hep-declarations/HepLean.AnomalyCancellation.SMNu.Ordinary.DimSevenPlane.jsonl

{"name":"SMRHN.SM.PlaneSeven.Bi_Bj_ne_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.Bi_Bj_ne_cubic {i : Fin 7} {j : Fin 7} (h : i ≠ j) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B i)) (SMRHN.SM.PlaneSeven.B j)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₁_B₁_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₁_B₁_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 1)) (SMRHN.SM.PlaneSeven.B 1)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.basis_linear_independent","declaration":"theorem SMRHN.SM.PlaneSeven.basis_linear_independent  : LinearIndependent ℚ SMRHN.SM.PlaneSeven.B"}
{"name":"SMRHN.SM.PlaneSeven.B₆_B₆_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₆_B₆_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 6)) (SMRHN.SM.PlaneSeven.B 6)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₄_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₄_Bi_cubic {i : Fin 7} (hi : 4 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 4)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₅_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₅_Bi_cubic {i : Fin 7} (hi : 5 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 5)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.Bi_Bi_Bj_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.Bi_Bi_Bj_cubic (i : Fin 7) (j : Fin 7) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B i)) (SMRHN.SM.PlaneSeven.B i)) (SMRHN.SM.PlaneSeven.B j) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₃_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₃_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₃) S) T = 2 * (S 9 * T 9 - S 10 * T 10)"}
{"name":"SMRHN.SM.PlaneSeven.B₁","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₁  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₂_B₂_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₂_B₂_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 2)) (SMRHN.SM.PlaneSeven.B 2)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.Bi_Bj_Bk_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.Bi_Bj_Bk_cubic (i : Fin 7) (j : Fin 7) (k : Fin 7) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B i)) (SMRHN.SM.PlaneSeven.B j)) (SMRHN.SM.PlaneSeven.B k) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₀","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₀  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₆_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₆_Bi_cubic {i : Fin 7} (hi : 6 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 6)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₂","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₂  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B_in_accCube","declaration":"theorem SMRHN.SM.PlaneSeven.B_in_accCube (f : Fin 7 → ℚ) : SMνACCs.accCube (Finset.sum Finset.univ fun i => f i • SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B_sum_is_sol","declaration":"theorem SMRHN.SM.PlaneSeven.B_sum_is_sol (f : Fin 7 → ℚ) : ACCSystem.IsSolution (SMRHN.SM 3) (Finset.sum Finset.univ fun i => f i • SMRHN.SM.PlaneSeven.B i)"}
{"name":"SMRHN.SM.PlaneSeven.B₅_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₅_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₅) S) T = S 15 * T 15 - S 16 * T 16"}
{"name":"SMRHN.SM.PlaneSeven.B₄_B₄_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₄_B₄_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 4)) (SMRHN.SM.PlaneSeven.B 4)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₀_B₀_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₀_B₀_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 0)) (SMRHN.SM.PlaneSeven.B 0)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₃_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₃_Bi_cubic {i : Fin 7} (hi : 3 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 3)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₆_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₆_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₆) S) T = 3 * (S 5 * T 5 - S 8 * T 8)"}
{"name":"SMRHN.SM.PlaneSeven.B₀_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₀_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₀) S) T = 6 * (S 0 * T 0 - S 1 * T 1)"}
{"name":"SMRHN.SM.PlaneSeven.B₁_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₁_Bi_cubic {i : Fin 7} (hi : 1 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 1)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₅_B₅_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₅_B₅_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 5)) (SMRHN.SM.PlaneSeven.B 5)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₃","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₃  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₀_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₀_Bi_cubic {i : Fin 7} (hi : 0 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 0)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B","declaration":"/-- The charge assignments forming a basis of the plane. -/\ndef SMRHN.SM.PlaneSeven.B  : Fin 7 → ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₂_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₂_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₂) S) T = 3 * (S 6 * T 6 - S 7 * T 7)"}
{"name":"SMRHN.SM.PlaneSeven.B₃_B₃_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₃_B₃_Bi_cubic {i : Fin 7} : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 3)) (SMRHN.SM.PlaneSeven.B 3)) (SMRHN.SM.PlaneSeven.B i) = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₂_Bi_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₂_Bi_cubic {i : Fin 7} (hi : 2 ≠ i) (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin (SMRHN.SM.PlaneSeven.B 2)) (SMRHN.SM.PlaneSeven.B i)) S = 0"}
{"name":"SMRHN.SM.PlaneSeven.B₄_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₄_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₄) S) T = S 12 * T 12 - S 13 * T 13"}
{"name":"SMRHN.SM.seven_dim_plane_exists","declaration":"theorem SMRHN.SM.seven_dim_plane_exists  : ∃ B,\n  LinearIndependent ℚ B ∧\n    ∀ (f : Fin 7 → ℚ), ACCSystem.IsSolution (SMRHN.SM 3) (Finset.sum Finset.univ fun i => f i • B i)"}
{"name":"SMRHN.SM.PlaneSeven.B₄","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₄  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₁_cubic","declaration":"theorem SMRHN.SM.PlaneSeven.B₁_cubic (S : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) (T : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges) : ((SMνACCs.cubeTriLin SMRHN.SM.PlaneSeven.B₁) S) T = 3 * (S 3 * T 3 - S 4 * T 4)"}
{"name":"SMRHN.SM.PlaneSeven.B₅","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₅  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}
{"name":"SMRHN.SM.PlaneSeven.B₆","declaration":"/-- A charge assignment forming one of the basis elements of the plane. -/\ndef SMRHN.SM.PlaneSeven.B₆  : ACCSystemCharges.Charges (SMRHN.SM 3).toACCSystemCharges"}