[JoyboyBrian]

The CRT key port in #4982 returns correctly encoded records, but its next radix consumer still ran through outer symbol decoding. This executes that actual consumer as a fixed three-tape binary program, including stable partition/merge, key rotation, bucket cleanup, head return and finite-control initialization/erasure.

For every finite valid stream of n opaque 12-bit payloads and nonempty keys of total length K, the written source-control proof gives the complete per-pass bound

7740 * (8*n + 12*K + 10) + 144 literal bit/control actions.

For equal key width L, L invocations stably sort the keys and restore their orientation. The finite program has 180 source instructions, 3885 binary instructions and 72 control bits. It reuses the unchanged #4982 thirteen-bit compiler/machine; no host key, stream length or address is supplied to the executor.

Entry requires aligned valid predecessor codewords, uniquely framed LEFT/END and clean owned buckets. Record/key grammar failures inside that boundary reject before output; duplicated/missing framing, unused codewords, dirty buckets and misaligned heads are outside the entry contract. The exact loop proof, boundary/ownership argument and complete obligation ledger are in research/crt-binary-radix-consumer/PROOF.md.

Validation (Python 3.12, standard library):

python3.12 -B scripts/research_package.py --package research/crt-binary-radix-consumer --check-only
python3.12 -B scripts/research_package.py --package research/crt-binary-radix-consumer
python3 -B scripts/check_research_commit.py --package research/crt-binary-radix-consumer --check-source-history

• Normal and optimized registered replay pass. All 371 complete bounded small stream cases agree with both the literal original bridge.one_pass and an independent stable-partition/rotation oracle. Three source-instruction-boundary simulations check every physical head, register result, written codeword and the exact backward-transfer count.
• Full sorting through three and 37 passes, variable positive key lengths for one pass, payload boundary values, eight uniquely framed grammar rejections and five behavior faults cover ordering, key rotation, physical strides, bucket erasure and finite-control lifecycle.
• The original source bridge.split, two complete binary key calls and continuation to the third hole feed the new consumer on the same physical tape objects. The consumer uses 37,969 actions and returns expected payloads/key rotations and clean state. The captured prefix is explicitly closed with END by verifier setup; no complete layer is claimed.
• Committed-byte/source-history, standard export integrity, read-only Git-free ordinary/optimized replay and source-corruption/typed-receipt corruption controls pass. These are replay/representation checks, not human or formal-kernel acceptance.

Canonical claim: #4709 (comment) . Card uniform-transfer-audit, refined to #4982 Open next question 1; base bee95ce88f9f19802f0613f92838895cd0e14a1f, priority revision 7. All thirteen live source inputs are pinned. Initial overlap covered 6690 local notes, 310 open PR bodies and 4096 Discussion records with complete inventory/pagination; targeted one_pass/binary matches were the predecessor and its canonical result. Search coverage does not exclude arbitrary diffs or unpublished work. #4990's paid two-target stencil is a complementary producer boundary.

Family decision: narrow to this actual consumer and stop. Full binary split/reinsert, uniform CRT key geometry, physical descriptor/ROM production, initial serialization, compiler creation cost and a common full CRT E(p,ell) invoice remain open. No full 2944-hole layer, historical suite, Lean/Docker or selected supplier replay; no new kappa or selected-frontier change. README.md and TASK.json give bounded next questions rather than authorizing an automatic implementation expansion.

Credit the unchanged #4982/#4795/#4752 key/binary lineage and original #4637 repair consumer: Cinna Davis, ToikY, Hiroki KUMAZAKI, Ryanson Jonathan, unpaidmoon, Jose Manuel, and the Douglas Colkitt/John-Michael Smith #763 lineage. Frozen predecessors and their source-specific notice remain unchanged. Prepared by JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0. A separate read-only agent reviewed the source assembly, uniform control bill and scope; no independent human or formal proof-kernel acceptance is claimed.

Submission refresh (2026-10-23 06:22–06:24 UTC): canonical main f259dabc7d70e0db8d6d36bfda888f008bbfecc1 was fetched; governing guidance, selected record and every declared scientific input for this package are unchanged. The scientific base remains bee95ce88f9f19802f0613f92838895cd0e14a1f intentionally; all new package paths are disjoint from upstream changes. Refreshed overlap paginated 304 open PRs and 4,114 discussion records; local coverage is all 6,690 notes at the pinned scientific base. Cached coverage is not a novelty certificate.

Supplemental AI peer review is local-only evidence; the committed written proof, source bindings and registered verifiers are the public reproduction artifacts. Peer-only observations do not constitute independent human or scientific acceptance.

Hosted CI triage (2026-10-23 06:50 UTC): the exact-head first attempt was cancelled because the planning job exceeded its ten-minute execution limit. Checkout consumed approximately nine minutes, then onboarding tests were interrupted before package selection; the package replay was skipped. The PR remains open at df8643a180652d08c970cfffa3d60010380bbc11, and no replacement run/attempt existed when checked. One routine rerun request from JoyboyBrian was denied by GitHub repository permissions; no second attempt started. Hosted CI remains incomplete and requires a maintainer to rerun; the local verification results above are separate evidence.

[jwr404]

Independent check at head df8643a1, on Linux with CPython 3.12.14.

Bound arithmetic. 7740 = 43 × 180 is #4982's 43-action block times the 180 source instructions. 144 = 2 × 72 covers initializing and erasing the control bits. The source-step bound T ≤ 180·(B+1) gives 43·180·(8n+12K+10) + 144, as stated.

Random streams. The package's fixtures are fixed, so I added random inputs and drove the package's own run() harness. Each run executes the literal binary program and checks the endpoint against the oracle, the original symbolic one_pass, bucket erasure, head return, control erasure and the proved action envelope.

• 30 single passes: 0–13 records, mixed key lengths 1–4, and a forced duplicate record whenever n > 3, to stress stability.
• 12 full L-pass runs: equal-width keys with L = 1…4. In each I also checked with my own oracle that L right-rotating stable passes by last bit equal Python's stable sort by full key, which is the LSD radix-sort identity the README relies on.

All 42 runs accept and pass every check, in 0.9 s total.

I did not re-derive the loop invariant or the rejection-boundary proof, and I did not test inputs outside the stated entry contract (duplicate framing, unused codewords, dirty buckets). This is an author-independent check, not acceptance, and κ is unchanged.

Reviewed by James Reed with substantial Anthropic Claude (Claude Code) assistance.