Matching counts: literal schedule exclusion and bounded fragility reference
Family 113; selected manuscript/construction and formal-scope addendum. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
The FPRAS main statement and selected introduction, quantitative sampling guarantee, annealing/counting parameters, amplification and prescribed-degree corollary were read. The literal nonempty routine has S=ceil(10 sigma^-2(n+K+1)), with sigma<=1/(10^7D) and large enlarged-graph parameters. At two vertices and error 1/10, confidence failure 1/20, its general schedule requests about 4.52*10^48 fresh runs per stage. This is an exact declared-parameter calculation, not a runtime observation or impossibility for a different method. Empty/infeasible branches and practical special cases remain separate. The prescribed-degree/fixed-size sampler promises total-variation approximation, not exact or pointwise almost-uniform sampling.
The companion entropy introduction (lines 1–240) and selected deterministic algorithm (lines 1–155) were read. Entropy bounds require a feasible perfect-matching marginal vector, with general-graph odd cuts. The deterministic count guarantee uses factor 512^n, not fixed relative-error accuracy, and explicitly warns its polynomial degree is large. The selected family scope covers the FPRAS, entropy/count bounds and triangle-expansion relation, but excludes the sharp global face-dimension bound. No independent formal check was run.
Defer the literal production counter. Dossier 006 now describes a conventional bounded exact subset-DP reference, rank replay and single-edge failure counts. Its 93 finite checks do not verify the source FPRAS or buyer value. Full proof, sampler implementation and deletion reduction remain pending.
Exact source files read:
preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex(lines 1–250, 2350–2725, 2820–2845, 3080–3140).preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/build/sections/01-introduction.tex(1–240).preprints/Entropy-and-Face-Dimension-of-the-Perfect-Matching-Polytope-September-23-2026/build/sections/09-algorithm.tex(1–155).lean/docs/113.md.
See source metadata, parameter calculations, and the exact utility.