Two FULL native calls with monomial-conjugate central functions — bounded feasibility

[Clear1nsight]

Status / UTC update / priority revision: DONE, published scoped ceiling and verification,2026-10-23T05:14Z,revision7. No new κ.

Concrete question and changed premise: ONE actual #4948 mixed-p2 word with nine passive boundary cuts and its three already-paid query responses.

Established result and evidence status: independent source/trace/grade review passes. For104 original source ports, all5408 late words have grade7; earlier grades0/1 cannot provide the required grade9 target under the declared finite-code grammar for all widths. Failure holds for sufficiently large width, not necessarily every small width. Author, independent, normal/optimized, source-history and Git-free read-only export checks pass; hosted CI passed at the exact head: hosted run39904239128;362 helpers/11 expected skips, both registered modes and integrity gate passed.

Public artifact URL + exact commit: PR #4978,db3f8456a3efb425e337337d85dcc43b797888cd; seven-part handoff. Official export SHA-256 26e547064affa51236aa52bd640de0d9c592ff242c5b457919cc4c252849eaeb. Prior physical raw dual #4943 and ordinary API support #4957 remain separate DONE contributions.

Next useful task, success/stop test and rough runtime: passive search stopped. Consult current ownership before testing one changed active paid input or native internal observation that supplies the missing original-input coefficient while preserving every owner and a favorable complete invoice. First derive one exact endpoint/cost gate; no broad census or physical expansion follows automatically. Published normal/optimized replay took7.012s combined; allow a minute.

Active claim / expiry, or released: completed passive experiment and portable publication reservation released. No active-feedback, native-prefix or new caller follow-up is reserved here.

Reviewed result and limits

The exact39-observation dependency trace has no D3 or later paid-query path for original input bank0. Its observed pure words have grades0/1/7 at104 unselected ports, while the Gaussian target has grade9. Left scalar/monomial finite-code expansion preserves support grades. The fixed17-axis projective Clifford universe is finite; tensor-power Gram separation is uniform at sufficiently large width, even for width-dependent scalar/control choices. This rejects an identity required at every positive width. All4368 dependent snapshots and their permitted owned reset/storage/precision bills can be granted free without changing the obstruction; no universal uncomputation or cleanup lower bound is used.

Author six-file manifest a7d684b92f2bc54ac2a201dcabdc52c549dba8089a1141bb54167806a92d6deb, plus separate uniform-alphabet and owned-reset clarifications. Independent review004a1e8d0fbb17f2ce3b6ca5cab4504a0b0432c9b22a0cc14659b328a5a4442d binds the trace, all5408 literal grades and the sufficiently-large-width argument. Source helpers remain816 original jobs counted once. No complete caller moment, compiler transfer or κ is admitted.

Completed prospective scope: stored paid responses (history)

The actual source is the most advanced dyadic typed caller #4948, following #4933 and #4935. The retained formal reverse-controller comparison is #4940. Canonical main was refreshed to b919568; guidance, priorities and selected record are unchanged from cef4. The source heads remain independently pinned.

This test changes the accessible-information premise. It retains owned copies of already-paid query responses and main X/Y states at macro boundaries. It does not buy another Gaussian query, tap a new native internal prefix, change the FULL paid profile, vary placements, or grant arbitrary Gaussian address operations. Use the ONE mixed chronology with stage0 L(C1 Q^-1), stage2 L(Q^-1 C1), stage4 L(Q^-1 C3), its actual two reverse FULLs, retained IDLE, bridges, signed swaps and standard boundaries.

First test finite recoveries from at most nine chronology boundaries and three query-response cuts. Allowed new left controls are scalar owner operations and the physically explicit finite codes C1/C3 and their words of length at most three, with each monomial/scalar program charged. Q itself is not a free control. A failed span test excludes only this declared observation/control model. A successful symbolic relation must then bind the actual source monomials, all-width operator identity, all four independent Gaussian main jobs and all816 original helper jobs once. Copied inputs, stored observations and code temporaries add no productive reward. COPY, ADD, owned reset, storage, movement and precision remain finite bills; no original input may be discarded.

The bounded04:15UTC all-author PR/4948/4933/4940-comment/4930/handoff check found no precise public competing owner. This is not exhaustive novelty or a statement about unpublished work. No emitter, large search, full compiler or new κ follows automatically from a positive cut identity. Construction, complete caller moment and funded compiler/outer improvement remain separate gates.

Completed adjacent gates and what must change

The fixed C1/C1/C3 post-query p2 policy with standard scalar boundaries fails: its first negative row has the cross-owner term (C1 D1-D1 C1)Q^-1 h'. Actual source (F^T)01=-1/2 and T=K0^-1 K1 give a nonzero block -1/2(TD1-D1T)Q^-1. Independent exact phase evaluation yields (TD1)|0> coordinate1=-i/16 versus (D1T)=0; the two-pure-word tensor argument preserves this at every positive width. This does not exclude different thin order or stored paid responses.

The common-full-Gaussian upgrade has a valid code-removal identity after appending charged Q to both FULL main outputs, but its full owner/rank census loses. Odd numbers m of upgraded stages give rank8m instead of8m+1 because the central axis is shared. Added recursive H1 counts are5600 for p16 and6496 for p19. Exact outward whole-interval margin upper bounds on C in [.0030217758,.0034] are respectively below -5920.12 and -7619.17, even before new finite costs. These are author-checked source-bound prices, replayed by root, for that explicit construction; they are not minimum native conversion costs.

The mixed placement eliminates the previous cross-owner terms except (C3C1-I)D1D3 and still needs two negative-bank Q^-1 C_s Q decoders. A rank-eight scalar factor alone does not create eight homogeneous physical queries. Its natural same-aggregate shortcut has distinct native query frames across its independent input support. #4958 supplies a useful invariant scalar-cache theorem and matching R/query-label provenance; its decorated-update grammar must be bound before applying a numerical cache count. Stored paid-query cuts change that grammar and motivate this one new test.

Credit Dugongue #4929/#4935/#4948, dillona #4933, SethBurkart123 #4940, aliromman #4958, Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv and all retained native/Clifford/compiler/outer contributors. Chris R/Clear1nsight with substantial OpenAI Codex assistance from separate construction, verification and monitoring agents. Ordinary API support is separately DONE in #4957; it does not close this complex bottleneck.

Released claim and source history (historical status text below)

Status / UTC update / priority revision: DONE physical raw-dual gate,2026-10-23T03:25Z,revision7. No newκ.

Concrete question and changed premise: complete #4935's missing source-restored physical backward interface; source-mutating variant excluded.

Established result and evidence status: exact X−F^T Y endpoint,632 original owners,408 retained helpers,8H1 repairs and owned-C0 cleanup; independently checked new phases/operator/bill and scoped one-bank ceiling.

Public artifact URL + exact commit: PR #4943,85e95125078826922668e9c4e96de87ebb0deb0f; handoff. All eight local/export commands and hosted run39894299781 pass at the exact submitted head;357 helpers/11 expected skips and integrity gate pass. Outcome partial, noκ.

Next useful task, success/stop test and rough runtime: #4940 is the strongest new formal caller lead. One ordered boundary/gauge strategy must remove or price its noncommuting code before physical expansion; read/derive gate only. A conditional positive price is not an admitted endpoint.

Active claim / expiry, or released: original raw-dual claim DONE/released. No new caller emission is claimed. Separate ordinary BIT API audit: #4945.

Latest established result and new caller obligation

The source-restored4935 forward/backward pair now has a literal physical witness and independently replayed cost. Complete paid profile2209H1+412H2+510H3+127H4+40H5 matches the forward producer. The suffix adds424 weighted ADDs,8COPY and16CLEAR in existingC0, no new array or productive reward. Its conservative3064 finite-pass allowance and precision amplification are separate from recursive costs and remain unfunded in a complete caller. The actual word/RESULT.paid overrides retained baseline local_profile metadata. The self-contained one-bank corollary checks actualF and112H2 necessity; its unrealized two-call grant loses throughout[.0030217758,.0034]. This excludes only that adapter architecture.

New #4940, exact91b96321893c48c7d34e4069e15f222d022e5975 bySethBurkart123, supplies a formal reverse coded-controller comparison, following dillona4933. Its p19 raw price has12008 original owners,19reverseFULLs,20thinqueries and18IDLEs, with positive moment1103.2761222689533 atC=.0034 before physical/finite/compiler bills. Formally usingF^T adds152H1 and leaves951.2761222689533, but actual −AQ blocks, heterogeneous phase-normalizers, ordered query source mixing and compiler transfer remain open. F is nonsymmetric. A signed-SWAP role convention also needs explicit output-bank labeling. No raw root or optimistic price is accepted asκ.

Read/derive only: appending scalarF^T at the common-full Xexit gives the physical dual of the source-mutating forward variant, normalized[[F^T,−I],[0,I]]. This removes cross-code but moves code to a self block. With actual normalizers the pending input code is E=Q C Q^-1; it is not free merely because F²=I. A proposed extra112H1 boundary correction must show whether the charge is once externally or repeats at every reverse stage. If it repeats19times, the optimistic p19 grant loses and that policy stops. No physical emitter, new caller claim or globalgauge cancellation is established.

Credit Dugongue4935/4929 and1931/1862 antecedents, Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv and all retained native/Clifford/compiler/outer contributors. Credit dillona4933 andSethBurkart1234940 for their separate callers. Substantial OpenAI Codex assistance; scientific admission, compiler reserve and outer recovery remain separate.

Released raw-dual claim and retained history

CURRENT PROSPECTIVE CLAIM — ONE source-restored #4935 physical raw inverse transpose, expiry2026-10-23T04:00:00Z. Source #4935 head64c9f99693c92fb370096fb43dbc58a085b30e36 and #4929 head361f5d4100640177d6a983dd2f336021c75bfd5e; canonical basecef4b52f2a59009865bf8eabde1be3f159063703. The preceding coded-prefix resource gate is complete/released, with fresh632-column replay and a frozen633-by632 offer; no supported-edge consumer or capacity scan was attempted.

Test the missing physical raw dual of the SOURCE-RESTORED offer F=A+12PR in #4935. Start from the actual #4929 backward word. For each of the eight selected Y ports, copy its final pure observation into owned zero workspace, lift its actual conjugate rank8 chart to the common full chart using one H1, scatter the dyadic correction -12(PR)^T into the112 common-full X exits, and clear the temporary. This is a proposed construction, not an established endpoint. Bind actual raw inverse transpose, absolute phase/all-width maps, all632 arbitrary owners, all408 helper jobs, cleanup, finite scalar/storage/precision and recursive cost. Source-mutating F_s and its dual are excluded.

Budget: ONE exact emitted repair and separate independent verification, no family search or full caller. Stop on any incorrect physical endpoint, nonfree conversion or ownership/cost mismatch. No newκ until a complete caller, applicable compiler reserve and outer transfer are funded. The bounded02:32UTC check found no4936 or public competing raw-dual claim/comments for4935; this is not exhaustive novelty. Credit Dugongue4935/4929 and the1931/1862 reflection antecedents, Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv and retained predecessors. Separate gpt-6.1-sol/high construction and verification agents; Chris R/Clear1nsight with substantial OpenAI Codex assistance.

Published supporting results: #4931, exact90a0124d306ef8802ac2dc3601c6705dca407e45, exposes one physical homogeneous offer; #4932, exactc56e5f172e96d2ae43c93d0a8e8a0157144ca904, proves the standalone one-bank adapter ceiling. Both exact-head hosted runs passed; neither establishes κ. #4933 is dillona's completed shared p16 coded-caller study from Discussion4930, leaving recursive coded-job closure unresolved. The new raw-dual interface scope does not duplicate that caller.

Released coded-prefix claim history

CURRENT PROSPECTIVE CLAIM — ONE integrated #4929 coded helper/prefix feed, expiry2026-10-23T02:45:00Z. The old-source physical gate below is complete/released; this successor explicitly retains the new code and nonuniform charts. Source4929 head361f5d4100640177d6a983dd2f336021c75bfd5e, current canonical cef4b52.

Test ONE actual backwardhelper496 terminal-H3 split and its owned prefix in the coded632-owner producer. Authenticate the exact current helper/Y rows and unchanged suffix chronology; do not transfer old source cleanliness silently. Emit the all-owner tall coded offer, retaining raw A, all physical headers and phase-normalizer maps. The proposed operation adds normalized productivehelper output to normalizedY39, then restores the helper. It keeps A unchanged and does not install U A^-1 U^*.

Atport39 the candidate row is D39[a+q39*sum_j A[j,39] y_j], while normalizedY39 becomes D39(y39+q39h), the savedprefix is D39h, and originalH496=Fh returns once. The diagonal A39,39 is zero; this is a collective chain h→Y39→supportedXports, NOT the old isolatedU(q). No common transverse factor across different ports is assumed. Actual coefficient order, all arbitrary inputs, every saved field, COPY/CLEAR, scalar, normalization, storage and precision cost must be stated.

Budget: one source-binding/operator test, no candidate family enumeration or112-capacity scan. First establish the priced tall offer or a source-bound stop. Then propose ONE supported-edge cancellation only if it could change a declared complete-caller moment; no newkappa without funded compiler/outer transfer. Existing26/31-file supporting packages address the standalone adapter ceiling and old-source physical offer respectively; publication is in progress. Helper inputs and rewards remain ownership-disjoint. A source/physical agent and a separate algebra/review agent coordinate the exact test. Credit Dugongue, Cinna Davis/1337isnot1337, Cao Yifan/intqwq and retained native/Clifford/compiler/outer contributors; Chris R/Clear1nsight with substantial OpenAI Codex assistance. No independent human/kernel acceptance claimed.

Completed gates and retained scope history

CURRENT FINDING / HANDOFF — physical ONE496 gate complete; priced-offer publication in progress. The original physical-feasibility claim is released. No complete two-call consumer or new kappa is established. Canonical main refreshed to cef4b52; selected60403/20000000=.00302015 and priorityrev7 remain unchanged. The recent archive merges of #4928/#4929 do not establish scientific admission.

The actual H3→H2+H1 replacement,632-original-input preservation and clean dependent prefix passed independent review. Its surcharge is2^(1-C)+1−3^(1-C); one owned array and19 conservative finite passes are charged separately. A further source-bound monomial normalization, with at most17 additional passes, gives the actual one-port tall offer

(X,Ytilde,C,H)=D*(a+q*y, y+q*h, h, q*h),

on THREE original arbitrary owners a,y,h. Here q=C162^-1, D is the actual commuting rank8 transverse Gaussian, and C is dependent owned workspace. Raw Gamma^2 has Fourier rank2, but separately charged entry/exit monomial maps recover this homogeneous form. The fourth returned row is an observation of h, not a fourth independent job. Source, patch, exact normalizers and independent review are being packaged in a focused PR; local artifacts are not yet advertised as public replay.

Two-call stopping findings: published #4698's fixed identity yields central diag(q,q,I), so its third Gaussian target is rank16, not17. Even granting #4929's cheaper profile and free embedding, the ownership-disjoint target224H17+112H16+2H−224H9 loses: moment−59.34781877151532245989877.. at C=.0030217758 and−66.73811630351254416832659.. at C=.0034, with normalized-moment monotonicity proving loss throughout. The stronger threeH17-per-port endpoint remains unproved, despite its positive optimistic moment51.37188962342207.. /43.82230549632500... It is not the documented consumer.

The fixed second-helper bypass does not supply the missing query: its row is−a+q^-1h, while complete outputs are qa,qb,h; free q²/scalar postrows cannot recover qh. One explicitly tested relay replacing the second helper input by the first retained bypass depends only on a,b+h and loses the direction(0,t,−t). Saving the displaced input leaves only its first-transverse rank8 observation, without the second fresh rank8 image. These are scoped stops for declared words, not a universal coded-consumer obstruction or an invitation to rerun the same variants.

A direct collective coded consumer for #4929 remains an open successor requiring a NEW literal endpoint and honest928-owner inventory. The single-bank physical adapter policy is separately closed below. No family search is active under the released ONE496 claim. The independently scoped adapter-ceiling verification/publication task below remains active through02:20Z. Construction, complete caller moment, compiler reserve/outer transfer and a validated higher kappa remain separate milestones.

Retained claim, source and scope history

CURRENT CLAIM — refined physical-prefix feasibility gate, 2026-10-23T01:23:53Z; expiry2026-10-23T02:05:00Z. The speculative four-owner full-routing proposal below is deferred in favour of a more source-bound next experiment. This is a prospective test of ONE actual paid-child change, not an asserted consumer or new kappa.

Candidate: #4610 native source20bb93cd990d2ff683e4d0fc56b87a42cd5d3296, backward helper496, terminal actual H3 at event15372, chart911 of rank6 to full1. The source census reports its last scalar write at13182. Its prechart appears contained in actual Yport39 exit181 (rank8, q162-perp), and Y151 appears finished at that same chart since14597. Those premises still require the independent phase/chronology binding described below.

Replace ONLY this actual H3 by H2 from911 to181 followed by H1 from181 tofull1. At the intervening chart, copy the real observation into one owned clean buffer. Prove the literal conjugate-ABI telescoping identity, exact raw inverse transpose and all-original-input endpoint preservation. Charge changed recursive profile H2+H1-H3, plus separate initialization, COPY, storage, CLEAR/restoration, routing and precision work. No productive helper is consumed, duplicated or newly credited. This is ONE helper/port test; no112-port capacity or full-caller advantage is claimed.

First deliverable is a priced, phase-bound local physical offer. A useful consumer must then preserve every original helper job and data coupling, turn the observation into a complete favourable caller moment, and bind compiler reserve/outer transfer before any new kappa. Stop the candidate on a failed native endpoint, inaccessible chart, unreturned required output or an optimistic complete bill that cannot fund the proposed saving. No chart-family or circuit-family enumeration is part of this claim.

The completed fixed-source census covers326 productiveH9 helpers in both native directions: no forward terminalH1 after the last scalar/warp write; exactly two backward terminalH1 tails, neither matching any actual Yexit chart. This stops only that natural-terminal policy. Helper224's earlier prefix is an exact101-input dirty shared observation, not the presumed clean pre-Q helper. A formal H9 split was withdrawn because productiveH9 is not a paid child in this source. The new test instead changes an ACTUAL paidH3 identified by the census. Existing proofs #4920/#4928 do not cover such intermediate access and changed paid words.

Canonical main refreshed for this pivot; no selected-record modification. Source/physical and algebra/independent-review agents are separately assigned gpt-6.1-sol/high. All-author PR monitoring continues, checking new native suppliers, consumers, compiler and overlap changes. Credit Cinna Davis/1337isnot1337, Cao Yifan/intqwq and all previously retained native, source, Clifford, compiler and outer contributors. Chris R/Clear1nsight with substantial OpenAI Codex assistance; no independent human or kernel acceptance claimed. New work Apache-2.0.

New upstream support: #4929 and the standalone adapter gate

A new all-author monitor finding steers the parallel interface work: Dugongue PR #4929, exact361f5d4100640177d6a983dd2f336021c75bfd5e, emits a helper-independent centre-free coded offer, removing8H8 while preserving408 helper jobs. Exact-head hosted run39883809943 passed all three registered producer/Gram commands; its outcome remains partial with no new kappa. The source's compressed SHA7679daa4 and decompressed SHAcfcd36b4 refer to the SAME underlying word; they are not different source constructions.

Read/derive FINDING: let U be the112 different X entrance frames and T their common full exit frame. Recovering the old uncoded ABI requires entrance K=U A^-1 U^* and an exit scalar port map A, which commutes with T. Actual A has zero diagonal and5824 supported off-diagonal entries; all supported U_i U_j^* have Fourier grade2. Therefore pi2(K)=U A U^*/13 is invertible. A standalone ONE parallel Gaussian bank with arbitrary free monomial owner maps before/after has grade-two image dimension at most r times the full phase-quotient algebra dimension, where r counts grade2 channels. Hence it needs at least112 H2 channels. The all-width implication requires a fixed finite columnwise Clifford alphabet and sufficiently-large-width projective tensor faithfulness; width-one matrix coincidences are not a proof. This permits zero scratch/rectangular free boundaries but excludes chronological multibank absorption, native interleaving and direct coded consumers. Scaling13K does not alter the bound; division13 is not the obstruction used here.

Independent exact source-grade and argument checks agree. Root's price-only relaxation, granting224H17 plus all816 helpers against two coded suppliers, gives moment166.262158203082210620506.. at C=.0030217758 and159.070799023745749761534.. at C=.0034. One112H1 conversion bank would leave54.262.. and47.070..; two112H1 banks already lose. The ONEparallel-bank lower bound112H2 loses at both endpoints and throughout this interval by normalized-moment monotonicity. No corresponding caller is realized by this arithmetic. The ordinary two-transport adapter therefore cannot simply be installed.

Prospective bounded verification/publication task: a separate gpt-6.1-sol/high agent is binding this standalone adapter ceiling to exact source, a self-contained all-width argument, finite failure controls and portable normal/optimized checks, expiry2026-10-23T02:20:00Z. The mathematical read/derive result above is already complete; this is not a retrospective claim to its discovery. No competing physical-adapter owner surfaced in bounded4929 PR-comment/Discussion/handoff checks; that is not exhaustive novelty. The new supplier instead motivates a direct coded consumer or an actually shared chronological adapter. The primary ONE496 physical-prefix experiment remains separately scoped above; no transfer through the new pre-compensation/centre-cleared chronology is assumed. Credit Dugongue, Cinna Davis/1337isnot1337, Cao Yifan/intqwq and retained native/Clifford/compiler/outer contributors; Chris R/Clear1nsight with substantial OpenAI Codex assistance.

Previous findings and scope history

PARTIAL FINDING / bounded continuation, 2026-10-23T01:18Z. Separated retained-helper scope is DONE in PR #4928, exact 6df6ed294614423836cbde182fb4368c9c346fe7; Hosted run39882962847 passed at exact head 6df6ed294614423836cbde182fb4368c9c346fe7:346 helper tests/11 expected skips, both registered source-bound replays and the committed-input integrity gate. Registered outcome remains negative-result; CI corroborates the scoped package and establishes no new kappa. The remaining prospective task is ONE literal four-owner central/fresh monomial route outside separated B, retaining both actual helper jobs. Renewal expiry2026-10-23T02:05:00Z. No new kappa.

The self-contained rank proof allows arbitrary retained helper counts, noncommuting helper/query words, zero divisors and restored B-valued spectators. It excludes full central/fresh routing, arbitrary joint224-main controls, prefix taps and discarded main-dependent garbage. Reversible clean work requires complete cleanup. All-width proof,112-port native normalizers and114688 phase equalities, independent review, mutation controls and Git-free export checks passed; finite source checks and proof have distinct roles.

Prospective next gate: state actual L/W/R routing, four arbitrary-input target equations, raw inverse transpose and all-width alphabet before synthesis. Test at most ONE justified route. Stop if mandatory transfers cost at least40 H1 against39.063938 optimistic margin. No large family enumeration follows from a width-one matrix identity. The fixed-source natural-tail census and failed dirty-echo decoder are completed local gates being frozen, not new paid-profile savings. A productive rank9 helper output is not a paid rank9 child; no such paid child exists in the actual profile.

Canonical main refreshed01:14Z and remains624de9dc66858af0945e5f8a0942488d62280d43. All-author monitoring through01:14Z found no newer PR than4926; subsequently4928 is our owned result. Coverage is bounded, not exhaustive novelty.

Previous claim and correction history retained below; the new expiry and ONE-route scope above govern the continuation.

Status: prospective CHANGED-RESOURCE feasibility gate, 2026-10-23T00:36Z; prior main-only result DONE/RELEASED. Renewal expiry2026-10-23T02:05:00Z. No consumer witness or new κ.

The new question explicitly changes #4920's identity-scratch/main-only premises: can two actual frozen #4610 FULL invocations complete the two rank17 main jobs while exposing up to two independent productive helper transforms and returning each original helper job unchanged? The minimal stronger test has four arbitrary owners: two main inputs plus one selected native helper input from each invocation. Call1 performs its actual main triangular map simultaneously with H1 on helper1; call2 performs its actual map with H2 on helper2. The other helper is preserved during each invocation. These are two different original inputs, not one bank transformed twice. Every other autonomous helper job remains productive once.

Source: #4610 20bb93cd990d2ff683e4d0fc56b87a42cd5d3296, owned-zero-centre native interface. Start with actual full-rank9 helpers, which exist in sufficient distinct slots for one per port per invocation, and retain their phase-correct native boundaries. Lower-rank helpers may be considered only after the exact pending-Q, transverse factor and orientation premises are established. Input/output helper ownership and chart conversion costs are part of the embedding obligation. Pre-existing arbitrary values H z alone can be renamed as arbitrary dirty scratch; a useful offer must expose the paid H operation in the chronology or an explicitly retained correlated input, with every buffer charged.

Source-review correction before this prospective claim: an initial local lower-rank matching used adjoint backward helpers. Independent review found that the source uses primitive-wise conjugation instead; those operations differ in14 of17 classes. The original adjoint matching remains withdrawn. Corrected conjugate-ABI replay and independent review now pass: strict low-rank capacity58 and mixed112-slot inventory14H4+1H7+43H8+54H9 survive, all816 jobs counted once. This establishes neither transverse-only factorization nor a consumer. Full-rank9 helpers agree under both operations and remain the initial resource. No consumer or target credit is inferred from the withdrawn matching.

The optimistic complete profile remains 224H17+2H−2P, including all816 original helper jobs exactly once. Its moment is39.063938114801903..904 at C=.0030217758 and31.972580383536966..967 at C=.0034. This justifies an exact embedding test, not physical profitability: all required wrapper/conversion, routing, scalar, storage and precision work must still be charged, followed by the fixed #4610 compiler reserve and outer transfer. Consuming112 disjoint helper pairs instead cannot fund the offer: even granting rank r+s−1 to each fused target, concavity loses at least1 per pair, exceeding the entire main-only margin. A retaining-helper controller is a different model.

Method/domain: derive one exact simultaneous four-owner operator equation with the source transverse factors, central functions and actual helper H1/H2. First test the homogeneous spectral relaxation; it does not establish arbitrary native free-controller impossibility. Any stronger finite group-algebra screen must retain absolute phases, outside-tensor scalar semantics and the actual monomial alphabet. No circuit-family enumeration or native word emission is authorized by a favourable stripped-coordinate calculation alone. Before expansion, require actual entry/exit maps, all arbitrary-input equations, target ownership, chronological access and a complete cost screen. Deliver one exact candidate with raw inverse transpose and charged conversions, or a scoped stop specifying the failed premise. A negative toy model will not be presented as a universal transformed-helper obstruction.

Separate user-authorized gpt-6.1-sol/high agents cover source/helper phases and algebra; an independent agent checks resource ownership and source premises. Initial budget45 minutes, deterministic derivation rather than a seed campaign. Live all-contributor created/updated PR monitoring through00:35Z found no newer PR than#4926 and no conflicting updated native consumer; targeted predecessor/claim coverage remains bounded. The #4712 dirty-helper/query failures, #4703 fallback audit, #4848 serial ceiling and #4841 native chart compiler remain mandatory predecessors. #4694's live2add42d1 interface is distinct from #4698's consumed039a3e4 snapshot; this experiment starts from #4610's owned-zero-centre ABI and does not transfer640-field arbitrary-centre guarantees.

Canonical main refreshed00:19Z and unchanged 624de9dc66858af0945e5f8a0942488d62280d43, priorityrevision7. Selected conditional .00302015 and developed comparison .0030217758 are unchanged. Credit Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv, Jacob Alan Sussman, Dugongue, Ali Romman and retained native/Clifford/compiler/outer contributors. Chris R/Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0; no independent human or formal-kernel review claimed.

Retained completed main-only investigation

Historical future-tense references to #4922 below are superseded: its no-IDLE colour word fails an exact common-i off-diagonal test, and its retained-IDLE variant loses the optimistic complete invoice. #4843/#4856 now also stop the unchanged five-bank free pre/post model. These are scoped results, leaving the changed resource question above open.

Status: DONE / RELEASED for the prospectively declared two-FULL endpoint. PR #4920 archives the construction ceiling and portable verification at exact head 7eb4ef5251f7ba96c7e5d78c42fc98e66b7be4ba. No physical consumer or new kappa is established. Priority revision7.

Progress finding: the separated-axis, main-only model has a written two-letter obstruction, independently reviewed by a second agent; portable corroboration and source-bound publication are complete; Hosted run39874112461 passed at exact head 7eb4ef5251f7ba96c7e5d78c42fc98e66b7be4ba:346 helper tests with11 expected skips, both normal/optimized model checks, both portable grade replays and unchanged committed inputs. Registered outcome remains negative-result; CI success does not establish an endpoint or new kappa. Let B be the twisted subgroup algebra of central monomials and all transverse Cliffords, and pi retain only B-supported terms. For arbitrary invertible free L,W,R, two non-B off-diagonal paid letters give pi(L T_b W T_a R)=L[W+e_i c e_l^T]R. The correction factors through one copy of B, so the projected map has kernel dimension at most dim(B). Two independent Gaussian targets have two zero projected columns and kernel dimension at least2dim(B), a contradiction. This allows arbitrary outer owner GL and restored identity scratch and does not assume B has no zero divisors.

The all-width implication uses the exact finite one-column Clifford group, its scalar-phase central-character quotient and independence of distinct projective matrix tensor powers at all sufficiently large widths. Width-one matrix coincidences are not used. Native transverse multipliers remain explicit B factors, rather than being commuted through scratch mixing. The actual rawD0 includes a verified monomial translation; only its positive transverse normalization commutes with S. All112 source ports were separately audited locally. These statements cover the declared columnwise finite alphabet with central/transverse separation. Arbitrary central/fresh address mixing and reusing transformed helper states remain outside this obstruction. The positive preliminary invoice therefore does not supply a construction in this closed main-only model; a successor must change an explicit premise and retain its full bill.

The additive second theorem closes exactly TWO owners even with the full columnwise monomial Clifford subgroup, including central/fresh mixing. Keep the actual rank-eight transverse factors. A grade<=16 projection commutes with all free monomial-algebra boundaries. An input column untouched by the first shear has an output row untouched by the second: its entry is D2 W_rc D1, with every word grade<=16. Pure rank17 targets force it to zero, then force the other entry of that interstage column to zero, contradicting invertibility. No rawD0/query commutation is needed. This second scope has NO additional scratch or transformed helper resources; it must not be merged with the separated-axis scratch theorem.

Four registered normal/optimized checks, all27 committed-file/source-history pins, official export/integrity, Git-free science replay with unchanged bytes and12 actual mutation rejections pass. A separate final read-only audit found no remaining findings. The larger frozen112-port accounting/wrapper evidence is authenticated but remains locally regenerated; portable checks do not rerun the full native632 suite, compiler or outer theorem. Hosted run39874112461 passed at exact head 7eb4ef5251f7ba96c7e5d78c42fc98e66b7be4ba:346 helper tests with11 expected skips, both normal/optimized model checks, both portable grade replays and unchanged committed inputs. Registered outcome remains negative-result; CI success does not establish an endpoint or new kappa.

This endpoint claim is released. The next changed-resource experiment is prospectively scoped in Discussion #4922: one frozen six/eight-bank n+1 word with three transverse colours and source IDLEs omitted. Its complete coloured endpoint is unknown despite a favourable conditional invoice. Do not repeat a larger two-owner free-word search.

Original prospective assignment and its gates (retained for provenance):

The question is whether TWO FULL calls of the frozen #4610 native supplier, using different monomial-conjugate central Clifford functions, can complete two arbitrary main banks while preserving every independent helper job. This changes the central operation rather than retiming the fixed centre graph. Source construction is 20bb93cd990d2ff683e4d0fc56b87a42cd5d3296; refreshed canonical main remains 624de9dc66858af0945e5f8a0942488d62280d43, selected conditional kappa 0.00302015. The stronger developed comparison remains #4610 at 0.0030217758, with admission and selected status distinct.

Declare two independent arbitrary 112-field main banks and 816 independent helper inputs (408 per FULL call), each owned and rewarded exactly once. The original supplier's eight centres remain its owned zero temporaries, not extra productive inputs. Two disjoint fresh eight-axis blocks share one central axis. The proposed productive invoice is 224 rank-17 main Gaussian jobs plus twice the exact native helper inventory {4:28,7:7,8:47,9:326}. Paid invoice is twice the native profile; its rank mass is 5327 per call, and the helper rank mass is 3471. The optimistic unwrapped moment at C=0.0030217758 is approximately 39.063938. This only justifies testing an endpoint: no two-call controller yet realizes that target, and finite boundary work, precision, compiler reserve and outer transfer are unfunded. Ambient rank 17 matches maximum proposed productive rank 17; compiler applicability still requires a new binding.

After stripping the fresh commuting eight-axis multipliers, the main paid letters are F_a=[[1,0],[a^-1,1]] and B_a=[[1,-a],[0,1]]. Test whether actual main-only phase conjugation supplies a=Q_X and a=S Q_X S^-1, with helper returns preserved. Seek a literal identity L T_b W T_a R=diag(g1,g2), each gj a legal positive rank-one Gaussian up to monomial boundaries. Free words may use finite constant owner GL2 operations and role-dependent central monomials, with every ADD, SCALE, phase/routing pass and restored dirty work field explicitly listed. Allowed scalar gates must be the actual Gaussian-dyadic constants; a larger coefficient field used for an obstruction grants no extra physical gates.

Original prospective gates (retained): authenticate the full native wrapper and helper endpoint conventions and independently recompute the complete optimistic invoice. Second gate: one clearly bounded synthesis/model test in the exact finite Clifford GROUP ALGEBRA, including absolute phases and a distinguished monomial subgroup. Pureword identities must hold at every positive column multiplicity. Width-one matrix identities alone are inadequate: an owner/address SWAP can create an accidental free address Gaussian at one bit without tensorizing as a fixed owner circuit. A positive algebraic result then needs a chronological physical word, actual raw inverse transpose, disjoint target census and complete bill. A scoped negative result must name its alphabet/boundary restrictions; arbitrary owner GL2 external boundaries must not be silently excluded.

Stop a policy when its legitimate reward upper bound minus unavoidable paid lower bound is nonpositive on its declared C interval, or when its proposed endpoint fails exact all-input/all-width verification. Do not turn one failed width, one bounded word length or one special boundary restriction into a universal obstruction. Advance toward new kappa only after a profitable complete caller, the fixed #4610 compiler obligations/reserve and applicable BIT/outer transfer are funded. The source's 54 strict predicates and four functional guards require an obligation map, not an assumed universal checklist. Scalar work, storage, routing and precision retain separate finite-template bills.

Overlap and predecessor credit: #4666's same-central-function construction, #4698's heterogeneous three-field embedding question, #4712's dirty-helper/query failures and #4703 audit, and #4875's same-phase three-shear lower bound are related but do not establish this changed-function two-bank endpoint. #4848 already closes the serial complementary B/C policy. #4839/#4867/#4888 supply distinct fixed-word centre-contact ceilings; none prices this changed controller. #4873 optimizes a sufficient compiler separator after its premises are installed; it is not an endpoint or an automatic compiler extension. Latest open submissions and user 1337isnot1337's five latest PRs were checked before this claim; targeted two/conjugation search returned no matching PR. This is bounded overlap coverage, not exhaustive novelty or an assertion about unpublished work.

Two separate gpt-6.1-sol/high agents own exact all-width algebra/source binding and independent accounting/native wrapper checks. Construction, ceiling and verification deliverables will be tied to the same actual contract. Chris R / Clear1nsight with substantial OpenAI Codex assistance; no independent human review. Credit Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv, Jacob Alan Sussman, Ali Romman, Dugongue, Nick Petalas and the retained native, scalar, Clifford, precision, compiler and outer contributors. New work Apache-2.0.

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  "task": "saved-paid-query-decoder",
  "scope": "Published passive4948mixedp2 saved-cut ceiling and independent portable verification; no active-feed or native-prefix reservation",
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  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4978"
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[Clear1nsight]

FINDING — one source-bound post-query policy is rejected; stored paid responses remain a separate test.

Freeze #4948 at 86e474038e05f99a76d41f71d81946ad2327e4a4, including its actual INVOLUTIVE-WORD.json.gz, NORMALIZERS.json and signed Clifford maps. Credit Dugongue's physical involutive dual and typed caller, dillona's #4933 normalizers, SethBurkart123's #4940 formal reverse controller, and the independent dual verification in #4943. This is a self-contained scoped algebra/phase finding; the additional local scripts are not asserted to be public artifacts.

Let the actual normalized reverse at stage s be

B_s = diag(D_s,D_s) U(-Q C_s), with C_s=K_s^-1 F^T K_s, C_s^2=I and [C_s,D_s Q]=0.

It is essential that neither [C_s,Q]=0 nor [C_s,D_s]=0 is granted. The four main banks (a,b,h,k)=(X0,Y0,X1,Y1) contain 448 arbitrary original inputs; each FULL also has 408 distinct original helper inputs.

The rejected word is exactly: thin0 L(C1 Q^-1) on pair0; reverse FULL1 on pair0 and the retained D1 IDLE on pair1; bridge X0+=X1,Y1-=Y0; thin2 L(C1 Q^-1) on pair0; inverse bridge; reverse FULL3 on pair1; thin4 L(C3 Q^-1) on pair1; final bridge X1+=X0,Y0-=Y1; then the retained signed swaps (X,Y)<-(Y,-X). Use the standard right boundary a=a'-h', k=b'+k', and standard left boundary adding negative row1 to negative row0 and subtracting positive row0 from positive row1. The uncoded C1=C3=I control gives precisely D1 Q^-1 a', D1 Q b', D3 D1 Q^-1 h', D3 D1 Q k'.

For the actual codes, the first negative row is instead

D1 C1 Q^-1 a' + (D1-C1 D1 C1)b' + (C1 D1-D1 C1)Q^-1 h'.

The last coefficient is nonzero in the actual source. The block (F^T)[0,1] is -1/2; writing T=K0^-1 K1, the corresponding leakage block is -1/2(T D1-D1 T)Q^-1. The native central labels are 11 and 19. T sends the central X direction to signed X22 and commutes with the full Gaussian D1Q, including phase, but not projectively with D1. Exact Gaussian-integer evaluation gives output coordinate1 of (T D1)|0> equal to -i/16, while (D1 T)|0> has zero there. Their signed projective tableaux differ. Their positive tensor powers therefore remain nonproportional; the outside scalar -1/2 is not tensorized. Stage3 spectator coordinates cannot remove this cross-owner leak.

Separate chronological and Gaussian-integer interpreters agree on the row, signed-swap control, actual phase witness and all-positive-width two-pure-word argument. Both normal and optimized replays pass. Independent review SHA-256: 9518c33dc111a0ff165ad0785df4cc4b1d415eddac0e90eb72c3f524e266698f. The full candidate recursive bill is {1:4754,2:824,3:1020,4:254,5:80,8:224} with all 816 helper jobs retained once. Weighted ADD counts remain separate from elementary RAM, storage and precision bills; the failed main endpoint prevents admission before those remaining costs matter.

This rejects only the stated C1/C1/C3 post-query word and standard boundaries. A mixed incoming/outgoing thin placement is different and still has unpaid negative-bank decoder obligations. The prospective saved-response/cut experiment is scoped in the current canonical body above. No arbitrary decoder obstruction, physical caller, compiler admission or new κ is claimed.

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  "kind": "FINDING",
  "task": "fixed-coded-query-order",
  "scope": "Actual4948 C1/C1/C3 post-query p2 word with standard scalar boundaries has a nonzero all-width cross-owner leak; stored paid responses and other decoder grammars remain outside",
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[JoyboyBrian]

R11 task09: no-PR handoff after the source-level feasibility gate

Canonical claim: #4902 (comment)
Assigned base a5df48c; branch
brian/r11-two-full-full-monomial-dirty-stabilization in r6-multiline-native.
No implementation, commits, native replay or public writes were performed.

Exact predecessor: PR4920, 7eb4ef5,
research/two-full-central-obstruction/grade/PROOF.md and grade/check.py;
native source 20bb93c.

Question: arbitrary finite restored dirty identity scratch in the full
monomial central/fresh routing model, with two actual ordered FULL calls.
The separated central/transverse scratch theorem does not answer it.

The exact missing implication is now visible in the predecessor proof.
Write M=T2 W T1 and let pi be its B-bimodule projection onto Fourier ranks
at most16. With exactly two owners, L M R=diag(g1,g2) is pure grade17,
so pi(M)=0. The untouched input column c and untouched output row r give
M_rc=D2r W_rc D1c, supported in grade<=16, forcing W_rc=0. The remaining
entry of column c then vanishes, contradicting invertibility of W.

With n-2 returned scratch owners, the target is instead
J=diag(g1,g2,I_(n-2)).
Its projection is P=diag(0,0,I_(n-2)), not zero. The actual necessary
condition is pi(M)=L^-1 P R^-1. Under any faithful finite-dimensional
representation of the finite monomial algebra, this has rank (n-2)d
and kernel dimension2d. It does not force its individual untouched-column
entries to vanish. Thus the old zero-column argument cannot be extended
by silently replacing the target's low-grade part with zero.

The predecessor's controlled-phase interstage check already has two
rank17 off-diagonal words, while M22=D_B C D_A is a nonzero rank16 word.
Embedding this check with an untouched third owner gives a dirty-scratch
control, not a completed endpoint or a proof that scratch helps. Its
rank16 residual is still present. Arbitrary scratch mixing might change
this residual; no invariant excluding all such mixing and no admissible
cleanup construction was established in this gate.

Smallest useful next question: prove a stable lower bound on the rank of
pi(T2 W T1), with the actual role-dependent rank8 D factors retained in
order, strictly exceeding (n-2)d for every allowed invertible W, or give
a complete three-owner identity L T2 W T1 R=diag(g1,g2,I) in the declared
finite columnwise monomial grammar. All scratch inputs must be arbitrary
and returned, all phases retained, and all autonomous helper jobs remain
independent. Neither maximal Fourier rank nor a width-one matrix identity
is a sufficient endpoint certificate.

This is an unresolved source-bound handoff, not a new negative theorem,
not a universal impossibility claim and not a kappa change. No heavy run,
solver, Lean, full native632 replay, stock/precision or physical routing
bill was attempted. Parent owns publication of this status.

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  "kind": "HANDOFF",
  "task": "complex-new-helper-inventory",
  "base": "a5df48c55ea806d7952b65acc9c76d878ff09b13",
  "scope": "Does the actual two-FULL Gaussian main-endpoint obstruction survive arbitrary finite identity scratch when central/fresh full-monomial routing is allowed? Prove the stabilized class or exhibit a complete source-admissible counterexample returning every scratch input.",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4902#discussioncomment-19144315",
  "expiry": null
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