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Prove a sharp 104-coordinate owner-local centre repair floor - #2461
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DONE — published exact artifact: #2598 at The conditional whole-payload observation theorem proves an additional 104*d complex dimensions per old owner. Both complete local orientations, every used native child/endpoint factor, and the pure-T backward query were checked; separate AI review independently reconstructed the query cuts and tested different payload maps. The global application retains the explicit equal-full-payload/invertible-view contract. No physical repair invoice, global compiler, recursive supplier or new exponent is claimed. Original advance claim retained below. CLAIM — full-payload owner-local observation lift, LOCAL-ONLY. UTC 2026-10-15T15:19:41.055093+00:00; expires 2026-10-15T16:19:41.055093+00:00. This is a bounded follow-up to PR2461 at Question: can the sharp 104 additional scalar-coordinate floor on constant payloads lift to 104 full payload-array equivalents, with an explicit native operator factorization? The source probe shows that all eight backward centre rows have zero source/helper coefficients and target coefficients exactly R/4. A possible proof would combine the first complete native source-to-target block, old-query conjugation, and the 112 distinct owner routes to establish a direct-sum rank of 112 times payload dimension, against eight saved arrays. These native hypotheses must be checked; the constant-input theorem does not supply them by itself. The intended result is an information-dimension theorem and sharp abstract recovery map in the same owner-local observation contract. It would not price 104 recursive children or rank units, supply native access/storage/restoration/hosting, prove a final-output-only bound, change the selected result, or rebuild the global 73-axis compiler. If the operator lift fails, retain the exact failure and narrow the result rather than promote scalar evidence. Overlap: complete cached 679-PR / 1,197 Discussion-record snapshots through 12:25 / 12:29 UTC, supplemented by fresh source PR comments and 100 recently updated open PRs. Cached discussions may miss newer claims. PR2048's different disjoint-forward-pair native lift, PR2199's calls-only census, and PR2461's constant slice are credited rather than repeated. Prepared for ywz65 with substantial OpenAI Codex assistance. Independent review will precede result publication. |
…t (answers #1166 c18956869) In the PR1664 scalar common-frame transport model, holding an array at a fixed frame is free (Lemma 2). The moment charges frame catch-up, exactly min over meeting levels of rho_r|L-h_r| + rho_p|L-h_p| + rho_o|L-h_c| (Proposition 3, both directions, consumer explicit). The pinned #1094 template advances every pair through nine 8-coordinate levels (own call or idle sweep), so a record consumed at its family's current frame pays 8 x levels advanced per independent row (Corollary 4). - Law vs conventions: equals (C)'s mass when the family advances one level per lifetime call; 0 for pair-3 Y streams across six calls (S 6, C 48); 48 vs C 24 for a deferred pair-0 record; (S) under-prices PR2540 16 vs 128. - INIT64 + d_A (P_final, P_rank, P4): 3648 units/replica >= 896 no-saving threshold, rejected under either convention; d_A alone 960; cheapest 62 stated captures 1952. Published (C) 3712 = law + d_A,0 lifetime off-by-one. - Gap-1 centre sharing (f0->f2): prior information obstructions (PR2199, #2391/#2461) plus catch-up >= 64 per set; rejected. - QQ16 retained caller: retention row = its 16 H8 (128), proved under rho = 16 and attained; dominated in the moment by pending #2707. - Pricing reproduces the #1166 break-evens 573 (S) / 71 (C) with pinned ceiling.py and independently with Decimal; frame model checks 10,748 + 4,044 instances by BFS and 2,432 by echelon Dijkstra; 12 + 2 controls. No new kappa, no supplier, selected frontier unchanged. Physical storage remains UNKNOWN. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Relabel as a research note (scoped lemma + conditional negative result) and state the stakes, base commit and premises up front. - Route (a): make the observation contract explicit (P_obs) and restate P_rank modulo everything the contract lets the consumer combine. Price the published all-initial variant (#2074 c18950926): 3456 end / 1152 earliest decoder, cheapest-62 1824 / 608 (kappa cap 0.0015234 < selected). Cite the price-gate capture times and check that local calls/bridges force them. Write the per-cut Theorem B argument with its premises. - Route (b): no predecessor information obstruction exists for f0->f2 (PR2199 OQ2 open; #2391/#2461 cover f0->b1 only); the no-gain verdict now rests on catch-up alone, under stated premises. - Route (c): reduced to the one-charge clarification; the #2707 comparison is credited to #2707/PR2681 and the maintainers' review (incorporated on main). - Withdraw the "48 vs (C) 24" lagging-pair example: X_(0,U) is last written at event 6, so the record duplicates an observed row (rho_r = 0). Checked, with a control. - Corollary 4 stated in coordinates with rho_r modulo available rows; hosting checked at all 17 route instants (2,300 distinct slots), and independently by a per-family hosted height replay under both tie conventions. - Frame model: GF(2)^3 now complete (34,454 instances). Independent controls rejected for their stated reasons, count enforced. PRICE-GATE.json storage ceiling reproduced exactly. Credit PR2511, PR2681; full fork SHAs recorded. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5); reviewed only by AI passes in the same automated loop. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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PR2391 leaves additional old-chart observations as a possible repair for selected centre reuse. This contribution proves a sharp lower bound for one explicit repair contract: recovering the entire later query field requires 104 additional scalar coordinates at each old cover owner when each new observation depends only on that owner's initial 112 source values. The decoder may subsequently mix all observations across owners. This is an information bound, not 104 recursive children or rank-mass units.
The new source-bound step is that all 112 selected stage-1 routes are distinct and every later coefficient column is nonzero. An input supported at one old owner therefore has a rank-112 later-field image, against rank eight in the saved first transcript. An explicit 104-coordinate extension attains the information bound. For one output owner, the distinct subsidiary minima are 112 owner-local evaluations versus eight arbitrary aggregate scalars; the README separates these contracts.
Adds only
research/centre-owner-observation-floor/. Main:0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Selected record and frozen sources are unchanged. Exact Git/SHA-256 source pins and four full-path archive-member pins precede decoding. The receipt contains 112 exact kernel witnesses, all route digests, the two coefficient matrices, and the sharp extension.Validation (Windows, CPython 3.12.14):
The registered replay passes the exact emitted-program checker, an independent canonical-word reconstruction with rational kernel checks and modular nonzero minors, and four semantic corruption tests.
git diff --checkalso passes. The prescribed first ceiling and lever screen were run; no changed centre profile is claimed.Native interpretation remains conditional on the inherited common-frame/source-adapter, constant endpoint, and local-view identities in PR2048/PR2391. This package does not run a native evaluator, global compiler, complete cold replay or Lean. No physical access, hosting, restoration, storage, precision or recursive cost saving is supplied, and no supplier/kappa change is claimed. Mixed-owner acquisition, nonlinear encodings and final-output-only contracts remain outside scope. The next question specifies an explicitly priced mixed-owner observation and tests all retained kernel witnesses.
Credit Aaron Wang/navinor (PR2391
5efcbb6058d27aa8b988db8f18c7b678166b2783), commdata2338 (PR2048a0e55f357344f1742f72942f94ae2a6f13ff7065), Sagar Thakrar (PR219930ec048eedcaca970f94bbec0fdd3c52eacf9fdcand Clifford conventions), Adam Gall (PR1918), DreamingOfClouds, and the selected lineage of Rohan Arun/Jeremy Kothe/Hao Yan/icekylinx. Prepared for ywz65 with substantial OpenAI Codex assistance in research, proof, implementation, writing and separate AI review. Apache-2.0; no independent human or formal review claimed.