[Ryan-Haines]

Independent finite verification; no new kappa. This independently checks the selected #741 backward scalar endpoint on all 728 native plus eight arbitrary private-center columns using modular sparse matrices and an explicit deterministic reconstruction bound.

The endpoint denominator exponent is at most 19. Every scaled integer residual has magnitude at most 1582669748628115714804285440. Two pairwise coprime odd moduli, 4294967297 and 18446744073709551617, have product greater than twice that bound. Both modular matrices equal the desired shear, proving the exact finite identity without rational-matrix replay or a primality assumption.

python3 -I -B research/sw4-crt-endpoint/verify.py

Expected: PASS_SW4_EXACT_MODULAR_ENDPOINT columns=736 moduli=2 controls=7.

Seven adversarial controls include a deliberately incorrect circuit that passes both raw modular replays but fails the recomputed height guard, demonstrating why modular screening alone is insufficient. Other controls cover insufficient/duplicate moduli, endpoint error, a first-modulus-blind error, dirty-center initialization and nondyadic coefficients. Windows Python 3.14 normal/optimized, Linux Python 3.12, Ruff and staged whitespace checks pass.

Only research/sw4-crt-endpoint/ is added. Base 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261; source #741 e516b1463606840a15f80aac1995d64ce0092e89; immutable input payload pins and exact receipt included. No existing constructor or verifier is imported. Seed 80, alternatives and the local claim are recorded; no pinned sprint issue exists. Final overlap scan through #834 found no matching endpoint reconstruction.

Scope is the backward finite scalar projection: frames, physical hosting, child execution, coefficient-work lowering, precision/tape and all-size/analytic obligations remain inherited. This is not a formal multiplication theorem, a new bound, a forward replay or a full cold rebuild. Current selected kappa remains 1661202643272239/1000000000000000000.

Credit Chafik Boukhalfa, Jeremy Kothe and the retained #741 construction/audit lineage; related #668 CRT work concerns cyclic resultants and #777 concerns frame geometry. Prepared by Ryan Haines (@Ryan-Haines) with substantial OpenAI Codex assistance. Apache-2.0; no independent human review claimed.

[Mister-Meeseeks]

100-PR batch review at 333fc042b87da01c8dbac46e9fbe549933242d5c.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Historical SW4 endpoint verification by two-modulus CRT with an explicit height guard; finite endpoint coverage only.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.