feat(uc): lift scheduled draws through factorization - #176
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Summary
Stacked on #174.
This PR connects the mass-aware scheduler algebra to the existing UC factorization path maps. For arbitrary component samplers, it proves that:
parLeftPathEquiv;parRightPathEquiv.Both results consume only
BinaryScheduler.IsCoherent. Their proofs flatten the nested Boolean draws to a common leaf continuation and then use the scheduler law underMonadRelFamily.bind_congr. No probability assumptions enter PolyFun.The three
*_bindlemmas expose the precise nested scheduler calls and make the bridge reusable by downstream process- and observation-level theorems. The concrete downstream consumer is Verified-zkEVM/VCVio#572, which pins this PR's exact head and proves coherence for proportionalProbCompscheduling.Validation
./scripts/validate.sh --lint --test --axioms