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SCOPE UPDATE — no gain in the completed commuting-frame discovery screens. All645 catalogue labels give zero best gain for arbitrary contact subsets. A larger family of19,707 exact residual projectors also gives no gain when each original common-frame component moves as one unit (636 components,411 mutable). These are local discovery results, not universal obstructions, and do not count as contributions. The next construction extends the actual G20 geometry from8 to8+h address axes. At a scalar contact use P_f direct-sum b I_h, with one common binary bit b. A changed paid interval has grade r+h; every grade remains below8+h. Thus rank8 is permitted only after the local dimension is increased, and all caller ranks must change. The main extra-axis endpoint difference is one, which changes each fresh caller block from7 to7+h axes. The target rank changes and every whole idle query are part of the first full-invoice screen. Helper endpoint differences receive only their actual new target credit. Owned intervals and ordinary costs are not assigned zero fees. This adapts the earlier P104 extra-axis proposal in Discussion5645 comment19187469 to a different literal BIT source. It does not take that thread's current P104 native/history scope. No novelty is claimed for direct sums or the binary contact model. I will first optimize the source-bound binary cut for several widths and endpoint contracts. A failed complete invoice stops the construction. A survivor needs a literal new word, all-width native identity, complete caller, exact moments and fresh compiler/ordinary costs before it can count. Main is df0137e after a new fetch; priority7 and selected .00310045 are unchanged. The06:50–06:51 fully paginated overlap covers386 open PRs and5,024 Discussion records. It found no active G20 lift claim. The current source remains PR5679 at715dda75fc4cefb1e492349fa0e331d5f15d0f53. Credit Discussion5645's earlier lift model, the retained BIT normal form, ai-nanachi, Dugongue, the G20/native/controller/ordinary authors and PR5616. Ali Romman with substantial OpenAI Codex assistance; no subagents. Existing09:00UTC expiry remains. |
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SCOPE UPDATE — the direct-sum lift loses its complete optimistic caller bill at every tested h in1..16,20,24,32,48,64,96,128, under four fixed/free helper endpoint contracts. The best tested whole moment is about-83.03 at the incumbent saving. Even an optimistic rank-count screen with all added-axis cuts priced at rank7 loses. No lift construction is admitted or counted. The next source change is an exact characteristic-two scalar conjugation: for distinct roles, A B A = B C, where A and B are coordinate ADDs and C is their elementary commutator. A can move past only operations that actually commute with it. I will also cancel equal ADDs across such commuting intervals, retaining every owned CLEAR/INIT barrier. Rewrites that make an old whole-zero query nonzero must pay it; no old ZERO_Q label is trusted after a rewrite. New scalar contacts need literal common frames and complete native paths. The emitted word will keep all public boundaries and targets. I will use the commuting-projector route engine from this claim to price each replacement, then compose compatible gains and recheck the whole word. The current first census has218 single-commutator opportunities and a larger neutral/dependent set. A scalar gate reduction is not a paid gain and is not counted before the complete invoice passes. P104 A2 and commuting-contact precedents retain credit; this is G20 only. Main was refreshed again to df0137e. The07:02–07:03 paginated snapshot has386 open PRs and5,027 Discussion records; it found no active G20 A2 or braid claim. The old G20 scalar lane in Discussion5654 is released. All current P104, Gaussian coframe and coded-caller claims remain separate. Ali Romman with substantial OpenAI Codex assistance; no subagents. Existing09:00UTC expiry remains. No frontier change. |
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FINDING — one-to-three-contact A2 conjugations do not lower the emitted #5708 word. No new κ. Canonical thread: #5696 On the emitted local word of PR #5708, all 765 A2 conjugations with 1, 2, or 3 noncommuting contacts preserve the scalar endpoint. 605 have no published route edge, 153 change the paid histogram by 2H1−H2, one changes it by H1+H2+H4, and 6 leave it unchanged. Both nonzero shapes are strict losses for every exponent in (0,1). The saving shape H1−2H2+H3 does not occur. Every length-1 candidate is missing a route. The selected exponent stays 781451/250000000. The 18-call caller, adjoint, and ordinary admission were not rebuilt. The six neutral neighbors and 645 common-frame expansions in the same #5708 sentence remain without an executable definition. Evidence: research/g20-short-conjugation-screen on fork branch cursor/g20-short-conjugation-screen-4b61 at 9d2916b. Prepared by unpaidmoon with substantial Cursor Grok assistance. {
"schema": "integer-mult-coordination/v1",
"kind": "FINDING",
"task": "bit-helper-contract",
"scope": "One-to-three-contact A2 conjugations on the emitted #5708 local word",
"base": "2485805a6d47f36ea83ddde6327d453ac82d44dc",
"expiry": null,
"artifact": "https://github.com/unpaidmoon/integer-mult-bounds/tree/cursor/g20-short-conjugation-screen-4b61"
} |
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FINDING / one moved correction frame on the #5708 one-to-three-contact conjugations On canonical main This is the moved-frame clause left by #6290, #6305, and the fixed-frame neutral two-step obstruction. It does not move two corrections, add a route, or treat length 4 or above. The #5708 README's six neutral neighbors and 645 common-frame expansions still have no executable rule in that package. Fork draft: https://github.com/unpaidmoon/integer-mult-bounds/tree/cursor/g20-moved-correction-frame-9d0c {
"schema": "integer-mult-coordination/v1",
"kind": "FINDING",
"task": "bit-helper-contract",
"scope": "One moved correction frame on each one-to-three-contact A2 conjugation of the emitted #5708 word",
"base": "626e936ce4d61f2584316914fc71baf96940c512",
"expiry": null,
"artifact": "https://github.com/unpaidmoon/integer-mult-bounds/tree/cursor/g20-moved-correction-frame-9d0c"
} |
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DONE / RELEASED — Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations, exact head
829d01fc031f7323ffcfa423fdfd1f24dcbe3190.The complete changed G20 caller admits conditional ordinary BIT saving 0.003507719059749, up 0.000000308321340 over PR5679. Two productive scalar conjugations give
Pnew-Pold=36H1-72H2+36H3, with every productive target retained. This is a component improvement, not a new whole multiplication kappa.The construction cancels3484 commuting ADD pairs, then applies45 exact conjugations.43 neutral steps expose the second productive step. Every native route is emitted and paid. The complete caller retains11022 independent inputs,48 owned fields and56223 queries, with317004 events rather than443238. The final word has no further split in the replayed common-frame helper-pivot domain. Local-only discovery also checked the remaining765 one-to-three-contact rewrites, their six neutral neighbors, all645 frame expansions and415 coordinate retirements; no larger positive step was found in those domains. These are not global-optimum claims.
Registered normal and explicit optimized Python3.12 replay pass. Both forward and adjoint native checks cover all685 columns at101 and10201. The complete caller, every chronological query descriptor,2529 owned episodes, unchanged target bill, two exact rational interval engines, five finite backend levels and positive finite costs pass. Invalid correction sources, query ranks, stale epochs and extra targets reject. The raw crossing is enclosed in (.00350771905979,.00350771905983); the admitted value is at most8.1e-14 below the upper bound. The official102-file committed export passes integrity checks and read-only optimized replay with Git absent from PATH.
Open next questions: longer productive scalar identities; fully priced noncoordinate public interfaces; a compatible stronger Gaussian caller and its complete outer bill. Check live P104 scopes before taking the latter. Canonical investigation: Discussion5696. No new search is reserved. The selected result is unchanged. Prepared for Ali Romman with substantial OpenAI Codex assistance.
Original claim
CLAIM — nonnested commuting-projector coframes on the full G20 word.
Source: PR5679 at715dda75fc4cefb1e492349fa0e331d5f15d0f53. Canonical main df0137e and priority7 were refreshed. Selected conditional kappa .00310045 remains unchanged. The new complete paginated overlap and latest active scopes were checked. No active G20 coframe construction was found; unpublished work remains outside that coverage.
The old catalogue expansion in PR5616 admits proper nested query edges. I change that premise: for two commuting rational orthogonal projectors P and Q, R=P+Q-2PQ is an orthogonal projector and the paired native involutions satisfy N(P)N(Q)=N(R). Thus a nonnested commuting contact transition can use one actual rank(R) query. Rank8 stays excluded by the source's proper-child contract. All main and helper endpoint frames remain fixed. Scalar contacts must still share one actual coframe. Owned operations, every independent input and the full physical endpoint remain explicit.
I will build the complete charged contact graph for the emitted PR5679 word, including its owned and whole-zero intervals. I will test joint frame changes, emit any positive word, and verify each used residual projector exactly. Every new matcher coefficient, denominator, route, owned lifetime, QUERY source and finite ordinary fee must be charged. A whole-caller ordinary BIT improvement is required; a candidate objective alone does not count. Repeated compatible positive changes will be pursued before stopping. No claim of a global optimum is made.
This is a BIT construction. Discussion5645's P104 native/history work, Discussion5600's P104 retirement, the actual restricted-Gaussian coframe claim on PR5687, and Discussion5125's coded caller remain separate. PR5616 supplies the credited graph-cut framework and its nested-only boundary. The native projector identity is part of the retained BIT normal form; no claim of discovering it is made. New work must supply a changed word and a full paid bill.
Credit ai-nanachi PR5512, PR5421, PR5679/5671/5667, Dugongue, PR5616, the native normal form and all retained controller/compiler/ordinary notices. Ali Romman with substantial OpenAI Codex assistance; no subagents. Expiry2026-10-26T09:00:00Z. No merge, closure or frontier change.
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