Research proof index

The anomaly coefficient of a FiveQuanta is given by the pair of integers: (∑ᵢ qᵢ Nᵢ, ∑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 : FiveQuanta 𝓩) : 𝓩 × 𝓩 := ((F...

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...