# Chronological families: checkpoint C791

Sixty sequential steps are complete. The common model now handles three layers: ordered source rows, mode-specific accumulation, and finite variants with named supports.

The finite regular rule has three binary choices: Sojourn placement215, Terah position60, and Cainan insertion130. Their supports restrict from eight upstream placements to four middle placements and two Abraham placements. Literal Terah and Cainan tables are recovered. The entire aligned SP-with-Cainan/LXX twelve-node birth suffix remains equal in all four matched Sojourn/Terah states.

Equal births do not force equal lives. On that suffix, the local LXX−SP lifespan differences accumulate to574; transferred rounding changes that to570 through two27→25 changes.

Terah supplies the clearest cross-mode distinction: SP textual(70,75), MT/LXX baseline(70,135), and common alternative(130,75) project to different regular/cumulative effects. A lifespan-preserving Terah+60 has zero raw cumulative effect. File51a’s secondary cumulative+60 display block is a separate operation.

Rounding commutes with the admitted multiples-of-five moves on their stated rows and domains. Existing coordinate residuals remain unchanged; an inserted Cainan boundary inherits the downstream residual rather than necessarily having zero.

Next: BJ supplies complete index, deletion, and biological/surface paths for testing the same grammar. Native frames, counted versus completed inputs, source versus generated states, and endpoint roles remain explicit.