Chronological families: checkpoint C751

The complete regular–cumulative gap is generated by local lifespan minus effective begetting rows, with an explicitly chosen terminal. Adjacent differences recover each generator, so an ordered field contains information that its total loses.

The MT/LXX/SP fields here use native Cainan states in a common full430 regular comparison frame. Their lower-envelope Adam gaps are9890,9400,8982. These are not three unqualified native regular frames: using the SP215 head4199 gives9197 instead.

Restoring the admitted regular Cainan130 row to SP reproduces the twelve LXX birth boundaries from Noah through Abraham in this common frame. Their death and cumulative profiles still differ according to local lifespans. The shared birth sequence is therefore a positive family correspondence with a precise domain.

Rounding has separate birth, theoretical-lifespan, and cumulative-lifespan operations. Both Methuselah and Reu have rounded parts five below rounded total in the literal MT tables. Preserve those values and qualify the source’s unbounded Methuselah uniqueness sentence.

Next: derive the finite rounding law and transfer the complete residual field across traditions. File52c remains primary; no second decimal inversion or new Gear transport is introduced.