C153 — Thirty squares reuse eleven typed diagonal comparisons
23 September 2026 · Bounded step 18 of 20 (C136–C155).
The 30-square count is a recombination count: five SP diagonals are paired with six MT diagonals. Each SP diagonal appears in six squares; each MT diagonal appears in five.
| Diagonal family | Endpoint pairs in paired-base shorthand | Uses per pair |
|---|---|---|
| Cumulative OFF D → reflected SP Noah X | 5284+3709, 5285+3708, 5286+3707, 5287+3706, 5288+3705 | 6 |
| Cumulative ON U → reflected alternate MT Flood M | 6343+2650, 6344+2649, 6345+2648, 6346+2647, 6347+2646, 6348+2645 | 5 |
This yields eleven distinct role-qualified diagonal records in this comparison inventory, all length 17K. It does not establish eleven statistically independent witnesses: their endpoint selections, native field offsets, and underlying equations are related. The existing graph already stores several of the relevant relations; two U endpoints are admitted by field rather than stored graph nodes.
The four exact squares arise where these pairings additionally satisfy δ=0. The remaining pairings reuse the same diagonal lengths with different side residuals. Reflection adds no new independent square count, and repeated computational checks add no source evidence.
No probability of coincidence or claim of statistical significance follows from this inventory alone. Such a claim would require a separately justified selection model and treatment of the shared dependencies. This bounded step records what is being counted so the larger Mirror synthesis does not inflate its evidence.
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; 23 passing assertions in RESULTS.json. The assertion list identifies the actual tests.