← Lebesgue Universal Covering Problem / II · Computation and Reproduction / UESFCM · Unbounded Expansion Self-Referential Closure

Lebesgue Universal Covering Problem II · Computation and Reproduction UESFCM · Unbounded Expansion Self-Referential Closure 懸衡 (Xuán Héng) NOT ESTABLISHED NOT AS STATED PARTIAL PASS

UESFCM: the method and its seventeen Lebesgue cycles

The seventeen cycles chain cleanly and never mark evidence as proof; every certificate passes again in exact arithmetic, leaf by leaf. The main counter-result is root 6217: the ρ₅ = 0 reduction drops the F3 constraint, so "Gate 6217-A: CLOSED" is not established (it holds numerically, by 2.05×10⁻⁴); and 44 % of root 6217's box was closed only by Cycle 11's search.

NOT ESTABLISHED · NOT AS STATED · PARTIAL · PASS This page is the second layer: the finite claims of the layer-1 document "UESFCM · Unbounded Expansion Self-Referential Closure" recomputed, its constructions reproduced, and its theorem-level steps read against the source. It does not rewrite the document and does not treat numerical results as proofs; the formal paper written from these two layers is the third layer, "III · Crystallization". Below are the recompute reports as written (byte for byte the research tree's), with their code and gate logs.

Connections

I · Precursor (the document)UESFCM · Unbounded Expansion Self-Referential Closure · UESFCM v0.1 (Unbounded Expansion–Self-Referential Finite Closure Methodology): Anchoring Unbounded Method Search onto a Single Fixed Target Proposition Q* via Mandatory LinkBack Classification and Finite Closure States
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Recompute reports · Runs

RUN-043UESFCM: seventeen Lebesgue cycles chain cleanly and never mark evidence as proof, but the target they anchor to is written down nowhere in the archive, the LinkBack types are used in one cycle, and the texts disagree on which states end the loop

Verdict: PASS for fourteen of UESFCM's fifteen judgments, PARTIAL for "Problem Closure: DEFINED". The other twenty are labels.

The report, the code and the gate log: report RUN-043.md · run043_uesfcm.py · gate log run043-uesfcm.json

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RUN-044UESFCM Cycles 01–03: the B7 separator LP reproduces to the last digit and the domain constants to the ulp; the "sharp root domain" is Mishra's Remark 20, which he notes saves no boxes; s7, the replacement family and the sublevel's thinness come out different from Cycle 03's figures

Verdict: PASS for the three cycles' theorems and for every number they compute from definitions. Three things differ from what the cycles report (see the report).

The report, the code and the gate log: report RUN-044.md · run044_uesfcm_cycles_01_03.py · gate log run044-uesfcm-cycles-01-03.json

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RUN-045UESFCM Cycles 04–06: Gate A's dual certificate holds under this tree's own integer intervals, but its verifier skips two premises; the D3 quotient, the symmetric anchor and the box bounds are right; the far-branch minima reported are search values that sit above better points

Verdict: PASS for every theorem of the three cycles and for Gate A's certificate. Two premises of that certificate are left unchecked by the verifier shipped with it. The far-set minima the cycles report are search values, and each sits above a lower point found here.

The report, the code and the gate log: report RUN-045.md · run045_uesfcm_cycles_04_06.py · gate log run045-uesfcm-cycles-04-06.json

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RUN-046UESFCM Cycles 07–09: the saved F3 frontier, its 24 skeletons and 1,332 signatures, the 12 reflection classes and the Taylor diagnostic all reproduce from this tree's own hull; the compilers they motivate ship as interfaces only

Verdict: PASS. Every number these three cycles compute on the saved frontier reproduces from this tree's own hull: the membership, the centre areas, the skeleton catalog, the reflection classes and the Taylor margins. The compilers they propose ship as interfaces with the proof steps not implemented, so the frontier and all the diagnostics come from code that is not in the archive.

The report, the code and the gate log: report RUN-046.md · run046_uesfcm_cycles_07_09.py · gate log run046-uesfcm-cycles-07-09.json

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RUN-047UESFCM Cycles 10–11: both erosion certificates decode exactly and all 56,149 of their area leaves hold in exact arithmetic with this tree's exact cores, by at least 2.28×10⁻⁵; the least slacks and η_model reproduce, the float split leaves 10⁻¹⁸ gaps that continuity closes, and Cycle 11's verifier cannot run from its own package

Verdict: PASS. Both certificates decode exactly and every count they state reproduces. All 56,149 area leaves also hold in exact arithmetic with this tree's exact cores: the tightest clears A3+ by 2.28×10⁻⁵, where the certificates' own least slacks are 3.8×10⁻⁸ and 2.5×10⁻⁹. Three things are noted (see the report).

The report, the code and the gate log: report RUN-047.md · run047_uesfcm_cycles_10_11.py · gate log run047-uesfcm-cycles-10-11.json

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RUN-048UESFCM Cycles 12–14: root 6217's three certificates replay and hold in exact arithmetic, and the symmetric triple contact reproduces to 80 digits; but the ρ₅ = 0 reduction drops the F3 constraint, so Cycle 13's 2-D certificate leaves the arc side of the slice uncovered — there the least area is again the contact point, so Gate 6217-A holds numerically and is not yet proved

Verdict: PASS for the three certificates and the contact; the rotation profile holds as a search. NOT ESTABLISHED for Gate 6217-A: the ρ₅ = 0 reduction of Cycles 12–13 does not keep the F3 constraint. So Cycle 13's certificate covers only part of the slice, and so does the "Gate 6217-A: CLOSED" that Cycle 14 and both crystals carry.

The report, the code and the gate log: report RUN-048.md · run048_uesfcm_cycles_12_14.py · gate log run048-uesfcm-cycles-12-14.json

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RUN-049UESFCM Cycles 15–17: the boundary-locking lemmas hold, both upper references and all three certificates reproduce, and all 115,511 area leaves hold in exact arithmetic; the references are loose to first order, Cycle 15's counterexample falls for only 1.6×10⁻⁷ along its ray, and "all other regions eliminated by finite certificates" includes 44 % of root 6217 that only a search closed

Verdict: PASS. The lemmas hold. Both upper references reproduce, and all three certificates decode and pass leaf for leaf. All 115,511 area leaves also hold in exact arithmetic, each against its own threshold, the least by 2.66×10⁻⁵. Three things are noted (see the report).

The report, the code and the gate log: report RUN-049.md · run049_uesfcm_cycles_15_17.py · gate log run049-uesfcm-cycles-15-17.json

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