Research proof index

The anomaly coefficient of a TenQuanta is given by the pair of integers: (∑ᵢ qᵢ Nᵢ, 3 * ∑ᵢ qᵢ² Nᵢ). The first components is for the mixed U(1)-MSSM, see equation (22) of arXiv:1401.5084. The second component is for the mixed U(1)Y-U(1)-U(1) gauge anomaly, see equation (23) of arXiv:1401.5084. -/ def anomalyCoefficient (F : TenQuanta 𝓩) : 𝓩 × 𝓩 := (...

The decomposition of a TenQuanta into a TenQuanta which has the same reduce by has fluxes {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} or {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} only. This only works for fluxes which have no exotics or zeros. -/ def decompose (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decompos...

The decomposition of a TenQuanta into a TenQuanta which has the same reduce by has fluxes {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} or {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} only. This only works for fluxes which have no exotics or zeros. -/ def decompose (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decompos...

The decomposition of a TenQuanta into a TenQuanta which has the same reduce by has fluxes {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} or {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} only. This only works for fluxes which have no exotics or zeros. -/ def decompose (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decompos...

The decomposition of a TenQuanta into a TenQuanta which has the same reduce by has fluxes {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} or {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} only. This only works for fluxes which have no exotics or zeros. -/ def decompose (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decompos...

Given a finite set of charges c the TenQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. This is defined to be as efficient as possible. -/ def liftCharge (c : Finset 𝓩) : Multiset (TenQuanta 𝓩) := /- The {(1, 0), (1, 0), (1, 0)} case. -/ /- The multisets of cardinality 3 containing 3 elements of c. -/ let...