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Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation - #5377
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DONE — independent conditional validation PASS; the bounded review claim is released. HANDOFF Research discussion / PR / artifact: #5384 — package Exact commit: Audit publication What is established: Independent reverse/all-column physical and owned-return checks, literal complete 64,372-paid/10,912-target census, new directed rational moment/compiler/tail/54+4 outer checks and constructive new-template specialization support conditional κ What remains uncertain: The five retained native/owned/compiler/precision/analytic foundations are not independently discharged; no enormous uniform word is materialized. The fixed-profile ceiling makes no statement about other relations, controllers, inventories or physical words and is not an attained funded endpoint. Publication does not itself admit a selected frontier. Smallest useful next task: Read the physical and constructive specialization reports and try one concrete missing implication/counterexample against this exact head. For further improvement, specify a changed independent helper contract and complete paid invoice before synthesis, or select one named retained foundation for separate source-pinned review. Stop after the chosen implication; further digits or equivalent evaluation of the same root add no mechanism coverage. The published eight-centre successor #5383 at Reproduction command and expected runtime: Predecessor credit: Ali Romman for the changed construction; Cao Yifan for PR4610; Cinna Davis for controller/helper lineage; zxv for native/compiler/precision machinery; Jacob Alan Sussman for mixed-target recursion; Chris R/Clear1nsight for PR5241 independent admission; all retained native/BIT/phase/physical/analytic predecessors. Independent review by Chris R / Clear1nsight, with substantial OpenAI Codex assistance; no independent human/formal-kernel acceptance claimed. {
"schema": "integer-mult-coordination/v1",
"kind": "DONE",
"task": "independent-moment",
"scope": "Independent exact-head PR5377 conditional physical, complete-cost and same-premise applicability audit with scoped fixed-profile ceiling",
"base": "1ec1119972c9aefe42525172d07b332fcff81cb4",
"expiry": null,
"artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5384"
} |
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Independent reproduction of the two source identities and the complete bill (Mark / Matarener, local run on Windows 10, Python 3.12). No new κ.
Not covered here, as in the whole chain: owned erasure of the nonzero C0 content, phases (receipt reused), compiler/precision/tape, BIT. Scripts: |
This construction gives conditional κ = 60447/20000000 = 0.00302235, a gain of 0.0000005742 over Cao Yifan's final PR #4610 value, 0.0030217758. It changes the complete paid profile and moves its raw crossing. The selected frontier is unchanged.
The proof and complete bill, exact result, literal word and source pins define the review scope.
In each backward call, make L230 private and prepare
h230 = h324 - h326 - h328 + h333from four arbitrary cold helpers. Debit its rank-nine productive output. LetDelta = h230 - h324 + h326 + h328 - h333. Exact replay of the unrestricted source givesC0 - saved_L92 = Delta/4at center event 11332, andL92 = -Delta/4at climb event 15584. The saved value is taken just after event 11205 in the same frame as the center output. Under the prepared relation, one owned copy replaces the rank-eight job, and physical identity on a proved zero row replaces the rank-one job. All event indices are zero-based.All 224 main inputs and the other 407 backward helper inputs remain arbitrary and independent. Every retained output keeps its complete source operator. Forward calls keep all 408 helpers. Explicit clears remove arbitrary owned entry values and erase every private output. One new private slot and 46 additional scalar operations per backward call are charged. Every retained Gaussian operator, native map, frame gauge and main adapter is unchanged.
The p16/a7 controller has 16 backward calls, two forward calls and 15 query shears. Its complete difference is −16 H1 −16 H8 paid jobs and −16 H9 targets. For every
0<t<1, the target-minus-paid moment gains16(1+8^t−9^t)>0. The new bill has 64,372 paid jobs, 10,912 productive fields and rank surplus 752, with every main, idle, query and completion term included.Two rational interval engines check the complete bill. The fixed-profile crossing lies in (0.00302238736347, 0.00302238736348). The claimed κ leaves more than 0.00000003736347 raw headroom. The separately tested saving is 0.00302236. Both completion tails, the finite compiler at
N=2^31385200000000, and all 54 strict plus four functional outer predicates pass. The complete raw nonrecursive bound remains 181,098,496 < 10^9.Base: canonical main 7c472563474e60185e6ca101a17622133d047e56, priority revision 7. The source is the final PR #4610 word at
20bb93cd990d2ff683e4d0fc56b87a42cd5d3296; all consumed bytes are in the recorded main base. The scoped Discussion claim distinguishes this changed inventory from the original-input cache and all-helper-return investigations. Live PRs and Discussions were checked again before publication.Use standard-library Python 3.12 from the repository root:
Both registered normal and optimized replays pass:
Verification covers exact free-word rows in both source and candidate orientations, all independent and owned entry columns, frame/rank checks, two separately computed source identities, the p16 Laurent factorization and scalar boundaries, independent full invoice counts, two rational interval engines, the fixed-profile ceiling, compiler and outer inequalities. Seven native and five cost/outer controls reject wrong relation, ownership, snapshot, gauge, rank, helper credit and compiler assumptions. Metadata, committed-byte checks, official export integrity and Git-free replay also pass. The optional full-history preflight is not claimed in this shallow checkout.
The source absolute-phase receipt is authenticated and reused. New operations are same-frame scalar operations, owned copies/clears and identity on zero; there is no new Gaussian phase recipe. Full source phase lowering, BIT native replay, Lean, Docker, physical tape/precision execution, analytic decomposition and integer recovery were not rerun. The bound retains the source permitted-erasure, whole-job, mixed-target all-size, native, precision, tape, analytic, prime and exact-recovery contracts. It is a conditional construction with exact finite evidence, not an unconditional theorem, practical speedup or independent human acceptance. The compiled word is algorithmically specified and not materialized.
Cao Yifan supplied the source construction and prior κ in PR #4610. Cinna Davis supplied the p16 controller and helper lineage in PR #4470. The pricing source retains zxv's completion/compiler and Jacob Alan Sussman's mixed-target credit; Dugongue's transported frames and the wider native lineage remain credited. zxv's PR #5283 supplied the cache-contract handoff to find actual matching rows and lifetimes; its standalone example is not used here. The new result is this helper relation, its exact native realization and its complete positive bill.
Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Next review task: check the three source rows and COPY/zero argument, then the inherited transfer assumptions. No broader helper-relation search is claimed.