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C136 — P6 admits a 1059-sided 17K square

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Study sequence: Finite 17K squares, P6 boundary and one residual (C129–C155) · Mirror & 529

C136 — P6 admits a 1059-sided 17K square

23 September 2026 · Bounded step 1 of 20 (C136–C155).

P6 supports an admitted 1059-sided equal-diagonal 17K square. This is a new comparison of four already sourced nodes, not restoration of its excluded 1058-sided C10 square.

StationPaired coordinateFrozen graph node
cum_LXX_ON_Shem6344t/6343n BCN04_u
cum_LXX_OFF_Flood5285t/5284n BCP6_c
MT_Flood_alternateAD 2650t/2651nN04_v
SP_Noah_birthAD 3709t/3710nP6_s

With rows U=6343, D=5284 (BC) and columns M=2650, X=3709 (reflected AD),

(U+MU+XD+MD+X)=(89931005279348993)=(17K19K+115K−117K). \begin{pmatrix}U+M&U+X\\D+M&D+X\end{pmatrix} =\begin{pmatrix}8993&10052\\7934&8993\end{pmatrix} =\begin{pmatrix}17K&19K+1\\15K-1&17K\end{pmatrix}.

Both side differences are 1059=2K+1. Both diagonals remain exact multiples of 529; the off-diagonal spans have opposite one-year residuals. For example, U→M is 6344+2650−1=6343+2651−1=8993 in the two seasonal components. The source roles are cumulative LXX ON Shem-birth/Noah-death, cumulative LXX OFF Flood, regular alternate MT G3 Flood start, and regular SP G3 companion Noah. Equal lengths do not equate those roles.

The next step asks whether this boundary choice is uniquely determined by the nearest admitted Flood endpoint.

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

Edition and provenance

490d_C136_529_Mirror_Bounded_Step_20260923.md

SHA-256 3a755724286f5b671da707f7af6e78d567b38067082a51d45fd4990c8759e715

C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C136_C155_529_Square_Batch_20260923/C136/490d_C136_529_Mirror_Bounded_Step_20260923.md