Commit 8669184
feat(Verified-zkEVM#141): MCA bad-scalar master bound E(a) ≤ C(n,e*) via projective injectivity
New self-contained mathlib-only file MCAMasterBound.lean:
- ncard_badScalars_le: for any field K, module M, syndromes s₀ s₁, and finite
subspace family 𝒱, the bad-scalar set {γ | ∃V∈𝒱, s₀+γ•s₁∈V ∧ s₁∉V} has
ncard ≤ 𝒱.card. One-line projective injectivity: distinct γ sharing a witness
V force (γ-γ')•s₁ ∈ V hence s₁∈V (γ-γ' invertible), contradiction.
- ncard_badScalars_le_choose: binomial master bound E(a) ≤ C(n,e*), valid in
EVERY agreement band, every MDS code, every domain — complements the exact
3e≤r UDR law and the CS25 volume bound; polynomial in the UDR band (the
mcaConjecture form). Verified against all 130 sweep data points (0 violations).
Both kernel-clean [propext, Classical.choice, Quot.sound], no sorry/axiom/native_decide.
Co-Authored-By: Eliza <elizamakesmagic@gmail.com>1 parent 6a31aa1 commit 8669184
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