Research proof index

The allowed subsets of a FluxesTen which has no exotics or zeros. -/ def noExoticsSubsets : (n : ℕ) → Finset (Multiset Fluxes) | 0 => {{}} | 1 => {{⟨1, -1⟩}, {⟨1, 0⟩}, {⟨1, 1⟩}, {⟨2, -1⟩}, {⟨2, 0⟩}, {⟨2, 1⟩}, {⟨3, 0⟩}} | 2 => {{⟨1, -1⟩, ⟨1, 0⟩}, {⟨1, -1⟩, ⟨1, 1⟩}, {⟨1, -1⟩, ⟨2, 1⟩}, {⟨1, 0⟩, ⟨1, 0⟩}, {⟨1, 0⟩, ⟨1, 1⟩}, {⟨1, 0⟩, ⟨2, 0⟩}, {⟨1, 1⟩, ⟨2, -1⟩}...

Completeness of elemsNoExotics, that is, every element of FluxesFive which obeys NoExotics is an element of elemsNoExotics, and every element of elemsNoExotics obeys NoExotics. -/ lemma noExotics_iff_mem_elemsNoExotics (F : FluxesFive) : F.NoExotics ∧ F.HasNoZero ↔ F ∈ elemsNoExotics := by constructor · exact fun ⟨h1, h2⟩ => mem_elemsNoExotics...

Completeness of elemsNoExotics, that is, every element of FluxesFive which obeys NoExotics is an element of elemsNoExotics, and every element of elemsNoExotics obeys NoExotics. -/ lemma noExotics_iff_mem_elemsNoExotics (F : FluxesFive) : F.NoExotics ∧ F.HasNoZero ↔ F ∈ elemsNoExotics := by constructor · exact fun ⟨h1, h2⟩ => mem_elemsNoExotics...

The quanta satisfy the linear anomaly cancellation conditions. -/ linear_anomalies : x.LinearAnomalyCancellation lemma isViable_iff_def (x : Quanta) : IsViable x ↔ x.toCharges.IsComplete ∧ ¬ x.toCharges.IsPhenoConstrained ∧ ¬ x.toCharges.YukawaGeneratesDangerousAtLevel 1 ∧ (∃ I : CodimensionOneConfig, x.toCharges ∈ ofFinset I.allowedBarFiveCharges I.allow...

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...