Source explanation of the MT–LXX cumulative 910 translation

Prepared for C1585–C1634. This reuses the already reconstructed source rows (C484–491, C733–746, C1132–C1181); it is an explanatory synthesis, not a new independent dataset, holdout, or endpoint scan. Native LXX Cainan remains ON. SP uses official Terah 145. The source rows are read from File_18, not inferred from the desired endpoints.

1. Exact local contributions

File_18 §§2.2 (lines 1244–1252), 3.2.1 (1600–1608), and 4.2 (1716–1725) supply the literal lifespan rows. File_51a §16.1 (1325–1355) specifies independently rounding each whole lifespan to the nearest 5; §16.2 gives the complete MT propagated dates. Blank Cainan in MT/SP means absent, not a zero-year biography.

Thus the LXX translation at Flood is

It is not 460 + 430 there. Terah contributes zero to the MT–LXX difference. The familiar 430 appears only after passing the Lamech row: rounded LXX 755 versus MT 775 subtracts 20, giving 450−20=430 after Cainan has been leveled, or 910−20=890 with native LXX Cainan retained. File_18 §6D (around 2071) gives the corresponding actual argument: 454−24=430; actual native Flood difference 914 becomes the same 890 at Lamech and Creation.

This is a useful rounding invariant:

Rounding moves four years from the MT–LXX post-Flood difference and simultaneously reduces the magnitude of the Lamech correction by four, so the Creation difference remains 890. No Terah +60 or Sojourn change is required.

2. Where the common translation begins and ends

All following coordinates are rounded cumulative Moses-line boundaries in BC, formed by stacking the selected lifespans backward from 1406; they are not ordinary historical birth dates. Abraham 2431 is File_51a §16.2's shared downstream cumulative boundary. The ancestry supplies the difference profile; it is not a globally imposed +910.

LXX second Cainan begins at 5281 and ends at Shelah 4821, a 460-year lifespan. There is no same-name native MT/SP boundary at that position. The jump from the Shelah difference +425 to Arphaxad +910 is Cainan 460 plus Arphaxad's lifespan increase 25.

MT and LXX have identical Shem 600 and Noah 950, explaining the 910 plateau through those two biographies. It stops at Lamech's birth because his rounded lifespan differs by −20; thereafter their remaining Adam–Methuselah lifespans match, so +890 carries unbroken to Creation. SP's −120 plateau likewise persists through Shem and Noah, then acquires the independent pre-Flood lifespan changes at Lamech, Methuselah, and Jared. SP's accepted five-year Fall shift is a separate endpoint choice and contributes nothing to its Flood −120.

3. Why the result belongs in the inverse-spine explanation

The source-generated lower legs are MT 3430, LXX 4340, SP 3310. Under the selected one-step decimal reversal they become 3430, 4340, 1330. MT and LXX retain the source difference 910 because each lower leg is self-reversing. SP moves by −1980. Therefore the source difference 120 between MT and SP becomes the inverse difference 120+1980=2100. The second relation is generated by the first inverse operation, not imposed by the target 536.

Completed from 6 BC with the shared inverse first leg 4100, the cumulative inverse Flood boundaries are:

Hence the MT–LXX source-row anatomy supplies the 13-unit increment in this common restoration grid, and the SP reversal supplies the 30-unit separation below MT. The LXX 7910 is the exact predicted third member of the already selected three-MSS comparison, not a newly searched harmonic endpoint. Whether it merits narrative prominence depends on the larger report; it needs no special theological claim.

The 910 is not preserved under every possible cut: if Conquest-to-Shem is reversed as one leg, MT I(4030)=3040 versus LXX I(4940)=4940 differs by 1900. If Flood and Shem are separate legs, I(3430)+I(600) versus I(4340)+I(600) retains 910. This gives a concrete explanation of why the partition grammar remains necessary even when the source biographies are translated copies. Do not label the whole inverse trees a uniform +910 translation.

4. Scope and source controls

• File_18 §6 defines serial lifespan stacking; §§6A/6D provide cumulative checkpoints and the 430-at-Lamech argument. Source lifespans can be reused from the regular tables because lifespan is the measured row; no regular birth dates are imported into the cumulative recurrence.
• File_18 §4.2 line 1732 explicitly corrects LXX Peleg/Reu/Serug to 339/339/330. Old copied 239/239/230 cells are nonoperative.
• File_18 §6C and clarification note 11 retain SP Terah 145 in cumulative execution.
• File_51a §16.1–16.2 controls rounded whole-lifespan values and the Moses/Aaron distinction. This note uses Moses; it adds no Aaron +5, Shem ±2, or regular Sojourn shift.
• File_09 registers cumulative second Cainan +460 separately from regular +130. File_22's actual 9890 must not be silently relabeled rounded; neither is needed to obtain this 910.
• Existing c1132_c1431/prep/postflood_source_packets.md and model/postflood_rows.json already contain the same literal rows and actual source contributions. Current source rows agree. This synthesis links those results to the new 7000/Flood narrative.
• Companion JSON includes source SHA256 bindings, row-by-row values, and regenerated cumulative boundary coordinates. No source files or sealed records were edited.