Pasta: GLV endomorphism eigenvalue anchors - #1
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The role names stated the Pasta cycle as a pun (VestaBaseField = PallasScalarField and vice versa) — four names for two fields. The fields now carry their standard absolute names: Fp (the Pallas base field, also the Vesta scalar field) and Fq (the Pallas scalar field, also the Vesta base field), matching proof-systems' own convention. Role information belongs to consumers' relative projections, not to which alias was picked. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Per curve: the endomorphism coefficient β, the scalar eigenvalue λ, and the native_decide certificate λ • G = φ(G) at the standard generator — the computational anchor from which downstream (l-adic/snarky's pasta package) derives φ = [λ] on the whole group (homomorphism + prime-order cyclicity), eliminating the eigen axioms. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Superseded: the anchors moved into l-adic/snarky's pasta package directly (l-adic/snarky#247) — no CompElliptic change needed. |
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CompElliptic/Curves/PastaEndo.lean: per Pasta curve, the GLV endomorphism data as concrete numerals (endoBeta,endoLam), the image of the fixed generator under the endomorphism (endoGpt := ⟨endoBeta * G.1, G.2, _⟩, on-curve by kerneldecidesinceβ³ = 1), and the single computational anchorfor both Pallas and Vesta, wired into the
CompElliptic.leanroot.These anchors let a consumer discharge the CM eigenvalue relations (
φ = [λ]on every point) as theorems: the endomorphism is an additive homomorphism (pure field algebra), the point group under the Hasse bound has prime order so it is cyclic on any nonzero point, and the anchor pins the eigenvalue on the generator. Downstream (l-adic/snarkyformal/pasta) this deletes the two eigen axioms from the trust surface.native_decideis the package's established certificate mechanism (same ascard_eq,scalarCard_nsmul_Gpt).🤖 Generated with Claude Code
https://claude.ai/code/session_01RhavGeUhGukSRQTRH6JEaD