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Lebesgue Universal Covering Problem DLMVC · Deep-Lag Verification Methodology Neo.K

DLMVC v0.1: A Deep-Lag Multi-Pass Verification—Closure Methodology Deliberately Desynchronized from the Frontier Line — Its First Field Audit Already Supplies Lebesgue Universal Covering Round 01 with a Missing Lemma and Falsifies One Active-Direction Classification

DLMVC v0.1 (Deep-Lag Multi-Pass Verification & Closure Methodology) is not a mathematical proof technique, but a general research topology and verification methodology for mathematical research that is multi-AI, long-duration, multi-round, asynchronous, correctable, and traceable: a Frontier/Canonical Line that continuously advances the canonical theorem chain, running in parallel with a Deep-Lag Verification/Expansion Line that is deliberately desynchronized from the main line, with the core thesis that “controlled desynchronization is itself a verification resource.” Lag is no longer measured only by round count, but is defined as the three-dimensional vector D_lag = (D_round, D_time, D_structure); every verification Target must declare a formal blindness-provenance state (BLIND-CLEAN / PARTIAL-EXPOSURE / CONTENT-EXPOSED / POST-HOC), and once the verification line reads substantive downstream content from the main line before completing independent verification, the contamination rule is triggered — it may no longer claim strict blind verification and must be downgraded, though the research is not thereby invalidated. The methodology further provides a tiered Deep-Pass Ladder, with each Pass outputting formal classifications such as INDEPENDENT-REPRODUCTION, CORRECTION, COUNTEREXAMPLE, and EXTENSION. v0.1 is honest and restrained about its own standing: Empirical validation is explicitly marked PARTIAL, and it does not claim to have already been universally proven the best multi-AI mathematical research workflow. Its first field application — Verification Round 01, applied to Lebesgue LUC-FC Round 01 — independently reconstructed the convexification–constant-width–support-function simplification chain, closed a genuine proof-graph gap with the new Lemma JPA-01, and falsified the geometric possibility of “only one active direction,” thereby correcting the active-direction classification; this round itself also accidentally read a future State Crystal due to a file-access error, and the contamination rule immediately marked its own STRICT-BLINDNESS as COMPROMISED, honestly downgrading its independence claim rather than concealing the exposure — an instance of the safety mechanism operating exactly as designed. Elsewhere across the full DLMVC audit trail, there is also an existing record of a round that underwent four consecutive independent deep-audit passes, each producing a substantive, mutually distinct tightening of the same numerical bound, for a cumulative tightening of more than 85%. The methodology was personally designed and proposed by Neo.K within this research's main line; this document was compiled and formalized by Aletheia / ChatGPT, GPT-5.6 Sol.

DLMVC v0.1 is a general deep-lag verification methodology designed by Neo.K. Its first field application — an independent audit of Lebesgue Universal Covering LUC-FC Round 01 — reconstructed that round's convexification–constant-width–support-function simplification chain, closed a genuine proof-graph gap with the new Lemma JPA-01 (joint placement attainment), and corrected its active-direction classification: falsifying the geometric possibility of “only one active direction,” in favor of two antipodal active directions or three active directions containing the origin. DLMVC itself is verification infrastructure, not a mathematical result: it strengthens and audits intermediate steps in an existing derivation chain, but establishes no new claim about the Lebesgue Universal Covering Problem itself — the problem remains OPEN throughout the entire process.

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