s1311 — the charge normalisation on the A1785 lattices
  Q1_Z_vector          {"Σ aᴹX_M − Z": "<1e-12", "|a| − 1 (canonical at o)": "<1e-12", "O a − a (electric)": "<1e-12", "|B₁â − â|, |B₂â − â| (active, not braid-fixed)": [0.707106781, 0.707106781]}
  Q2_parity_split      {"r = 0": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [268435456, 268435456], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 1": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [134217728, 134217728], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 2": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [67108864, 67108864], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 3": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [33554432, 33554432], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 4": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [16777216, 16777216], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 5": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [8388608, 8388608], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 6": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [4194304, 4194304], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 7": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [2097152, 2097152], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 8": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [1048576, 1048576], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 9": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [524288, 524288], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 10": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [262144, 262144], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 11": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [131072, 131072], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 12": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [65536, 65536], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 13": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [32768, 32768], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 14": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [16384, 16384], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 15": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [8192, 8192], "O integral in this basis (distance to ℤ)": "<1e-10"}, "r = 16": {"ranks (E, K)": [28, 28], "isotropic (E, K)": ["<1e-10", "<1e-10"], "index of E ⊕ K in Λ_r; |det Dirac pairing|": [4096, 4096], "O integral in this basis (distance to ℤ)": "<1e-10"}}
  Q3_Z_quantum         {"r = 0": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 1": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 2": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 3": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 4": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 5": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 6": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 7": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 8": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 9": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 10": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 11": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 12": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 13": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 14": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 15": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}, "r = 16": {"Z line rational (fit error)": "<1e-12", "λ²": 2.0}}
  Q4_family_reach      {"max_r |(L_r L_0⁻¹ − I) P_active|": "<1e-10", "P_active rank; P_active â = â": [24, "<1e-10"]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1423_maps_npz
  receipt   PASS s1307_results_house_checks_of_the_lattices
  computed  PASS Q1_Z_is_the_gauge_transformation_of_a_unit_electric_field_vector_in_the_active_sector
  computed  PASS Q2_O_splits_every_lattice_into_isotropic_electric_and_magnetic_sublattices_of_index_and_Dirac_determinant_2_to_the_28_minus_r
  computed  PASS Q3_in_all_seventeen_lattices_the_Z_line_is_rational_with_primitive_length_squared_2
  computed  PASS Q4_the_family_varies_only_off_the_active_sector_where_Z_lives_so_the_agreement_of_lambda_squared_is_structural
  argument  ARG  reading
  argument  ARG  scope
VERDICT: in all seventeen Γ-lattices the Z line has primitive length² 2 (N_L = 2N), so θ_Z has period ½ in the declared completion; O splits each lattice into electric and magnetic halves of index 2^{28−r}. The Z agreement is structural for this family; lattice-independence and the action normalisation remain open.
RESULT_HASH e5e3b7292156245f
s1311: 4 computed, 3 receipt, 2 argument, 0 failed
