` terminal. Its `18000` is a comparison span, whereas the Short native duration remains `17980`.

Three scale relations remain distinct:

| Relation | Operation and role |
|---|---|
| `2→20` | A decimal `10×` comparison |
| `2→720` | The SKL `360:1` dilation of a selected local Gear interval |
| `648→64800` | A separate `100×` span comparison, with square sides enlarged `10×` |

The full centered local wheel is `−2/0/+2`; its SKL dilation is `−720/0/+720`. A selected macro member may carry a separately declared local subrail under its parent controls. Apparent Mode `+30` is orthogonal to these wheels. The whole-year SKL durations and the appended fractional textual data retain separate roles; exact calendar-phase chains remain with File_34. The calculations here use the selected whole-year Nisan comparison coordinates.

### B.2. The decimal counterpart of `1656→1800`

Select the Short Flood's `−720` member `20166 BC`, with `20166=20886−720`, and the Jared/Pillar comparison coordinate `3606 BC` controlled by File_34 Appendix B.4. That coordinate is paired specifically with Jachin `AD 29515`: `3606+29515−1=33120`. The selected `20166→3606 BC` interval is a mixed-system comparison, not a native SKL reign total. Then:

$$
20166-3606=16560=23\times720.
$$

The Priestly Key gives:

$$
16560\times\frac{25}{23}=18000=25\times720,
\qquad18000-16560=1440=2\times720.
$$

This is exactly the decimal counterpart of the regular `1656=23×72 → 1800=25×72`, with gain `144=2×72`. The selected terminal labels also give:

$$
2906-2886=20=10\times2.
$$

Their `20`-year separation matches the decimal image of the local `2`; it does not turn the Short/Long terminal comparison into an unrestricted Gear operator. The cosmic dilation of `2` remains `2×360=720`.

### B.3. `2448/2450` and the generated `24480/24500`

The regular closure is:

$$
1800+648=2448,\qquad2448+2=2450=50\times49.
$$

The corresponding SKL comparison uses the two physical Floods and the Long `+30` terminal:

$$
27366-20886=6480,\qquad20886-2886=18000,
$$

$$
27366-2886=6480+18000=24480=10\times2448.
$$

Applying the separately declared decimal completion `+20` gives:

$$
24480+20=24500=500\times49=50\times490.
$$

The full correspondence is therefore:

$$
(1800+648)+2=2450,
\qquad(18000+6480)+20=24500.
$$

Equivalently, retaining the original pre-expansion inputs and their gains:

$$
16560+6480+1440+20=24500.
$$

`24500` is a generated Jubilee companion. It does not emend the Long source duration `24510=27366−2856`. Supplement A §8.9 controls that source/companion distinction and its separately declared alternative construction; the present study retains its original decimal route.

The exact `2448/2450 → 24480/24500` decimal correspondence is one of the report's clearest fractal scale correspondences.

### B.4. The Noah midpoint and the `405` field

On the held full-430 comparison plane, with Terah `+60` OFF, the LXX Cainan-OFF Gear-1 Noah birth `3706 BC` and MT Gear-1 Noah death `2106 BC` give:

$$
3706-2106=1600=40^2,
\qquad\frac{3706+2106}{2}=2906.
$$

Thus `3706→2906→2106 BC` has `800+800`. The generated midpoint co-registers with the independently controlled Short physical terminal `2906 BC`; it does not identify the SKL terminal event with a biblical Noah event.

Around this coordinate, the generated rail:

$$
3096\to2906\to2881\to2691\ \mathrm{BC}
$$

has:

$$
3096-2906=190,\qquad2906-2881=25,\qquad2881-2691=190,
$$

$$
3096-2691=405=190+25+190.
$$

The midpoint of the complete `405` span is `(3096+2691)/2=2893.5 BC`. The coordinates `2906/2881 BC` are the boundaries of its central `25`, rather than two midpoints of the complete span. A second shared-label comparison is:

$$
2106+650+130=2886.
$$

This adds the manuscript displacement and a declared regular Cainan insertion to the MT Noah-death comparison, reaching a label also used by the Long `+30` terminal. Its biblical and SKL roles remain distinct.

### B.5. Native SKL Creation and the two `360²` halves

The native Short SKL Alulim/Adam coordinate is generated by its own antediluvian source span:

$$
20886+241200=262086\ \mathrm{BC},
\qquad241200=670\times360.
$$

Measured to the Long `+30` terminal:

$$
20886-2886=18000=50\times360,
$$

$$
262086-2886=259200=(670+50)\times360
=720\times360=2\times360^2.
$$

Consequently `259200/2=129600=360²`: the selected comparison field is a `720×360` rectangle composed of two equal `360×360` squares. Under the repository's schematic Great-Year convention:

$$
25920=360\times72,\qquad259200=10\times25920.
$$

The selected `259200` field therefore displays ten Great-Year cycles. The regular `1656=23×72`, `1800=25×72`, and Gear-reduced `648=9×72` are day-sized subdivisions of that same schematic precessional vocabulary.

Native SKL Creation `262086 BC` belongs to Short Alulim/Adam. It remains distinct from hybrid or Berossus Creation projections controlled by File_34; their alternative source spans and anchors are not executed here.

### B.6. Projective Pillars and the `180²/540²` field

Boaz `AD 29465` and Jachin `AD 29515` are Projective Boundaries controlled by Files 21/34. Their conceptual derivation remains with the Temple-Time framework; the SKL arithmetic is a corroborating alignment. The civil cross-axis span is `BC+AD−1`.

| BC starting coordinate | AD Projective Pillar | Civil span |
|---|---|---|
| Short `+30` terminal `2936 BC` | Boaz `AD 29465` | `2936+29465−1=32400=180²` |
| Long `+30` terminal `2886 BC` | Jachin `AD 29515` | `2886+29515−1=32400=180²` |
| Native Short Alulim/Adam `262086 BC` | Jachin `AD 29515` | `262086+29515−1=291600=540²` |

The first two pairs preserve the common span because `2936−2886=29515−29465=50`: the BC starting coordinate moves later while the AD endpoint moves later by the same elapsed amount. The complete SKL/Pillar span partitions at `2886 BC`:

$$
259200+32400=291600=540^2=405\times720.
$$

Its square factorization is:

$$
405=9\times45,\qquad720=16\times45,
\qquad405\times720=(3\times4\times45)^2=540^2.
$$

This connects the local `405` variant width with the selected large-scale square. It remains a finite corroboration under the stated endpoints, rather than a rule for promoting remote coordinates to historical dates.

### B.7. Berossus: the computational Flood projection and two parallel Keys

File_34 derives the Berossus Flood projection from its figurative/computational anchor `486 BC` and post-Flood duration `34080`:

$$
486+34080=34566\ \mathrm{BC}.
$$

The computational `486 BC` remains distinct from historical restoration `536 BC`. The selected `+720` macro comparison member is `35286=34566+720 BC`. With the Long `+30` terminal and Jachin Pillar:

$$
35286-2886=32400=180^2,
$$

$$
2886+29515-1=32400=180^2,
$$

$$
35286+29515-1=64800=32400+32400
=180^2+180^2=100\times648.
$$

Since `648=324+324=18²+18²`, the last comparison enlarges each square's side from `18` to `180` and its area by `100`.

The held principal projection supplies the Exodus-directed counterpart of double `1656`:

$$
34566-1446=33120=16560+16560
=10\times3312=32400+720.
$$

The two exact expansions are:

$$
33120\times\frac{25}{23}=36000
=2\times18000,
\qquad33120\times\frac{70}{69}=33600.
$$

Thus `2×16560 → 2×18000` is the decimal counterpart of the regular `2×1656 → 2×1800 = 3600`: Berossus participates in the same double-`1656` architecture. The unexpanded Berossus-to-Exodus span remains `33120`; `36000` and `33600` are generated outputs of parallel operators. The SKL/Berossus witnesses are especially important to the report because they display the same arithmetic outside the ordinary MT/SP/LXX scale. These finite comparisons retain their corroborative weight and their parent-controlled chronology.

## Appendix C. The cumulative bridge and source provenance

### C.1 The Actual cumulative Shem preview

The bridge retained from original Report I §74 uses **Actual cumulative week-head coordinates**, with second Cainan OFF. `5436n BC` is the Nisan head of the cumulative Shem birth-week `5436n–5429n BC`; `4836n BC` is the corresponding head of the cumulative Shem-death/Flood/Arphaxad seam field `4836n–4829n BC`. These are lifespan-stacking coordinates controlled by `File_18` §6A, `File_09.Cumulative_Architecture.md`, and `File_22.Cumulative_MT_Harmonics.md` §0.1/§1.2. They are not regular Gear-1 or Gear-2 event dates.

The seam's Nisan envelope is obtained componentwise from the same Actual week: (5436n–5429n)−600=(4836n–4829n). No Regular Gear operation is applied. The original head comparison is:

$$
5436-4836=600,
\qquad
\frac{5436+4836}{2}=5136,
$$

$$
5436\rightarrow5136\rightarrow4836=300+300.
$$

`5136 BC` is a generated midpoint of the selected head coordinates. It is not independently attested as a historical event node.

Holding the repository restoration anchor `536 BC` gives:

$$
5436-536=4900,
\qquad
5136-536=4600,
\qquad
4836-536=4300.
$$

Therefore:

$$
4900\rightarrow4600\rightarrow4300
=10\times(490\rightarrow460\rightarrow430).
$$

This is a scalar relation among three spans with the same held target. The arrows do not turn those span values into new BC dates. The cumulative Shem `600` accepts the same `300+300` partition seen in the regular Noah/manuscript field; their chronological methods remain distinct.

The continuation is the dated Report III, `Cumulative_MT-SP-LXX_Creation-Shem_Comparative_Engine_Report_III_20260902.md`, especially §§5–16 and §§20–38. That report compares the three cumulative systems and their declared regular endpoints. It remains a separate research source pending its own canonical intake; its regular Gear-1 bindings must not be imposed on this cumulative week-head object.

The two Cainan operations remain:

$$
\text{Regular restored second Cainan}=+130,
\qquad
\text{Cumulative restored second Cainan}=+460.
$$

The Actual cumulative–regular bridge `9890` remains File_22-controlled, whereas `9900` belongs to the separate File_51a Rounded Scaffold. Shared clean year labels or multiples of `10` do not make this preview Rounded chronology. Current seven-year-object and phase discipline is registered at `State_Vocabulary_Register` §D.44.3.

### C.2 Operative correction ledger

The original dated report preserves the discussion history. This compact ledger retains its resolved arithmetic and terminology without reproducing restart instructions or treating superseded slips as alternative source states.

| Original Report I §75 item | Retained correct form or boundary |
|---|---|
| Flood `40` and `150` | The initial `40` days are contained within the `150`; elapsed time to the ark's resting is `150`, not the thematic sum `40 + 150 = 190`. The latter may be named only as a thematic sum of stated duration values. |
| `1000` | `1000 = 10³`, a decimal cube; it is not a technical perfect number. |
| `625` | `625 = 25² = 5⁴`. |
| `2898` | `4304 − 1406 = 2898 = 18 × 7 × 23 = 69 × 42`. |
| `805` | `805 = 5 × 7 × 23`. |
| `345` | `130 + 215 = 345`; the operation is addition. |
| `1224` | `900 + 324 = 1224`; separately `625 + 324 = 949`, `625 + 325 = 950`, and `900 + 325 = 1225 = 35²`. |
| `2304/2306` | Same-Gear center separation `2306 = 1656 + 650`; qualified cross-Gear separation `2304 = 1656 + 648 = 48²`. |
| `33120/36000` | `33120 = 2 × 16560`; the Priestly expansion `33120 × 25/23 = 36000` is a separate execution. |
| `598` | `598 × 300/299 = 600`. |
| Noah's `600` | Birth→Flood, rather than birth→death. |
| Noah's lifespan | `950`; `1656` is a manuscript-directed Creation/Noah span with separately stated endpoints. |
| `5149 BC` | Lowest theoretical LXX endpoint in the full variant rail; not ordinary LXX Regular-Minimum. |
| `5555 BC` | LXX Maximum Year-7 opening/rest boundary; not the opening of the complete seven-year Creation week. |
| `45` and `450` | `405 \| 45 \| 405`; `405 + 45 = 45 + 405 = 450` are overlapping spans. |

Source-counting controls: Genesis 7:4, 12, 17, 24 and 8:3–4 supply the Flood-duration sequence; `File_02.Flood_Sumerian_Integration.md` and `File_11.Three_Gear_Protocol_Harmonic_Engine.md` control its repository application. `File_18` supplies the Noah biographies and current Flood start/close bindings. `File_46` controls the distinct exact expansion operators. The main argument and Appendices A/B retain the operative equations above in their appropriate comparative settings.

### C.3 Provenance and continuation boundary

The source is the August 31, 2026 discussion synthesis `Regular_MT-SP-LXX_Creation-to-Noah_Engine_Report_I_20260831.md`. Its original §§75–82 and final working formula set remain part of that dated research record. The revision routes that material as follows:

| Original material | Retained function |
|---|---|
| §74 cumulative preview | Appendix C.1; Actual week-head comparison and generated midpoint. |
| §75 corrections | Appendix C.2 and the corrected equations at their point of use. |
| §76 non-collapse rules | Current local state register and guards, with source-controller references. |
| §§77–78 regular result and primary spine | Main comparative synthesis, preserving conditional compression and inherited source inputs. |
| §79 geometric corroboration | Main hub comparison plus Appendix A square patterns; corroborative weight retained. |
| §80 scale corroboration | Appendix B; decimal, `100×`, and `360:1` scales remain distinct. |
| §81 anchor corroboration | Main anchored Exodus/Conquest applications; generated `1441` stays qualified. |
| §82 and final restart formulas | Source archive; the unique cumulative equations remain in C.1 and the regular formulas in the main synthesis. |

Later controls clarify the source states used in the revision: `State_Vocabulary_Register` §D.43 governs the common main LXX Lamech `182/753` reconstruction and appendix-only LXX `777`; §D.44 governs Terah state roles, selected regular Shem stations, and cumulative seven-year ontology. The September 18, 2026 File_18 amendment governs SP primary/lower Noah–Shem stations and ordinary cross-tradition Flood Gears. Its source header records outstanding central registration; this revision does not represent that registration as completed.

The original §82 research programme is retained as historical scope:

1. The cumulative Shem 600 partition into 300+300.
2. Cumulative Creation/Flood coordinates compared with the Regular 1250/650 manuscript field.
3. Cumulative Cainan +460 versus Regular Cainan +130, preserving their states.
4. The cumulative 490/460/430 triad compared with Regular 600/300/405/430.
5. The 4836 BC cumulative Flood seam, Enoch, and their proposed hinge role.
6. Integration with Files 09/22/63/68/69/70 under each controller's authority.
7. The source-bound objective of one master equation plus one Key-of-23 transformation.

Historical research scope: The Regular result is the proposed base geometry for a cumulative continuation, which builds on that geometry without redefining it. Each system retains its distinct source data and modal states.

The unresolved structural question is whether the cumulative systems can be expressed as a source-bound continuation of the same reduced comparison grammar. It is a research question, not a final master theorem. The original next-chat instructions are preserved as historical source material rather than issued as instructions in this edition.

## Revision Log

October 7 2026 — First Final Repository edition, File_71, retaining the Report I study identity.

- Authorization: explicit author instruction, “Make it final. Spot will add it to the website.”
- Source basis: verified October 7 Report I revision; immediate pre-Finalization source SHA-256 `bb10b34c9fd7a421d771dd50a7199da639263c6e296fc8a5faba1fcf5f5259f2`.
- Finalization: stable Repository identity, Final status, source/publication metadata, removal of temporary document-status wording, and this revision record. All 96 displayed mathematical blocks, all 21 tables' numerical data, and all six local guards are retained. Research hypotheses and interpretation ceilings remain unchanged.
- Verification: the complete source-preservation/change-class review is retained as the trust basis; the Final file passes the exact arithmetic recheck and focused Finalization comparison. No full pressure-test certification is claimed.
- Unresolved editorial decisions: none. Conditional compression, minimality, intentional architecture, and cumulative continuation remain qualified research questions.
- Parent matters: existing caption-alignment recommendations and the File_18 September 18 SP central-registration debt remain with their owning controls. This Finalization introduces no new primary anchor or generic operator.
- Cross-file installation: add File_71 to the raw-source index, Knowledge Catalog, and publication manifest; register its six local guards and source-owner boundaries in the State Vocabulary Register and Restart Capsule; preserve the change history. These additions are prepared for Spot and are not represented as installed here.