Finite bit construction: compose four R439 blocks, saving 72 ADDs (no new kappa)

[woklerx]

Change and mathematical scope

The individually reviewed R439 phase-B schedules from #880, #873, #908 and #914 were not previously composed by the maintainer review. This finite construction combines their frame 507/508/519/524 replacements on the pinned PR589 word and rebuilds literal cleanup, reducing the complete local word from 24,305 to 24,233 ADDs. All paid ranks, frame paths and nine COPY/ERASE pairs are unchanged; the reverse positive bound falls from 1,113,070 to 942,262. No new kappa or global optimum is claimed.

The new contribution is independently checked composition and complete accounting: all 16 subsets, all 32 subset-cover relations, 11,264 local Boolean inputs, 447 combined B columns, and every one of the 661 dirty-input columns in each complete word. Source pins and exact receipts are in research/r439-four-block-composition/.

Validation

Validation completed: nine mathematical mutation controls; five isolated-package tests including all 13 consumed-source corruptions and four rehashed bad circuits; unchanged native legality and 5/9/11-stage replay of both words (883/1327/1549 formal columns, 96 rejected bridge controls); selected-record integrity and staged whitespace checks. Native verification ran locally with MSVC 19.51.36260 and Boost 1.88.0; hosted Linux CI is not claimed. The readable reproduction command is:

python -I -B research/r439-four-block-composition/verify.py

Expected: PASS_R439_FOUR_BLOCK_COMPOSITION subsets=16 cover_edges=32 adds=24305->24233 columns=661 controls=9.

Exact base: 407d52ff15b2217b6e22bce44728b4c3907b6515; OS assignment seed 1, bit-supplier track. The selected PR942 conditional kappa remains 0.001661960547713947. The refreshed main through 55645f9d4d806d67875c1c8b9840b0b039ece22e leaves all consumed sources unchanged. Nearby #973 changes frame509 and #980 changes phase A; their implementations/savings are not composed here. This is not presented as the smallest known R439 circuit. Full hosted invoice, supplier adoption and outer assembly remain open, along with inherited all-size/compiler, realization, hosting, precision/tape/recovery and analytic assumptions.

Credit: Krishnendu Purohit / Deftsalt-debug (#880), Aaron Wang / navinor (#873), Ross Richardson (#908/#914), DreamingOfClouds (#589/#545), eumemic (#555/#543), and the retained exporter/native-checker lineage. Prepared for @woklerx with substantial OpenAI Codex assistance, including separate AI block-replay and package-review workers. Apache-2.0; no independent human peer review or full multiplication-theorem formalization is implied.