# C141 — A finite 5×6 family of equal-diagonal comparisons

23 September 2026 · Bounded step 6 of 20 (C136–C155).

**The five retained Noah rows and six retained MT Flood selectors give 30 source-qualified 17K comparison squares.** This is a finite recombination of established endpoint fields, not a repeat of C10's broader candidate campaign.

For Noah-row index d=1,…,5 and Flood-selector index j=0,…,5, use

\[
D=5289-d,\quad X=3704+d,\quad M=2645+j,\quad U=6348-j.
\]

Then D+X=U+M=8993=17K. The shared side width is X−M=U−D=1058+δ with δ=d+1−j.

| Noah row | d | D (BC) | X (reflected AD) | δ at j=0…5 |
|---|---|---|---|---|
| N01 | 1 | 5288 | 3705 | 2, 1, 0, -1, -2, -3 |
| N02 | 2 | 5287 | 3706 | 3, 2, 1, 0, -1, -2 |
| N03 | 3 | 5286 | 3707 | 4, 3, 2, 1, 0, -1 |
| N04 | 4 | 5285 | 3708 | 5, 4, 3, 2, 1, 0 |
| P6 | 5 | 5284 | 3709 | 6, 5, 4, 3, 2, 1 |

Every square uses admitted source-field endpoints. Where U=6347 or 6348, field admission is recorded without claiming an existing graph node. The 30 count measures possible pairings of two finite sets. It neither enlarges the historical graph nor counts 30 independent 17K attestations. C142 identifies which pairings recover the exact 529-grid square.

## 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`; **88 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.