Pallas projective msm - #3
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September 10, 2026 00:26
Complete Renes-Costello-Batina projective addition, its completeness (threading hy0 and 2 != 0), the affine bridge toAffine/ofAffine, and the binary smulFast ladder proven equal to n . p -- all generic over [Field F] for any y^2 = x^3 + 5 curve. Vesta and Pallas instantiate this in Projective.lean. Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
PVes := Core.PPoint Fq; padd/toAffine/ofAffine/smulFast and their lemmas delegate to the field-generic Core, fed Vesta's facts (curve A=0, B=5, 2!=0, 5!=0, no_onCurve_y_zero). The internal RCB certificates now live once in Core. paddFast/padd_eq_paddFast stay Vesta-local. MsmProj: drop three toAffine_pid simp args now redundant (toAffine is a reducible abbrev). Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
namespace Pallas mirrors the flat Vesta decls: PPal := Core.PPoint Fp, G := SWPoint Pallas.curve, and padd/toAffine/ofAffine/smulFast with their lemmas delegating to the generic Core fed Pallas's facts (curve A=0, B=5, 2!=0, 5!=0, Pallas.no_onCurve_y_zero). smulFast_eq gives the projective fast ladder = n . p over Pallas. Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
The windowed Pippenger MSM run entirely in projective coordinates (basic, single-pass-scatter, and windows-parallel paths), generic over the Core.PPoint projective core for any y^2 = x^3 + 5 curve, proving pippengerProj_eq_msm = the naive MSM for c >= 1. Vesta and Pallas instantiate it. Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
MsmProj's projective-Pippenger decls delegate to MsmProj.Core at Vesta (commit_lagrange wrappers stay Vesta-local: coeffs in VestaScalarField). ProjectiveMontEquiv tracks the refactor: PVes.mk.injEq -> Core.PPoint.mk.injEq (from the Projective PVes abbrev) and Core.* names added to the scatter simp-normal-forms. Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
The Pallas instantiation of MsmProj.Core: basic, scatter, and parallel pippengerProj variants, each proven equal to the naive MSM. This is the fast Pallas MSM the snarky verifier's 2^15-point sg-check needs. Claude-Session: https://claude.ai/code/session_01Y4Wf3zPJYCwXzHDgdBUytv
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