Research proof index

Auxiliary lemma for proving that the polynomial sent by the honest prover is of degree at most deg

Telescoping identity (the core sum-check completeness step): summing over the (k+1)-coordinate cube equals summing coordinate 0 over its domain, then the rest over the tail cube. This is the piFinset "cons decomposition" 𝔻^{k+1} ↔ 𝔻₀ × 𝔻^k.

Summability of (m+1)^k * exp(-2πm) via comparison with shifted sum.

The proposition for which says, given a charge x adding a charge q5 permits the existence of a potential term T due to the addition of that charge. -/ def AllowsTermQ10 (x : ChargeSpectrum 𝓩) (q10 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => false | .Λ => (0 : 𝓩) ∈ (x.Q5.product x.Q5).val.map (fun (y, z) => y + z + q10) |...

The proposition for which says, given a charge x adding a charge q5 permits the existence of a potential term T due to the addition of that charge. -/ def AllowsTermQ5 (x : ChargeSpectrum 𝓩) (q5 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => match x with | ⟨_, some qHu, _, _⟩ => q5 = qHu | _ => false | .Λ => (0 : 𝓩) ∈ ((ins...

The charge spectrum allowsTermForm a b c T allows the potential term T.