Research proof index

A collection of charges x : Charges is said to minimally allow the potential term T if it allows T and no strict subset of it allows T. -/ def MinimallyAllowsTerm (x : ChargeSpectrum 𝓩) (T : PotentialTerm) : Prop := ∀ y ∈ x.powerset, y = x ↔ y.AllowsTerm T /-! ### A.1. Decidability of MinimallyAllowsTerm We show that MinimallyAllowsTerm is de...

For charges x : Charges, the proposition which states that the singlets needed to regenerate the Yukawa couplings regenerate a dangerous coupling (in the superpotential) with up-to n insertions of the scalars. Note: If defined as (x.ofYukawaTermsNSum n).toFinset ∩ x.phenoConstrainingChargesSP.toFinset ≠ ∅ the execution time is greatly increased. -/ de...

The contr_metric law (two-module): contracting the inner M/N legs of deltaCap b ⊗ deltaCap b' yields deltaCap₂ b' b.

The snake identity (two-module, contr_unit law): contracting x ∈ M into the M-leg of deltaCap₂ b' b ∈ N ⊗ M returns x.

Component formula for the holomorphic covector conjugate: the ![I] basis component of conjChiralCovector t is the complex conjugate of the ![I] component of t.

For scalar tensors, toField of the normalized tensor conjugate is the complex conjugate of toField.