# Moses-centred rounded construction

Frozen preparation for File51a §§7A.1–7A.5. Exact source SHA256: `d8aa38afb2a2df8f3bb57937f5d3dea897c286c034a1bee7398938d30e7bd77c`. **18/18 preparatory checks pass.** No numbered steps or source edits.

## What the complete reconstruction explains

The entire MT regular path is generated from the frozen source begettings, component rounding and the declared Joseph→Entry→Moses tail. Its25 labelled nodes reproduce all23 births in File51a §3.1 and add Entry1876 and Moses1526. The totals2580,2450 and1960 are outputs, not primitive numeric inputs. Native LXX likewise regenerates its full3960-year path with Cainan present exactly once.

The useful connection to the new post-Flood work is local: Actual strict MT has the partition129 | 801; row rounding changes it to130 | 800 while preserving930. The shared post-Flood begetting-amplitude model then explains the corresponding SP530 | 1050 and native LXX660 | 1050 partitions. This is a complete two-part source-path transfer, not an endpoint fit.

## The source packet and counting choices

MT uses Terah70, native Cainan OFF and the File51a strict comparison that excludes Shem’s+2. The rounded row operation is `Q(n)=5 floor((n+2)/5)` on selected intervals, followed by accumulation. It is not direct rounding of BC labels or the addition of full patriarchal lives. The fixed lower path has Jacob2006, Joseph1916, Entry1876 and Moses1526.

Joseph’s age39 at Entry is30+7+2; Jacob’s age at Joseph’s birth is130−39=91. The rounded90 and40 still sum130. Entry→Moses350 is the declared1876−1526 interval, equivalently430−80. The word “Egypt” in §7A.4 therefore denotes the segment up to Moses’ birth, not the full interval to the Exodus. No missing Levi/Kohath/Amram begetting ages are invented.

All raw b/L rows remain bound to the frozen File18 packet. Adam’s separate biography130+800=930 and Shem’s100+500=600 supply the biographical comparison; their lifespans are not substituted for regular genealogical edges.

## Complete MT block structure

| Ordered segment | Rounded span | Source generation |
|---|---:|---|
| Adam→Seth |130| Adam’s begetting age |
| Seth→Enoch |490|105+90+70+65+160|
| Enoch→Arphaxad |1030|65+185+180+500+100|
| Arphaxad→Reu |130|35+30+35+30|
| Reu→Moses |800|30+30+30+70+100+60+90+40+350|
| Entire path |2580| Sum of all five blocks |

Subtracting the first block gives Seth→Moses2450=5×490. Subtracting the first two gives Enoch→Moses1960=4×490. The full span is2580=6×430=2×1290. The source’s bridge6×430−5×490=130 correctly expresses a necessary compatibility of those targets. It does **not** show that Adam’s130 alone selects Moses; the entire downstream placement must still be supplied by the source path.

## Why the post-Flood partition changes but its total does not

| Part | Actual strict MT | Rounded MT | Local residual source |
|---|---:|---:|---|
| Arphaxad→Reu |129|130| Eber34→35 adds1 |
| Reu→Moses |801|800| Reu32→30 andNahor29→30 net−1; Joseph91→90 and39→40 cancel |
| Total |930|930| Opposite internal residuals cancel |

Thus both130 and800 are generated by a declared operation on the complete source path. Comparing them with Adam’s biography supplies two component equalities; the930 total then follows and should not be counted as a third independent equality. Shem’s death comparison also follows once the path and his biography are held:100+930−600=430, hence1956→1526. The source’s “second Adam” reading remains typological.

## Transfer to the whole post-Flood family

The frozen common begetting amplitude is `u=100`, with Nahor taking `u/2`. Four changed rows occur before Reu, and two full-century changes plus Nahor’s half-century occur from Reu to Moses. Native Cainan adds130 to the first block only.

| Source state | Arphaxad→Reu | Reu→Moses | Whole span |
|---|---:|---:|---:|
| MT native OFF |130|800|930|
| SP native OFF |130+4u=530|800+5u/2=1050|1580|
| LXX native ON |130+4u+130=660|800+5u/2=1050|1710|

This regular-path transfer sees the shared begetting amplitude; the lifespan amplitudes60 and27 are invisible here. Those belong to other projections of the same source packet. Native LXX’s full head5486 and fixed Moses1526 yield3960, retaining the source’s9×440=12×330=11×360 comparison.

File51a supplies SP4411 as the lower transmitted rounded block boundary, yielding2885 to Moses. Rounding the counted Lamech53 to55 reconstructs that head only as the inherited C762 conditional diagnostic. Selecting52 completed years gives the distinct4406 comparison. Neither calculation promotes a new derivation of the transmitted block or replaces it.

## Finite admitted variants, with Moses fixed

| MT state | Adam→Moses | Seth→Moses | Enoch→Moses | Arphaxad→Reu | Reu→Moses |
|---|---:|---:|---:|---:|---:|
| Terah70, Cainan OFF | 2580 | 2450 | 1960 | 130 | 800 |
| Terah70, Cainan restored | 2710 | 2580 | 2090 | 260 | 800 |
| Terah130, Cainan OFF | 2640 | 2510 | 2020 | 130 | 860 |
| Terah130, Cainan restored | 2770 | 2640 | 2150 | 260 | 860 |

These are derived responses on explicitly admitted supports: Terah+60 changes the tail across that hinge; Cainan+130 changes the upstream part containing the insertion. They do not preserve every selected cycle equality. The source packet does not authorize repeated+130 additions, a second native LXX Cainan, or a Gear change.

## Prior work and next bounded questions

The path/rounding rules are inherited from C733–788; the SP branch caution from C761–762; the source amplitude dictionary from C1151–1170. Every named target span already appears in File51a §7A. The useful additional work is to state a minimal conditional constraint basis for this complete family, test exactly which equalities survive the finite admitted states, and explain how row-level residuals preserve930 while changing its partition.

A follow-on rank analysis should first declare whether cycle units, full path coordinates, biographies or row measurements are fixed. The bridge equation, the930 sum, and the Shem430 display have different dependencies. No global uniqueness, statistical rarity, historical transmission order or source intention is established here.

The JSON retains ten questions declared before calculation, all25/26-node source paths, literal-table checks, exact excerpts, source and frozen-packet hashes, finite-state responses, premises, caveats and validation results. These preparation files are frozen after delivery.