# Chronological families: checkpoint after C891

Sixty actions are complete in the current cycle.

The common model now explains complete list paths, File_52c paired inversions, the NT display and finite Key domains. Each comparison retains the information its operation needs: category, order, digit register, grid, anchor and source role.

The operator result is precise. A reduced p/q Key preserves hZ on hqZ. A staged word preserves it on h times the least common multiple of its reduced prefix denominators. Consequently equal final scalar products can have different admissible intermediate grids. Different held anchors create a separate constant placement displacement.

Whole-field tests matter: File46's outer920→1000 completion does not make all interior heads integral, and no common anchor can repair that. The five-row quarter-carrier family follows one divisor rule per Key. The authorized File51a civil-count chains satisfy the stagewise criterion; neighboring Rounded widths do not replace their inputs.

C850–858 and C859–870 passed independent source-based review. No second inversion, new probability tally, canonical edit or scope extension has been introduced.

Next: the complete six-pair twelvefold carrier lift, its endpoint-response field and the retained147-year terminal biography; then integrate the mechanisms into a reader-facing explanation.