C145 — One alignment condition links the 10K, 13K and 17K constructions

23 September 2026 · Bounded step 10 of 20 (C136–C155).

An exact named Flood midpoint in the Noah construction is equivalent, within this finite source product, to the exact 13K Creation prefix and the exact 529 square. These are three consequences of δ=0, not three independent constraints.

For the all-BC comparison A→X→M→Z, with A=5291+d and Z=1+d,

10K=3K+(2K+\delta)+(5K-\delta), \qquad 10K=(5K+\delta)+(5K-\delta).

The ordinary 3+7 Noah partition holds throughout: A−X=3K and X−Z=7K. The inserted alternate MT Flood gives exact 3+2+5 and 5+5 only when δ=0. Z is the retained Christ-period comparison landing, not a new historical birth claim.

For P6 with the actual G3 Flood start M=2650, the source route is 5296→3709→2650→6 in paired BC bases. Its lengths are 1587+1059+2644, or 3K+(2K+1)+(5K−1). The two halves are 2646 and 2644. The exact midpoint 2651 remains outside the held alternate MT field.

This result supplies the sought connection between the 529 constructions while preserving source identity. Equal algebraic conditions do not imply that the original events or constructions have identical provenance.

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; 108 passing assertions in RESULTS.json. The assertion list identifies the actual tests.