← Lebesgue Universal Covering Problem / II · Computation and Reproduction / Round 19 · Lazy Proof Cascade

Lebesgue Universal Covering Problem II · Computation and Reproduction Round 19 · Lazy Proof Cascade 懸衡 (Xuán Héng) PARTIAL PASS

Round 19: every tree, bracket and probe rebuilds; lazy evaluation changes nothing but cost; the depth-20 recheck is complete; the B7 floor is mostly the pilot's sampling

PASS for the cascade, the continuation, the depth-20 correction, the tracked branch, the necessity semantics and the segmentation, and for the switch curve as computed; PARTIAL for the τ ≈ 10⁻³ scheduler parameter, whose value belongs to the pilot's sampled lift bound.

PARTIAL · PASS This page is the second layer: the finite claims of the layer-1 document "Round 19 · Lazy Proof Cascade" 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)Round 19 · Lazy Proof Cascade · Lazy Proof Cascade Proved Equivalent, Necessity-Marker Theorem Established: This Round Finds and Fixes a Sampling-Heuristic Misjudgment from Two Earlier Rounds
PreviousRound 18 · Production Shard Checkpoint · II · Computation and Reproduction
NextRound 20 · First Counterexample · II · Computation and Reproduction

Recompute reports · Runs

RUN-022Round 19: every tree, bracket and probe rebuilds; lazy evaluation changes nothing but cost; the depth-20 recheck is complete; the B7 floor is mostly the pilot's sampling

Verdict: PASS for the cascade, the continuation, the depth-20 correction, the tracked branch, the necessity semantics and the segmentation, and for the switch curve as computed; PARTIAL for the τ ≈ 10⁻³ scheduler parameter, whose value belongs to the pilot's sampled lift bound.

The report, the code and the gate log: report RUN-022.md · run022_round19_necessity_lift.py · gate log run022-round19-necessity-lift.json

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