PR4268 half-cut heads in the literal eight-stream operator

[ToikY]

DONE / RELEASED — current status, 2026-10-21 UTC, priority7.

PR #4342, exact head ace842de022dfd4365d611b3dec4c4f2e5ea9359, binds the unchanged T74 fill to the identity-cover eight-stream model: 16,086 structural first-touch heads; four fixtures pass every dirty input column; a wrong non-head cut fails at 2^25. Separate dense arithmetic agrees on all344 tested matrices; source extraction is shared. Both public cold commands and hosted run39590422972 pass. Full evidence, limits and credit.

This claim and hubclaim19095089 are released; no follow-up claim is active. Nonidentity covers, native realization, inherited geometry, physical costs and mixed outer admission remain open. No new supplier/kappa or human/kernel acceptance. Maintainer edits disabled; PR unmerged, selected frontier unchanged.

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Original public claim (released; retained for history):

CLAIM / 2026-10-21 10:48 UTC / priority7 — independently bind PR4268 Open question2 (the half-cut on PR2979's published T74 fill) to the actual eight-stream Gaussian-integer operator. No new artifact yet; LOCAL-ONLY, claim expires12:48UTC.

Base12fa8c5c844be21bfefb38a19503fbd867a11244; proposal45323d210ebf6f4b201b1d2a27729d14d059f2e2; PR2979 be19134; operator predecessorPR3187 85cc6be. Take the named replay handoff, scope changed from complex-new-helper-inventory to this acceptance audit. Latest PR4268 comments report A-fc Lean progress; that older open question is excluded.

Plan: authenticate the unchanged actual fill/order/dispatch/plan/template and geometry; reconstruct literal chronological operations, retained hosted-helper phases and all8 dirty input columns; sample certified child8/10 heads across replica classes; delete24 actual unhosted axes. Compare against the original operator composed on the INPUT side with exactly that omitted head's inverse phase. Empty cut is a positive control; a wrong non-head cut must fail. A precise counterexample or missing binding is a valid stopping outcome. Finite identity-cover character tests do not claim all-cover/native/supplier/outer acceptance.

Family decision NARROW: the source reports a favorable changed-recursion budget, but its own package leaves this operator binding open. The check can decide whether its cut enters the physical caller model. The mixed-recursion outer interface, all-cover geometry, physical precision/stock and complete supplier remain unproved here. No pricing-only optimization, Lean build or full admission suite. Science stops by11:31UTC, preserving final15minutes for verification/handoff; useful earlier findings can end the session. No merge/frontier change.

Overlap: refreshed444 open/draft PR bodies, current main/guidance and active Discussions plus focused4268 Discussion search and predecessor comments; coverage outside those surfaces partial, no novelty inferred. Credit Jacob Sussman's lever/head test, Marius-Paul Dumitrean's2979 allocation, Nick Petalas's3187 eight-stream semantics, and all retained native/owner/geometry lineage. New work by ToikY with substantial OpenAI Codex assistance and separate AI contexts.

[ToikY]

DONE / RELEASED — PR4268 half-cut eight-stream binding. PR #4342, exact head ace842de022dfd4365d611b3dec4c4f2e5ea9359, adds only research/mixed-cut-eight-stream-binding/. Claim4337 and hub claim 19095089 are released. Maintainer edits disabled; no merge, selected-frontier change or new kappa. Canonical main 12fa8c5, priority 7 unchanged.

Actual unchanged PR2979 T74 source binding: 271,728 fill rows, 666 call positions, 74 replicas and 112 port recipes. The actual first-touch classification finds 8,064 child-8 heads and 8,022 child-10 heads, split 4,032/4,011 in each replica class. The 12,104 other rank-48 blocks are non-heads. PLAN.T=37 is historical metadata; the literal74-replica ORDER is used. The unrelated PR3148/T740 loader is never called.

Four named fixtures (owner 0/37, port 0, child 8/10) pass 79 characters each, with all 8 arbitrary dirty input columns and all 29 hosted occurrences, 26 from foreign callers. Removing 24 actual residual axes implements the required INPUT-side inverse-phase correction. The wrong non-head cut (owner 0, port 0, child 12) fails at chi=2^25, leaking 1-i from Y0 to Y1 where the required map is zero; complete axes/events/matrices retained. The written first-touch lemma gives the all-character implication only under its actual structural and completed-invocation premises. Four matrix fixtures do not establish symmetry or enumerate 2^73 characters.

Separate dense Gaussian-integer matrix multiplication agrees on all 344 complete matrices / 22,016 entries,113 active phase cases, including the rejecting control. Source event extraction is explicitly shared and separately reviewed, not independently reconstructed twice. Wrong-side/read-guard/XOR controls are separate embedded examples; the literal identity-cover baseline is scalar, so its samples cannot distinguish correction side alone.

Verification: both registered normal and optimized Python 3.12 commands explicitly use -I -W error -B; fresh complete typed generated data and meaningful corruptions are checked. Exact public Git-free export passes both commands with 33 files unchanged, 19 declared inputs; historical source pins/ancestry and public bytes authenticate. The initial clean-export failure was a real runtime/provenance packaging mismatch; its frozen commits and complete failed export remain preserved. The corrected public head is the result reviewed here. Hosted run 39590422972 succeeds: both complete verifier payloads match the public cold export, one registered marker, inputs unchanged, helper suite reports 312 tests / 11 skipped. Tested checkout a6f6c83 has exactly public tree 0b0d0275c56f064efd58e04a28e24432b1c29566; this is GitHub's temporary PR test checkout, not a merge action.

Reproduce: python3.12 -B scripts/research_package.py --package research/mixed-cut-eight-stream-binding. Standard library only. Final freeze 11:11:19.666862UTC; the verification/handoff window runs through at least 11:26:19.666862UTC.

Remaining / smallest useful next task: bind one explicit nonidentity cover or actual native invocation, including its producer/consumer and complete invoice; or state the outer theorem's exact mixed-job supplier hypotheses. Native internals, source Gram geometry/49-axis-job interpretation, finite precision, routing, restoration, stock and mixed-recursion outer admission are inherited or UNKNOWN as detailed in README. No complete physical supplier, multiplication theorem, human or proof-kernel acceptance is claimed. Stop construction without a named missing boundary and full budget. The latest PR4268 comments report external A-fc Lean work; the stale Lean question is excluded.

Credit Jacob Sussman's PR4268 lever/replay request, Marius-Paul Dumitrean's PR2979 word/allocation, Nick Petalas's PR3187 exact algebra, Gareth Davidson/1387 and Rohan Arun, and all unchanged E8/native/owner notices and credits. New binding, structural application, dense arithmetic and integration by ToikY with substantial OpenAI Codex assistance and separate AI contexts. This is an independently reviewable scoped result, not maintainer or independent human acceptance. Fresh 444 open/draft bodies plus 100 updated records and live Discussion/source surfaces checked; broader coverage partial, no novelty inferred. Previous-batch PRs excluded; B5 result 3 of 5.