C143 — The square residual also controls the Creation-to-Flood 13K span

23 September 2026 · Bounded step 8 of 20 (C136–C155).

The same δ that displaces the square's off-diagonals gives the Creation→ordinary-Flood span 13K−δ. The 6877 family and the equal-diagonal square therefore share a finite algebraic alignment condition.

Keep C133/C134's native alignment b=4421−d and reflected Conquest q=1398+d. With f=2455+j,

b+q=11K,\qquad f-q=2K-\delta,\qquad b+f=13K-\delta.

An exact 13K route through an admitted Conquest is obtained at the same four positions δ=0 as the exact C10 squares. At P6's nearest admitted G3 start, b=4416 and f=2460 give 6876=13K−1. Its q=1403 is sourced; the absent endpoint is the exact f=2461 continuation.

The opening13 case stays separate: b=4421 and f=2456 give a fifth direct sourced 6877 comparison, but its required q=1398 lies outside the held Conquest field. That boundary corresponds to d=0, outside this five-Noah-row product; it cannot be substituted for P6 at d=5.

This unifies exactness conditions, not source events. The square's U/D cumulative roles, regular Noah/Flood roles, and native Creation/Conquest roles remain distinct. Both phase components obey the same formula under the paired convention.

Source and scope control

All numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.

Regular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.

Evidence: CERTIFICATE.json; 109 passing assertions in RESULTS.json. The assertion list identifies the actual tests.