[codex] Add Mersenne31 circle domain skeleton#3
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Require logSize bounds on subgroupGen, document toPoint limitations, add toPoint/add_zero lemmas, and expand circle regression tests. Co-authored-by: Cursor <cursoragent@cursor.com>
- Rename `Point.add_zero` (proves `0 + p = p`) to `Point.zero_add` to match the repo's Mathlib-style naming convention. - Drop the discarded `logSize ≤ logOrder` argument from `CirclePointIndex.subgroupGen`; the body is total, and callers (`Coset.new`, `odds`, `halfOdds`) carry the bound where it is needed. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Summary
Adds a STWO-style circle-domain skeleton on top of the Mersenne31 field work in Verified-zkEVM#257.
Changes
CompPoly.Fields.Mersenne31.Circle.x^2 + y^2 = 1.(2, 1268011823)and proves it lies on the circle.CirclePointIndexmodulo2^31, subgroup generator indices, cosets, conjugate cosets, circle domains, and canonical cosets.Non-goals
This intentionally does not prove the generator has order
2^31, nor does it formalize FRI or circle polynomial evaluation. Those are follow-on PRs after the domain skeleton stabilizes.Validation
lake build CompPoly.Fields.Mersenne31.Circlelake build CompPolyTests.Fields.Mersenne31.Circle./scripts/check-imports.sh./scripts/lint-style.shlake build CompPolyTestslake build CompPolylake test