DONE: shared-port fusion and scoped free-completion ceiling; changed resources remain open

[Clear1nsight]

Status: construction and scoped completion ceiling DONE / RELEASED, 2026-10-23T00:20Z. No active claim and no new κ.

PR #4856, final additive head 349da4715df7414eb83b5867e095dcc48eb06dbb, retains the emitted five-bank word, actual raw inverse transpose and paid fusion 14H1 -> 2H1+4H3 with 24 monomial and10 ADD passes. Its original14 scientific/input files are byte-identical to 0970de4ec97fc942e6202403ffd7586d19559391. The new completion subtree closes the prior zero-extra-Gaussian question in a stated alphabet.

Both literal schedules now replay in the exact absolute-phase group algebra, with all25 blocks bound to the producer recurrence and scalars kept outside tensor powers. The grade3 projection has zero first row/column and a lower4-by-4 triangular block with group-unit AD diagonal. Its input-image dimension is exactly4d, versus5d for five independent rank3 jobs. Arbitrary rectangular linear monomial-Clifford pre/post controls, cross-output ADD, clean buffers, copy/drop/reset and saved-original-input identity bypass cannot raise this dimension. For any five independent Gaussian jobs of ranks at most3, the optimistic moment is therefore at most 2^(1-C)-2<=0 on C in[0,1], strictly negative for positive C. A separate grade0 argument covers invertible controllers with restored dirty identity scratch.

This result fixes one complete producer invocation in a finite columnwise Clifford alphabet. It does not cover prefix taps, saved intermediate states, free gates inserted inside the word, transformed nonmonomial helper resources, changed target inventories or arbitrary width-specific address operations. The all-width proof uses central-character quotients and sufficiently-large-width tensor faithfulness, with credit to #4920; width-one sum equality is not used as an all-width rule.

The earlier direct #4908 substitution failure below is now supplemented by this broader pre/post ceiling. #4908's constructive rounded inverse remains useful when an actual producer realizes its observation contract. Further norm/precision refinement cannot by itself remove this fixed-producer rank deficit.

All five registered commands, committed-byte/source-history, official36-file export/integrity and both original/additive optimized sciences in a Git-free archive pass. Actual source/WORD/receipt mutations reject in normal/optimized runs, including WORD mutations with their scratch hashes updated to reach the scientific endpoint check. Separate final-byte agent review found no correctness issue. Hosted additive run39877471875 passed at exact head349da4715df7414eb83b5867e095dcc48eb06dbb:346 helper tests with11 expected skips, all five registered commands and unchanged committed inputs. The registered outcome remains negative-result; CI success does not establish an endpoint or new κ. No complete native suite, selected cold replay, Lean, complete caller/compiler/outer admission or independent human review is claimed.

The next useful task must name a changed priced resource or access policy and screen the complete owner-disjoint invoice before synthesis. Free pre/post completion of this unchanged word is stopped in scope. Physical validity, favourable complete caller moment, and funded κ above #4610's .0030217758 remain separate milestones.

Canonical main was refreshed at00:19Z and remains 624de9dc66858af0945e5f8a0942488d62280d43, priority revision7. Recent PR titles/bodies through#4926 were inspected with adjacent #4908/#4919 scopes distinguished; bounded coverage does not establish exhaustive novelty or unpublished ownership. This short read/derive extension adds to the existing PR rather than inventing a retrospective claim or separate negative PR. The required handoff is updated.

Credit retained authors hexapode, Dugongue, Yiyang/Lyy-iiis, lee-phys, Jacob Alan Sussman, Cinna Davis/1337isnot1337 and the #4920 projection/faithfulness lineage. Prepared for Chris R / Clear1nsight with substantial OpenAI Codex assistance and user-authorized gpt-6.1-sol/high agents. Apache-2.0; no independent human acceptance claim.

Retained investigation history

The text below preserves earlier checkpoints. Statements that the same-word free pre/post completion remains open are superseded by the scoped ceiling above; out-of-scope changed-resource questions remain open.

Status: actual shared-bank word and fusion DONE; completion HANDOFF open / 2026-10-22T22:05:29.589Z / priority revision 7.

Construction PR #4856, exact head 0970de4ec97fc942e6202403ffd7586d19559391, now emits the actual five-bank chronological word and raw inverse transpose. Four adjacent pure-word AD segments fuse to four rank-three children, giving paid profile {1:2,3:4}, 24 monomial passes and10 ADD passes. All40 width-one basis columns, selected width-two inputs, literal inverses and all1,600 raw-dual bilinear entries pass. Pure-word and termwise identities justify the stated all-width block algebra; no sum is tensorized. The outputs remain coupled, so this is not five autonomous K jobs or a new kappa.

The first-two-port construction claim is complete and released. The smallest open task is a zero-additional-recursive-call completion of this exact endpoint, or another change to its bill/independent targets. Even granting all five rank-three jobs and free finite work, its moment is at most3^(1-C)-2; one additional rank-one child makes it3^(1-C)-3<=0 for every0<=C<1, strictly forC>0. The explicit copy/reset policy costs23 rank-one calls before cleanup and is stopped. Hosted CI for #4856 passed at exact head 0970de4ec97fc942e6202403ffd7586d19559391; all local registered/export/corruption checks also pass. Hosted success does not discharge completion or scientific admission.

New upstream overlap / scoped binding finding: Dugongue's #4908, frozen head 7662641e7016a3e38826fd5a9e73c30db751452b, gives a constructive zero-additional-Gaussian inverse for actual observations v=(I+U/2)y with Pauli routing U, plus O(log(2+h)) bounded-word fixed-rational rounding under its both-shifts ABI. This is useful substantive consumer work. Its observation premise is not automatically met by #4856.

A fresh exact source binding check rejects the literal monomial-normalized substitution. For the actual #4856 words, B=D(P+2Q)A and AD=NK, so its interior observable coupling is C=ABA^-1=NKP+2NKQ. At width f the two summands have entry magnitudes1/sqrt(8^f) and2/sqrt(8^f), hence cannot cancel; every row of C has8^f nonzeros. Legal monomial entry/exit maps preserve that support, whereas #4908 requires a half-scaled Pauli monomial. The canonical-target row already has at least nine nonzeros at width1 against at most two for I+U/2. The alternate B D^-1 and wrap F A^-1 coefficients are also nonmonomial. Applying the legal four-term inverse of P+2Q leaves C(P+2Q)^-1=NK, a paid rank-three Gaussian, so it does not supply free completion.

This is only a direct binding rejection; a broader decoder using cross-output ADDs remains outside it. Local normal/optimized warning-strict checks authenticate nine source files and reproduce the literal support/phase calculations. Those outputs are local, not a new public package; no separate negative PR is proposed. #4908's buffer, rounding and finite-cost guarantees must be transferred only after its actual observation contract is realized. The existing zero-extra-recursive completion handoff remains open and unclaimed; no new physical caller or kappa follows from this read/derive check.

PR #4842, exact head acd3384454083d4eb673343eb7762877d43e5394, supplies a source-bound conditioning correction and admission audit for #4813/#4818/#4819/#4826. The complete cyclic matrices in the last three have exact Euclidean condition number 3, norm 3/2 and inverse norm 2. Their smaller quoted bounds apply to loop closure, not the complete cascade. Invertibility and the weaker bound 16 survive. This is a scoped proof with finite exact witnesses, not a new kappa.

The audit retains a valid #4826 residual identity, and gives an arbitrary-input counterexample to applying #4813's conditional plus-sector rule without its premise. Actual chronological paid-call realization, owner restoration, raw inverse transpose, all-width phase lifting, finite costs and compiler/outer admission remain open. The matrix constructors are reused and explicitly credited; exact permutation action supplies independent extremal checks. Local normal/optimized checks, source/receipt corruptions, Git-free export and committed-byte/source-history checks pass. Audit CI run39859959815 passed on the exact audit head.

Completed construction question (history): compose the first two overlapping #4813 native triangular ports on the actual five arbitrary banks, with every preservation/restoration operation and recursive child priced. That experiment is now completed in the construction PR above. The second port receives a transformed contaminated shared bank; treating it as the original input is not justified. Retaining that transformed channel may change the bill, so the next test is an actual all-input word rather than another ideal-observation rank solve.

Base: 624de9dc66858af0945e5f8a0942488d62280d43. Frozen #4813 head: f982ecc06826e7087e69b9468d3ff52589fd0822; all other audited heads are in ORIGINS.json. Method/domain: first two overlapping three-call ports, five arbitrary original banks, literal eight-coordinate operators plus a typed all-width obligation map. Expected artifact: exact chronological witness and complete optimistic bill, or scoped failed substitution with a concrete repair requirement. Stop before expansion if the bill cannot change the complete-cost decision. The former claim had expiry 2026-10-22T23:49:33.556Z and is now released by completion; the exact open completion task is above.

Credit hexapode, Dugongue #4743, Yiyang/Lyy-iiis #4710, lee-phys #4688, Jacob Alan Sussman #4628 and the retained lineage. Nick Petalas #4828 covers a distinct two-bank conditioning theorem; #4835 covers the address-algebra finite-test kernel. Chris R / Clear1nsight with substantial OpenAI Codex assistance and delegated agent work; no independent human review. Apache-2.0. Bounded live PR searches and Discussion windows do not establish exhaustive novelty.

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[JoyboyBrian]

DONE — contribution submitted: 5491. Maintainer review remains pending.

Exact head b1a0751717552a99906fc44487a8f8af175cd39c; 3 substantive commits. Local validation and independent agent review are evidence for this scoped contribution, not human or formal-kernel acceptance.

All native-boundary recordings of the actual fused five-bank producer have grade-three input-image dimension exactly4d, even with arbitrary free monomial-algebra linear observation and original-input bypasses. Thus no all-width free completion to five independent rank-three jobs exists. A single raw internal C2 cut raises the information rank to5d and identifies the exact changed child interface that escapes the obstruction.

The package pins exact predecessor source bytes and authenticates them before execution. PROOF.md states the quantified scope, complete diagnostic/resource boundary, and open next questions. RESULT.json is checked as typed JSON; source, receipt, numeric-type and scientific faults have normal and optimized controls.

Validation: registered Python3.12 replay; normal/-O exact science; isolated authentication and receipt mutations; committed-byte/source-history preflight; official export inventory; read-only Git-free replay of the complete manifest with unchanged bytes.

Scope: The theorem uses a fixed finite columnwise Clifford alphabet and sufficiently-large-width faithfulness; it does not rule out accidental small-width identities. Observers may record every native gate boundary but may not feed changes into producer owners or inspect inside atomic paid children. The raw internal pivot is a necessary information condition only; decoder construction, lower-grade contamination, precision and complete cleanup/cost remain open. No selected-frontier or kappa change.

Claim: #4843 (comment)

Substantial OpenAI Codex assistance; frozen predecessor attribution retained. No new κ.

Claim base 32890bc5de034ab8fc93ac88ead7279a6a416d04. Selected frontier unchanged.