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Prove an unbounded FULL/QUERY controller ceiling (no κ gain) - #5405
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DONE / HANDOFF — independent verification published; first hosted CI passed. Research discussion / PR / artifact: PR #5409, Exact commit: What is established: Independently checked directed-rational C18>0, C18−C17<0 and C19−C18>0 at κ=.00302728825. Frozen analytic exchange reduction plus strict discrete convexity over all n>=0 make n=18 the unique minimizing FULL count and close fixed-κ positivity for every equation-(1) invoice. A separate normalized whole-invoice monotonicity proof extends positivity to .00302728825<=κ<1. Exact symbolic invoice controls cover 456 tiny masks/splits and 11 canonical counts; five surgical numerical/accounting mutations reject. The independent auditor issued PASS_SCOPED_FIXED_FAMILY_CEILING. V3 explicit acceptance works under normal/O Python; raw v1/v2 code/receipts/logs and the correction remain unchanged. Source monitor is exactly original+one LF; both forms and explicit bridge remain retained. Registered normal/O pair passed 1.494s, empty stderr, all 69 inputs unchanged. Final Git-free normal/O pair passed 0.327/1.042s with PATH empty, no .git and all 70 export files unchanged. What remains uncertain: Source equation (1), autonomous P/H profile and family interpretation are premises; their derivation from original Laurent/native/physical programs was not replayed. No native/compiler/supplier admission, physical/global optimum, new κ, PR5402 transfer, human/kernel acceptance, selected-record change or hosted-CI equivalence. The registered pair ran before eight raw logs were explicitly retained in Git; all were already present/authenticated. Mandatory REGISTERED-COMMITTED-BYTE-BRIDGE.json proves final wrapper/inventory identity and only eight log additions; final export pair executes the sealed bytes. Earlier incomplete transport archive/receipts remain under pre-log-retention-*. Smallest useful next task: Review the published analytic derivations and independently replay the small certificate; report any missing implication on PR #5409. The pre-submission source and overlap refresh found no changed source or competing published verification through 23:51:56 UTC. Do not repeat author DP/native/cold/Lean work or expand into changed-profile PR5402. A separate human/formal reviewer may inspect the retained analytic derivations; a changed mechanism needs a new complete invoice. Reproduction command and expected runtime: Predecessor credit: Ali Romman original PR5405 family/invoice/ceiling/DP and owned/transposed profile; Cinna Davis controller/helpers; Cao Yifan native source; zxv interval/preflight/compiler/precision; Chris R prior controller/admission; Dugongue, Jacob Alan Sussman and every retained native/helper/compiler/analytic notice. Root conjectures and sole Astra frozen theory proofs remain credited. New independent numerical work, audit and packaging by Chris R / Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0. No new construction priority or independent human review. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"independent-moment","scope":"Independent exchange/discrete-convexity and exact rational verification of the pinned PR5405 fixed-profile unbounded ceiling","base":"1ec1119972c9aefe42525172d07b332fcff81cb4","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5409"} |
This scoped proof puts a ceiling on the entire prefix/suffix FULL/QUERY invoice family with the current owned local profile: no pair count, split or stage mask can fund
0.00302728825 <= κ < 1through its strict moment test. No higher κ is claimed. This removes the pair-count and stage-neighborhood limits of the earlier checks.The proof, exact receipt, verifier and source pins define the review object. The current complete conditional comparison is κ = 0.00302728823, from PR #5398, with independent validation in PR #5400. Its remaining room in this family is less than
2e-11; this package does not rerun that positive admission.The proof fixes the local paid/helper profiles, 112 ports, rank-eight stage blocks, rank-one query price and prefix/suffix idle law. A concavity bound rejects every allocation with at least 96 FULL stages. Deleting pairs of QUERY stages reduces the remaining unbounded family to at most 96 pairs. An integer dynamic program checks all 10,290,000 remaining state combinations. The minimum certified paid-minus-target margin is greater than 0.000000014914967918767741908079, at the current p16/a7 invoice. A separate monotonicity argument extends the sign from the tested saving to the full stated interval.
This covers all masks and all pair counts, unlike the at-most-two-stage screen in PR #5393. PR #5397 supplies the related fixed 144-exchange invoice ceiling. It does not exclude another native profile, connection graph, idle law or recursive contract. In particular, the coupled outputs of PR #5402 require a different completed caller and are outside this theorem.
Base: canonical main
1ec1119972c9aefe42525172d07b332fcff81cb4, priority 7. The exact PR #5392 result at329b2ff35d2994b11abbb59f770d12da75c494acis retained byte for byte in this branch's ancestor6919161525e69b687630cb6468aa32b9414d7206. Replay needs no pending predecessor checkout. The selected frontier is unchanged.Python 3.12 and the standard library:
Expected result in both registered modes:
Normal and optimized registered replays pass. Checks include source authentication, exact outward rational arithmetic, the infinite-tail inequalities, the complete dynamic program, 15 exact Laurent factorizations and all 12,744 masks through five pairs. The literal invoices and exhaustive minima agree with the new formula and dynamic program. Controls detect an omitted idle that falsely funds the moment, unearned helper credit and the middle-idle charge at an even FULL stage. All 16 committed-file bindings and official export integrity pass. An optimized read-only replay with Git absent passes; all 17 exported files remain unchanged. The optional full-history check is unavailable in this shallow checkout; direct base and retained-source ancestry checks pass. Hosted CI run 40037676191 passes at the published head.
The native phase suite, complete compiler/outer and selected cold replays, physical tape execution and formal kernel were not run. The cited positive bounds retain the five selected framework assumptions. This is an author-checked mathematical ceiling for the stated invoices, not a global circuit optimum or a new multiplication theorem.
Credit: Cinna Davis (@1337isnot1337) for the controller, Ali Romman (@aliromman) for the owned/transposed profile, Cao Yifan (@intqwq) for the native source, @zxv for the reused interval engine and invoice preflight, Chris R (@Clear1nsight) for the earlier stage screen and independent admission, and @Dugongue for the frame and compiler lineage. The retained source notice preserves Jacob Alan Sussman and the earlier native, compiler and analytic credit. New proof and dynamic program by Ali Romman with substantial OpenAI Codex assistance; no subagents; Apache-2.0.