Research/r439 block522 seed17 112112

[CubeJerry]

PR589's selected R439 phase-B block at frame 522 uses 43 ADDs. This replaces the complete B[361:404] block with a 33-ADD circuit computing the identical integer map on the same twelve registers. Rebuilding literal reverse cleanup reduces the full local word from 24,305 to 24,285 ADDs.

Finite bit-supplier construction; no new kappa. All 661 register frame paths, 439 helpers, nine copies and paid rank mass 5,129 are preserved. The forward positive bound remains 49,347; the reverse bound falls from 1,113,070 to 1,045,786. Payload remains 93 bits, within the unchanged 104-bit cap. The reverse block map is not entrywise dominated, so the full-stream bound is recomputed rather than inferred from a local heuristic.

Reproduce from the repository root:

python3 -I -B research/r439-block522-factor/verify.py
python3 -I -B research/r439-block522-factor/test_package.py
python3 -I -B research/r439-block522-factor/native.py

The first two use only Python's standard library; the native replay needs C++17 and Boost (BOOST_INCLUDE is supported). Expected markers are PASS_R439_BLOCK522_FACTOR, PASS_R439_BLOCK522_PACKAGE, and PASS_R439_BLOCK522_NATIVE.

Completed verification covers twelve exact integer columns, 4,096 Boolean block inputs, 661 arbitrary dirty-input columns, the original H1–H5 interface, eleven mathematical/record controls and six package controls. Fresh unchanged C++ legality and 5/9/11-stage checks pass for both words on 883 / 1,327 / 1,549 columns, with 96 omitted-bridge controls rejected. The five-stage/general-checker regression agrees. Optimized Python, minimal-source relocation, deterministic search regeneration, committed native receipts and selected-record integrity pass.

OS seed 17, bit-supplier track. Exactly 12,000 nonnegative row-subtraction trajectories completed; 492 reached identity and seven produced 33-ADD circuits. No optimality claim. PR891's single-write exclusion for frame 522 does not cover this circuit's repeated writes and intermediate donors.

The final overlap refresh includes PR904: its certificate selects one four-register interval within frame 522, saving one B ADD. This contribution removes ten from the whole twelve-register block. PR904's broader 254-ADD package has not been combined with this result; no additive combined saving is claimed. Its certificate is unchanged between inspected heads 33b9175c345bcd0f21b95d29f37cb95fffd5a134 and 883a0bdf7792693e57c16be660824b57aacfbe05.

Base f567884aeb8851b6e794af1184119a3bfbe1e631; bit supplier PR589 head a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46. Only research/r439-block522-factor/ is added, with exact input pins, candidate, receipts, proof, claim, validation and attribution. No pinned sprint coordination issue existed, so the claim is local.

Credit eumemic, DreamingOfClouds, Dylan Crow, DaysSky and retained predecessors; related factorization work in PR857/873/880/884/891 and Gareth Davidson's concurrent PR904 is credited. Prepared by Jerry Chen (@CubeJerry) with substantial OpenAI Codex assistance; Apache-2.0. No subagents or independent human review.

No hosted supplier rebuild, outer assembly, remote CI or full theorem formalization is claimed. Inherited realization/compiler, hosting, precision/tape, exact-recovery and analytic obligations remain. The selected frontier and upstream/ are unchanged.