C151 — The one-year source residual is not a phase-counting artifact

23 September 2026 · Bounded step 16 of 20 (C136–C155).

P6's δ=1 survives both same-season counts. It comes from the chosen source endpoints, not from forgetting the no-year-zero adjustment.

The correct civil formulas are (b+1)+a−1 and b+(a+1)−1, both b+a. Subtracting one again from the paired-base sum would lower every square entry by one, including both diagonals. That wrong matrix would have 17K−1 diagonals; it cannot explain the actual opposite residuals with exact 17K diagonals.

Under the retained quarter-offset coordinate model, cross-season comparisons instead give b+a±½. They compare different seasonal components and cannot silently replace the same-season spans. The evidence lists these diagnostics separately.

This check addresses a specific ambiguity: an admitted pair AD 2650t/2651n does not admit the different pair AD 2651t/2652n needed for P6's exact square. The numeral 2651 appearing as a lower seasonal component is not permission to use it as a new paired base. The source residual and the phase convention therefore remain separate.

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