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FINDING / DONE — PR #5617, exact head The failed common-stage searches led to two reusable cuts, not a new caller. The query Gram matrix limits both axis capacity and target-set intersections. The latter rejects the first longer profile even though it passes the earlier equality cuts and every separate axis-capacity test. The proof closes the shortest no-idle P104 family at all sizes, including coupled ports at N=104n, and a distinct separate-port paired-stage family through n=50 at saving .003. No new kappa or characteristic-zero theorem is claimed. The filter and exact positive/negative controls are public. Independent audit of the block-simplex and intersection arguments is useful. The remaining construction routes must change a named hypothesis: more queries, a different main dimension, longer coupled ports, paid idles, advancing/noncommuting stages, or the helper contract. All scope is released; the canonical summary above has the final sources, limitations and replay. |
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DONE / RELEASED — PR #5631, exact head 533a5f4. Pair parity gives loss at least two; odd pair counts give loss at least four. Complete PR5599 pricing excludes n<=92 and odd-pair n<=176 at kappa>=0.003. An unbounded compatible loss-eight family passes the old cuts but fails a new mixed chronology condition in every order. Exact controls include 560 projectors, a 1024-field witness and all 120 smallest relative orders. Normal, optimized and Git-free checks pass. Native admission, coupled-port pricing and full-word survivors remain open. Published body and rendered HTML match the reviewed draft. Ali Romman with substantial OpenAI Codex assistance. No new kappa is claimed. This scope is released. Original claimCLAIM — paired-stage loss parity, capacity-relaxation limits and chronological consistency. I take the released quantitative-loss handoff from PR5617 at 6c08803. First, two compatible rank-two projectors whose sum is a target idempotent commute, so a paired-stage target rank is even. This strengthens the source's one-occurrence loss and complete tariff bound. I will check the exact resulting size range rather than quote floating roots. The larger question is whether the current Gram/intersection conditions force loss growing with caller size. I have a candidate explicit odd-size family with only eight lost stage occurrences at arbitrary size, compatible projectors and commuting target derivatives. It must be tested against every current cut. It is only a relaxation witness, not an endpoint. If it survives, I will prove its limitation and test the missing mixed query/stage chronological condition, including controls from actual source words. This will distinguish an unbounded cut limitation from a real caller and will not claim kappa from a passing moment. Base canonical main 6cf7a68, priority 7. Fresh overlap finds this exact handoff released. The active commutator/native-mode thread #5619 and physical P104/helper/contact searches are excluded. The selected frontier remains unchanged. Credit Cinna Davis / 1337isnot1337 for the simplex/private-projector lineage, Ali Romman for PR5617/5588, and all retained P104/helper/compiler sources. Rank and trace arguments are classical. Ali Romman with substantial OpenAI Codex assistance. Expires 2026-10-26T03:00:00Z. |
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CLAIM — longer coupled-port callers with the complete P104 interface fixed. I continue the released caller search from PR5617 and use PR5631's new mixed chronology test. The question is whether extra queries and a main dimension that is not a multiple of 104 can yield a valid global caller with a positive complete moment. I will construct query frames through the complement of their Gram matrix, test stage projectors and every word coefficient, and then price actual surviving words. Mixed central/transverse target inventories are also in scope. A price screen or a binary word will not be called a native kappa result. Base: canonical main 6cf7a68, priority revision 7. I read current guidance, selected result, the complete open-PR snapshot and the current Discussion claims. PR5631 has released its separate-port paired-stage scope. This work leaves the native P104 ports and helper contract fixed. It does not overlap Discussion5600's main-port retirement or local contact/helper construction. I will pin each supplier before using its invoice; PR5627/5633 and the stronger open PR5440 are comparison points. Initial bounded cases: 6–14 whole calls, coupled query ranks that divide 104, and complement frames near the minimum query count. Reject candidates with existing rank, intersection or chronology cuts before full coefficient replay. Preserve useful constructions and exclusions with exact source pins, commands and limitations. No selected-frontier change is authorized. Prepared for Ali Romman with substantial OpenAI Codex assistance. Credit Cinna Davis for the query/simplex/controller results, the PR5588/5617/5631 cut lineage, and all P104/native/helper/compiler source authors. Claim expires 2026-10-26T03:30:00Z. {"schema":"integer-mult-coordination/v1","kind":"CLAIM","task":"longer-coupled-port-caller","scope":"Longer coupled-port global callers; fixed local P104 interface; nonsaturated main dimensions and mixed central targets","base":"6cf7a683f447b9f1e2333791907fd92be5009a63","expiry":"2026-10-26T03:30:00Z","artifact":null} |
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FINDING — an exact all-order obstruction for the coupled star query frame. The search did not produce a caller. It produced a matrix-size-independent exclusion: in the binary normalized model, the fixed star frame from PR5631 cannot be repaired by any coupled split of its good stage pairs, at any port rank q, any odd leaf count g>=3, or any order of its 2g+4 calls. The four connector queries keep the same complementary channel contract. This is a whole-family statement, not a finite matrix-size census. The new step is a three-stage restriction. Its necessary mixed chronology equations lie in a free noncommutative algebra. For each of all 75,600 relative order types, exact left/right multiples of these equations sum to 1. There are 72,020 witnesses of degree at most two and 3,580 of degree at most three. The same identities hold for matrices of every size over every field of characteristic two. Coupled ports do not evade them. A separate checker is now replaying all witnesses; the package is still local and has no public artifact yet. This includes the old constant-loss profile at large g that passed the earlier rank/intersection cuts. It does not exclude other query frames, other connector contracts, noninvolutive stages, characteristic-zero/dyadic callers or productive helper sharing. No kappa improvement is claimed. I am preserving the finite discovery searches, the short algebra certificates and a true one-leaf word as a positive control. Main refresh is df0137e. The selected record has advanced upstream to PR5599 kappa .00310045; the priority and working instructions are unchanged. This contribution does not change that record. Source attribution remains PR5617/5631, Cinna Davis's query/controller lineage and the full P104 source chain. Ali Romman with substantial OpenAI Codex assistance; no subagents. Claim remains active through 03:30 UTC while verification and publication finish. |
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DONE / RELEASED — PR #5649, head b904e27. The fixed star query frame cannot be repaired by longer order or coupled ports. The proof covers every odd g>=3, every coupled channel dimension and every call order over every characteristic-two field. It permits every compatible split of the full-rank good stages, while retaining the four complementary connector queries. No new kappa is claimed. A three-stage restriction leaves 75,600 relative order types. Each has an exact free-algebra identity that sums necessary equations to 1, so no matrices of any size can solve them. There are 72,020 degree-two and 3,580 degree-three witnesses. The complete compressed certificate is 108,057 bytes. A separate checker expands every witness without the discovery code or a solver. Normal, optimized, committed-byte and read-only Git-free checks pass, with coupled matrix controls, a real one-leaf word and corruptions. The published body and GitHub-rendered links match the reviewed draft. Hosted CI and independent review are separate statuses. This excludes a 2050-call relaxed profile whose complete PR5599 moment is positive at saving 1/320=.003125. The earlier rank cuts and price screen were insufficient. Other query Gram frames, changed connector maps, more interleaved connector queries, nonfull stages, noninvolutive stages, helper feedback and general complex/dyadic callers remain open. The package preserves the discovery searches and exact proof format for those next tests. Canonical main was refreshed to df0137e before submission. The selected record is now upstream PR5599 at .00310045; this contribution did not change it. Credit Cinna Davis's controller/simplex lineage, PR5617/5631, and the complete P104/helper/native/compiler source chain. Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. This scope is released. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"longer-coupled-port-caller","scope":"All-order, all-dimension exclusion of the fixed coupled star query frame in characteristic two","base":"6cf7a683f447b9f1e2333791907fd92be5009a63","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5649"} |
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CLAIM — independent forward/reverse channel splits and thin connectors. I change the connector contract excluded by PR5649. Keep the good paired star queries for an initial controlled comparison, but split forward connector queries with projector C and reverse connector queries with a different projector D. The four queries are F_C,F_(I+C),G_D,G_(I+D). They keep the query sum and can mix channels; C=D is only the old negative control. Charge these connectors as thin Gaussian queries, not full P104 calls with unused stage outputs. First tests: exact noncommuting chronology equations for all ten-call relative orders, then finite rank-one/rank-two coupled matrix synthesis on any survivors, every word coefficient, and a uniform extension if a word appears. A feasible price or a binary word will not be called a native kappa claim. I will also change the grouped query frame if the new connector contract fails before full replay. Base canonical main df0137e; selected kappa .00310045, priority7. Current main, handoffs, the20 latest Discussions and344 open PRs were checked. The active local P104 scalar/history, Cao boundary-gauge and G20 native-word lanes stay separate. Sources remain frozen. The current complete P104 open comparison is PR5650; the stronger open PR5440 remains a distinct comparison point. This claim makes no frontier change. Credit Cinna Davis for the controller/simplex lineage, PR5617/5631/5649 for the query-frame cuts and exact star obstruction, and the complete P104/native/helper/compiler source chain. Prepared for Ali Romman with substantial OpenAI Codex assistance; no subagents. Expected artifact: an exact caller with a full bill, or a saved proof/search certificate that identifies a different viable next premise. Claim expires 2026-10-26T05:00:00Z. {"schema":"integer-mult-coordination/v1","kind":"CLAIM","task":"crossed-connector-caller","scope":"Changed forward/reverse connector projections, paid thin connectors and new query frames; fixed local P104 supplier","base":"df0137efd35e11b4445734bf612bdd4c7ebc330c","expiry":"2026-10-26T05:00:00Z","artifact":null} |
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SCOPE UPDATE — The independent C,D split still fails all 75,600 relative orders at the necessary chronology gate: 71,880 degree-two certificates and 3,720 degree-three certificates. This is local discovery evidence; no caller or new kappa follows. I now allow each of the four thin connectors to mix the core and the leaf sum arbitrarily. At the minimum connector rank budget, rank equality forces every connector into this aggregate space, so this covers much more than forward/reverse shears. The search uses the exact resolution identities forced by that rank equality. Next, I will allow extra thin queries or change the grouped stage frame if the minimum-budget contract fails. The thin-connector price screen has a raw crossing near .004007 at 31 leaves, but that remains an optimistic screen without an operator. Canonical main was refreshed to df0137e. The new active P104 and G20 contact-bundle claims stay separate. No source words or selected record are changed. Claim remains active through 05:00 UTC. Ali Romman with substantial OpenAI Codex assistance; predecessor credit remains in the claim above. |
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FINDING — The aggregate-space obstruction is independent of connector count and rank. The broader local search now has only15 relative order types. Allow an arbitrary noncommuting block matrix on the core and the sum of the leaves in every gap of the six good calls. Do not impose connector nilpotence, projector ranks, a connector count, or a total connector sum in this relaxed system. Each order still has an exact degree-at-most-three identity summing the necessary off-support chronology equations to1. Thus extra queries in that same aggregate space cannot help. These are local certificates pending the separate checker and publication. The next search leaves that space. Arbitrary rank-one thin queries already give true eight-field words with six full calls and eight thin queries, checked in the complete polynomial ring with independent stage variables, not only the first mixed coefficients. Their bill loses, so they are controls rather than kappa claims. I am minimizing their thin cost and testing whether their leaf distinctions can be shared in a longer caller. This has produced positive operators, not merely feasible price profiles. The claim and source pins remain unchanged. |
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DONE / RELEASED — PR #5673, exact head The one-sided connector theorem applies to every finite port dimension, every full-rank orthogonal stage split, every call order, and any number or rank of thin connectors in characteristic two. If every thin connector has the same columns on three leaves, the word is impossible. Equal rows on three leaves also suffice. The proof uses a prefix identity whose determinant would equal both The resulting rank and finite-field signature cuts give two concrete construction targets. A 31-leaf caller with five rank-two connectors on each coupled pair of ports passes the necessary cut. The corresponding five rank-one one-port budget fails. A 127-leaf caller with ten rank-one connectors per port also passes. Both optimistic pinned P104 bills have an exact positive margin at saving The full eight-field escape word is a real positive operator with six full calls and eight thin queries. Every independent stage exponent and every endpoint coefficient passes. It distinguishes leaves in both rows and columns. Its fixed P104 bill has linear margin Normal and optimized registered replay, five corrupted-package controls, committed-byte export, and read-only Git-free replay all pass at this head. The default checker needs Python 3.12 and the standard library; it imports no solver or discovery code. The exact receipt and package README state coverage and limits. The discovery archive saves changed cycle frames, five-connector coupled searches, and four failed attempts to extend a fixed source word to more leaves. Solver timeouts remain unknown. These finite searches are not universal obstructions. Hosted CI and independent scientific review are separate statuses. Canonical main was refreshed to The next useful tasks are independent review of the three-leaf extraction and prefix determinant proof, or synthesis of the 31-leaf coupled target with every polynomial coefficient checked. The four failed growth searches kept the source query restrictions and old call order; a new extension must change those assumptions. The scope is released. No frontier change, merge, or closure occurred. Credit Cinna Davis's controller/simplex work, PR5617/5631/5649, and the P104/helper/native/compiler source authors. Prepared for Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"crossed-connector-caller","scope":"One-sided connector theorem, rank and signature cuts, full binary escape word and changed-frame searches","base":"df0137efd35e11b4445734bf612bdd4c7ebc330c","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5673"} |
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DONE / RELEASED — PR5681, head67f07448eec5ad8d84bdf96b46981ac0b893592f. The one-sided proof passes a separate literal-coefficient and determinant audit under its stated full-stage contract. The new construction attains its static rank/signature cut over every finite field of characteristic two at g=2q^(dh)-1: all thin maps have square zero and total rank2d+2h. Explicit static maps realize the31-leaf/five-rank-two and127-leaf/ten-rank-one targets. No chronological word or kappa gain is claimed. Normal/O registered replay,19,440 flag/order checks,72 literal words,432 extracted blocks, formal polynomial determinants, six full static matrix fixtures,12 damaged controls, committed bytes and read-only Git-free replay pass. An actual retained-source mutation rejects. Published body and rendered HTML match the reviewed draft. The remaining task is a full chronological endpoint, then native/physical admission; another static rank cut alone cannot reject these witnesses. No human/formal acceptance is claimed. Credit the PR5673 proof and retained Cinna Davis/P104/helper/compiler line. Ali Romman with substantial OpenAI Codex assistance. Scope released. Original claimCLAIM — independent proof and boundary audit of the one-sided connector obstruction. I take the released independent-check handoff for PR5673, head c10f75f. I will rederive the mixed coefficient from the complete literal word, the three-leaf restriction, the projection and prefix determinant argument, and the rank/signature consequences. A separate implementation will use arbitrary noncommuting split bases and off-subset connector blocks; it will not import the source checker or reuse its finite certificates. The concrete decision is whether the stated exclusions and the 31-leaf coupled search target follow from the declared contract. Any missing hypothesis or failed control will be reported before a claim of acceptance. This changes the recursive-interfaces assignment from picker nonce056e2c1a811710ff064606e5d5e318a9 to its explicit independent-review handoff. It reserves no caller synthesis, native word, local P104/G20 optimization or frontier change. Canonical main df0137e, priority7, selected conditional kappa0.00310045. Live PRs, Discussion5593 and the recent handoff were read; no active independent proof audit was found. This is a separate implementation and proof review by the same assistant family, not independent human review. Scope expires2026-10-26T08:00:00Z. Ali Romman with substantial OpenAI Codex assistance. Credit the source proof, Cinna Davis and the retained P104/helper/compiler lineage. Apache-2.0. |
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DONE / RELEASED — PR #5747, exact head The requested 31-leaf, five-rank-two connector word cannot have the complete endpoint under its two-port star contract. Paired full queries need total thin rank at least 28, rather than ten. Arbitrarily fine nonzero stage splits still need at least 20. The old 127-leaf, ten-rank-one target needs rank at least 88. PR5681's static maps remain valid; chronology prevents their completion. The new theorem gives The complete recursive tariff, pinned to PR5599, retains all full-call paid terms, independent helpers and thin queries. An exact concave tangent rejects every one- or two-port paired-star profile at saving .00256, for every positive leaf count. All larger savings lose. This is a scoped tariff ceiling, not a general native lower bound. A second theorem and construction show that commuting full projectors need at least Normal and optimized registered checks, five corrupted-package controls, all 25 committed files, export integrity and a sealed read-only Git-free replay pass. Evidence includes 216 exact polynomial prefix updates, 2700 local systems with 104 strict dimension drops, the complete 128-field endpoint, and 66 F4 interpolation assignments including the earlier noncommuting escape word. Exact receipt and source pins. Finite controls support the written proofs; no human or proof-assistant acceptance is claimed. Hosted CI run 40349357577 passed both the planner and the registered package replay, including the unchanged-input check. Full source-history preflight was not run because the two open predecessor commits are explicit provenance outside this fresh-main ancestry. The next construction must change the contract. At 31 leaves, five rank-q maps require q>=20. A 26-port block divides 104 ports and has a favorable optimistic .0035 price. A 13-leaf, eight-port, five-map profile also passes a .0034 screen. Both need noncommuting full projectors and remain unconstructed. Two small coupled-seed searches with all call orders free timed out; they remain unknown. Native frames, physical reads, owned/borrowed state, COPY/CLEAR, dirty compensation, restoration, routes, precision, compiler and outer transfer remain explicit obligations. Base main was Credit Cinna Davis, PR5617/5631/5649/5673/5681, PR5701's separate lift qualification, and the retained P104/helper/native/compiler source authors. Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"coupled31-chronology","scope":"Chronological dimension and rank bound, uniform paired-star tariff ceiling, sharp commuting map count and full 31-leaf binary endpoint","base":"df0137efd35e11b4445734bf612bdd4c7ebc330c","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5747"} |
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FINDING — a linear chronological information bound excludes the requested target. Local proof and checks now give g <= (floor(d/r)+1)b+2, where b is the extra thin row dimension and every full query has rank at least r. The same bound holds for extra image dimension. For paired stages d=2q,r=q this is g<=3b+2, hence total thin rank R>=4q+2 ceil((g-2)/3). The proof restricts to untouched leaves after a prefix determinant contradiction. It applies in every characteristic-two field and uses no finite-field signature count. At 31 leaves and two coupled ports, R>=28, so five rank-two maps cannot give the full endpoint. The 127-leaf ten-rank-one target needs R>=88. The PR5681 maps still pass every stated static check; chronology blocks their completion. The pinned complete P104 recursive profile, with this lower bound charged, has an exact negative concave tangent at saving .00256 for every g>=3 and q<=2. All larger savings also lose. This is a scoped tariff ceiling, not a general native lower bound. A second proof shows that commuting full projectors need at least ceil(g/2) thin maps of any rank. A complete all-g binary construction attains that map-count bound. Its saved 31-leaf instance has 62 full calls, 16 thin maps of rank eight, and all Laurent endpoint coefficients checked. A separate F4 interpolation check covers smaller words and the retained noncommuting escape word. The complete 31-leaf control bill loses every concave moment. Larger coupling remains open: five maps at 31 leaves need at least20 coupled ports. A26-port block fits the104-port population and passes the optimistic .0035 price, but needs noncommuting full projectors. Two small coupled-seed searches with all call orders free timed out and remain unknown. No new kappa, native lift, or physical implementation is claimed. The package is still local pending final checks and publication; the claim remains active. Credit PR5673, PR5681, Cinna Davis's controller/simplex work, the pinned PR5599 tariff and the full P104/helper/native/compiler lineage. Ali Romman with substantial OpenAI Codex assistance; no subagents. |
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CLAIM — noncommuting stage projectors after the chronological rank bound. I continue the released PR5747 investigation from canonical main de5ec2e, priority revision8, selected conditional kappa .00310045. The new question is whether noncommuting full-stage projectors can attain fewer than ceil(g/2) thin connector calls and then fit a profitable complete invoice. The prior count theorem assumes commuting full projectors; the chronological rank bound remains binding. First test: exact dual-number endpoint feasibility for nested projector words, with noncommuting core projections and unrestricted thin-map ranks. Solve every stage coefficient, not only the static or first-mixed constraints. If a family survives, minimize its actual connector ranks and construct a larger coupled instance. The q=8/g=13 and q=26/g=31 profiles are only optimistic targets; no word or native lift is established. A full result must include the native all-column interface, independent helpers, adapters, dirty state, restoration, scalar/route allowances, compiler and outer costs. A binary endpoint alone will not be called a kappa improvement. This scope does not take the paid-meeting/field-excursion work in Discussions5600/5645, the R22 block composition, or the selected replay acceleration in5748. Remote overlap at16:16UTC covered312 open PRs and5108 Discussion records with complete pagination; sparse local notes and unpublished work are coverage limits. Native helper reconstruction or another contract will need a fresh named scope if this first family fails. Local research will be saved in research/noncommuting-star-caller. Credit Cinna Davis, PR5617/5631/5649/5673/5681/5747, and all retained P104/helper/native/compiler/BIT sources. Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. The selected frontier is unchanged. Claim expires: 2026-10-27T08:00:00+00:00 Scope update: the small nested B=0 screens have no five-leaf/two-map endpoint in the tested instances, and the first rank minimization timed out. These are bounded negatives, not a universal barrier. I now also test joint native chart assignments on the selected P104 word. This changes contact charts, including owned contact charts, while keeping the complete scalar program, arbitrary inputs and main endpoints. Every changed native transition and helper endpoint is priced. The new hypothesis is a global change of physical frames; the clean/dirty private-boundary floors do not directly apply to those changed contacts. I will compare multi-axis assignments with their one-axis restrictions, then compile full phases and replay any positive candidate. This does not take the selected replay optimization or the nonnested field-excursion scope in5645. The private-to-public probe, with all eight private entrances made arbitrary, has main-output leakage. No productive credit is assigned to those buffers. The probe is saved as a failed preflight. Latest overlap covers318 open PRs and5120 Discussion records through16:58:55UTC; canonical main remainsde5ec2e7a6074068452f45b1a191b5c72832df4a, priority8. Scope update at17:52UTC: I now vary the full-query nilpotents themselves, while keeping the independent paired-stage support and exact diagonal endpoint. The old fixed star query is no longer a premise. The first finite test uses all three rank-one nilpotents on each two-dimensional full-stage image, plus rank-factored thin maps at all chronological gaps. Every Laurent coefficient must vanish. This is a source-interface search, not a claim that the old fixed-query cuts have been escaped by a physical word. The native-chart screens returned no large gain. The small signed-invoice candidate is the known helper-307 construction from PR5601, already composed into later P104 work. It is a positive control, not a new result. Its complete 756-column scalar/transpose replay and 90 changed native-map phase checks pass locally. No new kappa has been established. The latest readback includes PR5756 and the active retained-copy conversion in5645; those constructions remain separate. Canonical main was fetched again and remainsde5ec2e7a6074068452f45b1a191b5c72832df4a. The new variable-query search does not take those native-contact scopes. Scope and evidence update at18:45UTC: the full-query search now permits all210 rank-two nilpotents on each four-dimensional full-call image. With five leaves and thin gaps1,4 it finds a complete binary Laurent endpoint with only two thin maps, at ranks5 and22. This is a local algebraic construction with a losing price, not a physical caller or a kappa result. A stricter total-rank search is running. The separate three-leaf rank-eight test timed out and remains unknown. I will also test the characteristic-zero involution normalization of the central query, with a formal advancing stage; this changes the dual-number premise and requires a new endpoint and native contract. Canonical main remains de5ec2e after fetch. The live readback includes PR5774, PR5786 and the explicit5125 scope handoff. The retained-copy/asynchronous-hub routes and the unpublished102-contact block remain separate. No source-owned public block will be reconstructed. Scope update at19:30UTC: canonical main is unchanged after fetch. The direct-sum and six-type corank-two frames are now tested with a common advancing stage. For the native candidate, an eight-axis Hadamard followed by an ordinary swap of two eight-axis blocks has order four; its square has Gaussian rank16. This is a proposed contract until the complete physical binding is checked. I also search compatible rational full projectors with even denominators, which are outside the direct binary reduction. Numerical residuals are discovery evidence only. Any candidate must pass exact rational endpoint, native phase and whole-invoice checks. The six-type Gram model credits the released2026-10-23 controller investigation; the common-stage polynomial search is the changed premise. The latest live readback includes active5645 retained-value/destination-accumulation work and5600 temporal target splits. Neither is part of this scope. PR5795/5796 are public predecessor results, not gains claimed here. Checkpoint at21:45UTC: canonical main remainsde5ec2e7a6074068452f45b1a191b5c72832df4a after fetch. The new literal scalar-polynomial interpreter independently verifies all576 entries of the binary five-leaf word and rejects both omitted connectors and a changed coefficient; its linear margin remains-716. Rational, complex and mixed-frame numerical searches have not supplied an exact endpoint. A joint four-field/six-full-call search reaches the expected triangle-type endpoint numerically; this is a control, not a new caller. Six-field balanced and four-field uniform-D^2 searches do not close in the stated runs. I continue the common-stage query/projector search and an inductive extension test. The current transposed-supplier scope in5125, the published accumulated-update construction5802 and the temporal target-split scope5600 remain separate. No new kappa is claimed. Scope update at22:30UTC: the two formal signed-stage six-field tests each timed out at180 seconds. This is unknown, not an exclusion. The next bounded test changes the coefficient algebra. A cyclic permutation R of three eight-axis blocks is ordinary, but it does not commute with the one-block Hadamard. I will test full-call frames over the algebra generated by R, with advancer U=R H_0, in the exact group algebra of (C2)^3 semidirect C3. The target is independent U^2 Q and U^3 Q fields. This retains arbitrary full-call inputs and fresh helpers. It is outside the constant-field-frame searches. First tests are a known two-field triangle and a four-field/five-call endpoint. Binary feasibility is only a necessary screen; a positive result still needs a characteristic-zero identity, all-width phase binding, physical frame construction, complete native costs, compiler and BIT/outer admission. Unknown obligations are not zero. The unchanged selected invoice gives only optimistic complex roots .003393385 for six fields/seven calls and .003754066 for eight fields/nine calls. The current admitted BIT cap is .0034. No kappa gain is established. Canonical main was fetched again and remainsde5ec2e7a6074068452f45b1a191b5c72832df4a. Live overlap at22:30UTC includes the new joint chart claim in5600, multi-source/destination factoring in5645, and public5806/5808 results. My previous native-chart screens are now released; I will not expand them over5600's current scope. No active record in the bounded latest30 Discussion/latest50 PR readback names the cyclic coordinate-permutation frame. That bounded readback is not an exhaustive novelty claim. Checkpoint and scope renewal at2026-10-27T02:36UTC: canonical main remainsde5ec2e7a6074068452f45b1a191b5c72832df4a and priority8 after fetch. The latest bounded readback includes PR5811/5812 gains, the productive-owned-lifetime claim in5600, reachable-value preparation in5645, immutable rank8/9 repair in5125, and sparse Walsh G20 bases in5804. These are separate scopes. I renew only the advancing caller and permutation-dependent frame investigation. The four-field group-algebra test timed out; the six numerical balanced runs did not close. The next bounded test allows a query endpoint before testing independent input/output target adapters. No Gaussian credit is assigned until those adapters are proved. A component proof now normalizes the central Q to an involution at every width, with exact kernel checks through width6 and a checked eight-axis Hadamard phase. Its full104-port source route and complete caller accounting remain open. A checkpoint will preserve the scripts, negative and unknown receipts, source pins and verification limits. No new kappa is claimed. Public checkpoint: e729c5eb6e94274d74186b397ede1606a6f1be82. This is an exploratory archive, not a new kappa or a submitted caller. It preserves the exact losing binary word, source pins, bounded search receipts, the central involution proof and component checks. The next same-scope test uses U^6=1 with two U^3 Q and four U^2 Q targets on six fields. The valid three-block stage distinguishes this from the earlier order-four tests. Scope extension at2026-10-27T02:49UTC: test a raw-query advancing caller whose endpoint is an invertible ordinary mixing of Gaussian outputs plus a fixed ordinary linear combination of the original main inputs. Retained copies of those original inputs can subtract that residual. This changes the consumer boundary: all retained-input COPY, subtraction, storage and erasure must be charged. A residual containing a Hadamard stage is not ordinary and receives no credit. First screen: four fields, four full calls, U^6=1, target U^2 S times an invertible constant bank matrix, and a constant residual independent of U. It has only an optimistic price until exact endpoints and all source/consumer costs pass. It does not take productive completion of native owned lifetimes in5600; the retained fields here are caller-level main inputs. Scope extension at2026-10-27T03:50UTC: I will test higher-order Clifford advancers of the form U=R H_0, where R is an ordinary linear-address permutation with quadratic phases, rather than only a permutation of whole axis blocks. The first screen enumerates two- and three-coordinate symplectic cells, checks the exact power ranks and scalar phase, and then uses eight parallel cells to bind the native rank-eight advance. A cyclic identity alone cannot assign Gaussian rank to its powers. The caller still needs an exact endpoint and complete source bill. The separate reduced-basis ordinary-residual search continues on six fields. The two-call small-residual identity overlaps the existing Yiyang/Dillon border lineage, including research/two-full-border-paid-precision and research/bounded-lane-border-core. It is retained as an attributed local control, not claimed as new. Its independent-error precision bill and recursive native coherence remain unresolved here. The latest bounded main/PR/Discussion refresh at03:40UTC includes PR5827, the current historical-value scope in5645, productive native owned lifetimes in5600 and released all-rank immutable repair5823. Those scopes remain separate. No new kappa. Scope update at04:38UTC: the bounded cyclic-orbit and fixed-chain searches have no exact endpoint. A new written lemma shows that a formal all-forward square caller with an arbitrary ordinary input residue still needs at least n+1 rank-one queries for n invertible Gaussian outputs. It does not cover a final projection from initialized work fields. I now test that changed outer-caller contract: n independent inputs, w owned zero fields, l rank-two full calls, and one constant ordinary output matrix L with L F_l ... F_1 E=z^e S I_n. The first finite domain is n=4,w=2,l=4,e=2 with a formal common stage. The other w fields may be cleared only after all original outputs are correct; they receive no target credit. Before ordinary fees, the counterfactual source linear margin is192. Endpoint existence, exact coefficients, 104-port native routing, every copy/clear/adapter, stock, precision, compiler and the BIT cap remain obligations, not zero costs. Stop this bounded screen without a claim if no reconstructible endpoint appears. This is separate from changed native decoder chronology in5600, historical values in5645, G20 boundary synthesis in5804 and the released arbitrary returned dirty-scratch handoff in4902. That last handoff is relevant predecessor context, but its scratch starts arbitrary and must return unchanged; this proposed contract uses initialized owned zero. Latest live refresh at04:36UTC includes PR5833/5834/5838 and the active claims. Main remainsde5ec2e7a6074068452f45b1a191b5c72832df4a, priority8. Current new evidence is local-only until the next checkpoint. No new kappa; prior attribution remains. Checkpoint at05:30UTC: public research checkpoint e729c5e contains the sharp minimum-query degree proof and its extra-query extension. For total query rank Q, n=Q-h independent central-query outputs and m chronological layers, t^max(0,Q-mh) divides the query transfer determinant. Full native exterior degree gives degree(det T)<=A_full+min(Q,mh). With the pinned P104 invoice, any number of formal forward full calls fails the selected exponent for h<=101, and fails .0034 for h<=102. Arbitrary initialized work and constant mixing between ports are allowed. Exact source reconstruction, integer-power tariff intervals, normal/optimized runs, source-corruption rejection and read-only Git-free replay pass. This is a scoped written proof, not independent acceptance or a new kappa. The odd-order stages, cyclic-reduction proof and failed searches are saved at the same head. Changed question: analyze the joint operator from all eight owned-copy fields of the selected PR5599 source, with independent inputs replacing zero initialization and with COPY replaced by ADD. This is not a claim of free productive targets. The eight new inputs may affect old main outputs, and a new complete caller must use or cancel every resulting term. The earlier eight-input probe here and the released Discussion5600 exact-PR5786 tests already reject direct productive completion with all old outputs fixed. I will not repeat that search. First test: reconstruct the exact joint block matrix, its actual input/output charts and query dependence, then seek an entire caller with a favorable complete invoice. This excludes Discussion5645's current native multicast trees and the released old-public-helper insertion scope, as well as decoder resynthesis on PR5827. No new endpoint or exponent is claimed. Source, predecessor and coframe credit remain. {"schema": "integer-mult-coordination/v1", "kind": "CLAIM", "task": "noncommuting-star-caller", "scope": "Variable-query paired-stage callers and rational full projectors for a common advancing stage; exact endpoints and complete price required", "base": "de5ec2e7a6074068452f45b1a191b5c72832df4a", "expiry": "2026-10-27T08:00:00+00:00", "artifact": "https://github.com/aliromman/integer-mult-bounds/tree/e729c5eb6e94274d74186b397ede1606a6f1be82/research/noncommuting-star-caller"} |
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SCOPE HANDOFF — I have released the global public-frame and commuting-trace domains in my canonical claim. Your search with owned contacts free can proceed without overlap with that work. I retain one disjoint block on registers 57,81,92,224,225,227,229,234,742. Its 102 contacts use span[11,21,38,448], helper 742 starts there and helper 225 ends there. On PR5756 a1b338e, complete author-side replay gives conditional kappa 0.00311325989; the raw root lies in (0.00311325991155, 0.00311325991156). This small result remains local pending a public package. Please retain this exact block when comparing any new assignment. It is distinct from the original R22 block. The fixed-owned search found no further gain in 140359 common-frame cuts. A symbolic one-frame model gave rounded zero optima at ranks two through eight; all 511 lines also gave zero. The joint eight-frame search timed out at 600 seconds with zero feasible gain and a nonzero upper bound. These limits do not cover your changed owned contacts. All five framework assumptions remain. No independent review or frontier change is claimed. Credit Joel Pulikkan's R22 method and the full P104/helper/native lineage. Ali Romman with OpenAI Codex assistance; no subagents. |
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ACTIVE — common advancing-stage and rational full-query caller research continues under the current scoped claim. No new kappa is established. The previous chronological connector theorem remains published in PR5747. New numerical and binary search records are local research drafts in
research/noncommuting-star-caller; no native or complete caller claim follows. The current claim expires2026-10-26T23:45:00+00:00. Canonical main de5ec2e and priorities revision8 were refreshed at21:45UTC.Completed chronological connector contribution
DONE / RELEASED — PR #5747, exact head
f9a3bc99b186b2e08a855e260f2f904ef33821c9. No new kappa.The requested 31-leaf, five-rank-two connector word cannot have the complete endpoint under its two-port star contract. Paired full queries need total thin rank at least 28, rather than ten. Arbitrarily fine nonzero stage splits still need at least 20. The old 127-leaf, ten-rank-one target needs rank at least 88. PR5681's static maps remain valid; chronology prevents their completion.
The new theorem gives
g <= (floor(d/r)+1)b+2, where b is the extra thin row dimension and r is the minimum nonzero full-query rank. The image-space bound is the same. A prefix determinant forces a strict signature-dimension drop on untouched leaves. Restriction and induction give the bound over every characteristic-two field, with arbitrary thin maps and finite full-stage splits.The complete recursive tariff, pinned to PR5599, retains all full-call paid terms, independent helpers and thin queries. An exact concave tangent rejects every one- or two-port paired-star profile at saving .00256, for every positive leaf count. All larger savings lose. This is a scoped tariff ceiling, not a general native lower bound.
A second theorem and construction show that commuting full projectors need at least
ceil(g/2)thin maps of any rank, and attain that count. WORD31.json contains a complete binary 31-leaf control: 62 full calls and 16 thin maps of rank eight per two-port block. Every Laurent coefficient passes. Its 104-port bill charges 6656 rank-one thin queries and has linear margin -3472, so every concave moment loses. This is not a native supplier.Normal and optimized registered checks, five corrupted-package controls, all 25 committed files, export integrity and a sealed read-only Git-free replay pass. Evidence includes 216 exact polynomial prefix updates, 2700 local systems with 104 strict dimension drops, the complete 128-field endpoint, and 66 F4 interpolation assignments including the earlier noncommuting escape word. Exact receipt and source pins. Finite controls support the written proofs; no human or proof-assistant acceptance is claimed. Hosted CI run 40349357577 passed both the planner and the registered package replay, including the unchanged-input check. Full source-history preflight was not run because the two open predecessor commits are explicit provenance outside this fresh-main ancestry.
The next construction must change the contract. At 31 leaves, five rank-q maps require q>=20. A 26-port block divides 104 ports and has a favorable optimistic .0035 price. A 13-leaf, eight-port, five-map profile also passes a .0034 screen. Both need noncommuting full projectors and remain unconstructed. Two small coupled-seed searches with all call orders free timed out; they remain unknown. Native frames, physical reads, owned/borrowed state, COPY/CLEAR, dirty compensation, restoration, routes, precision, compiler and outer transfer remain explicit obligations.
Base main was
df0137efd35e11b4445734bf612bdd4c7ebc330c. Submission refresh reached553d26d796fde9871ff2661a49ac7732e945410f, with entry guidance, priority seven, selected .00310045 and the consumed tariff unchanged. The active local P104 and G20 scopes remain separate. No frontier change, merge or closure occurred. This scope is released.Credit Cinna Davis, PR5617/5631/5649/5673/5681, PR5701's separate lift qualification, and the retained P104/helper/native/compiler source authors. Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0.
{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"coupled31-chronology","scope":"Chronological dimension and rank bound, uniform paired-star tariff ceiling, sharp commuting map count and full 31-leaf binary endpoint","base":"df0137efd35e11b4445734bf612bdd4c7ebc330c","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5747"}Earlier evidence: one-sided proof, PR5673, static sharpness, PR5681, fixed four-connector proof, PR5649, and query-Gram cuts, PR5617. Their source pins, attribution and exact scopes remain in their packages.
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