s1268 — the torus and the two U(1)s in the SL(8) frame
  Q1_sl8_dictionary        {"ρ(E68) − ρ-model check: ρ(E87 − E78) − Z": "<1e-12", "ρ-residuals": {"D56": "<1e-12", "D_sol": "<1e-12", "S": "<1e-12", "Δ": "<1e-12", "D56_anchor": "<1e-12", "D_sol_anchor": "<1e-12", "Z": "<1e-12"}, "diagonal preimages": {"D56": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -3.0, -3.0], "D_sol": [-3.0, -3.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "S": [-0.5, -0.5, 0.5, 0.5, 0.5, 0.5, -0.5, -0.5], "Δ": [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0]}, "off-diagonal of those": "<1e-12", "D56_anchor as (7,8) rotation [A78, A87, rest]": [0.707107, -0.707107, "<1e-12"], "D_sol_anchor as (1,2) rotation [A12, A21, rest]": [-0.707107, 0.707107, "<1e-12"], "max ρ-residual over the 56 gauge generators": "<1e-12", "vectors that gauge": 56, "‖X on Λ²8‖ − ‖X on Λ²8*‖": "<1e-09", "invariant forms of the gauge algebra": 1, "its diagonal (normalised)": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0], "its off-diagonal": "<1e-09"}
  Q2_dyonic_blocks         {"piece kinds": {"(-6, 2)": "electric", "(6, -2)": "magnetic", "(-2, -2)": "magnetic", "(2, 2)": "electric", "(-2, 6)": "magnetic", "(2, -6)": "electric"}, "piece → (block, kind)": {"(-6, 2)": ["78", "electric"], "(6, -2)": ["78", "magnetic"], "(-2, -2)": ["4", "magnetic"], "(2, 2)": ["4", "electric"], "(-2, 6)": ["12", "magnetic"], "(2, -6)": ["12", "electric"]}, "locality rule == consistency on all 32 classes": true, "consistent classes": 8, "signature classes": {"(6,2)": 4, "(4,4)": 2, "definite": 2}, "minority blocks of the invariant form (counts)": {"78": 2, "12+78": 2, "12": 2, "none": 2}, "algebras": {"(28, 28, (12, 16, 0))": 4, "(28, 28, (16, 12, 0))": 2, "(28, 28, (0, 28, 0))": 2}}
  Q3_complex_torus_reach   {"per class": {"(1, 1, 1, 1, 1, 1)": {"reached": true, "signature class": "(6,2)"}, "(1, 1, 1, 1, -1, -1)": {"reached": false, "signature class": "(4,4)"}, "(1, 1, -1, -1, 1, 1)": {"reached": true, "signature class": "(6,2)"}, "(1, 1, -1, -1, -1, -1)": {"reached": false, "signature class": "definite"}, "(1, -1, 1, -1, 1, -1)": {"reached": false, "signature class": "definite"}, "(1, -1, 1, -1, -1, 1)": {"reached": true, "signature class": "(6,2)"}, "(1, -1, -1, 1, 1, -1)": {"reached": false, "signature class": "(4,4)"}, "(1, -1, -1, 1, -1, 1)": {"reached": true, "signature class": "(6,2)"}}, "reached == (electric signs of the two 2-planes agree)": true, "reached signature classes": {"(6,2)": 4}, "unreached signature classes": {"(4,4)": 2, "definite": 2}, "block-weight relation d12 + 2 d4 + d78": [0, 0]}
  Q4_cascade_fan           {"limits": {"[(6, -2)]": {"directions (deg)": [-44, 44], "count": 89, "constraints": ["<1e-10", "<1e-10"], "algebra": [13, 12, [0, 1, 12]]}, "[(6, -2), (2, 2), (-2, 6)]": {"directions (deg)": [45, 45], "count": 1, "constraints": ["<1e-10", "<1e-10"], "algebra": [28, 28, [4, 8, 16]]}, "[(-2, 6)]": {"directions (deg)": [46, 134], "count": 89, "constraints": ["<1e-10", "<1e-10"], "algebra": [13, 12, [0, 1, 12]]}, "[(-6, 2), (-2, 6)]": {"directions (deg)": [135, 135], "count": 1, "constraints": ["<1e-10", "<1e-10"], "algebra": [22, 20, [0, 2, 20]]}, "[(-6, 2)]": {"directions (deg)": [136, 224], "count": 89, "constraints": ["<1e-10", "<1e-10"], "algebra": [13, 12, [0, 1, 12]]}, "[(-6, 2), (-2, -2), (2, -6)]": {"directions (deg)": [225, 225], "count": 1, "constraints": ["<1e-10", "<1e-10"], "algebra": [28, 28, [4, 8, 16]]}, "[(2, -6)]": {"directions (deg)": [226, 314], "count": 89, "constraints": ["<1e-10", "<1e-10"], "algebra": [13, 12, [0, 1, 12]]}, "[(6, -2), (2, -6)]": {"directions (deg)": [315, 315], "count": 1, "constraints": ["<1e-10", "<1e-10"], "algebra": [22, 20, [0, 2, 20]]}}, "finite flow t = (0.37, −0.21)": {"constraints": ["<1e-09", "<1e-09"], "algebra": [28, 28, [12, 16, 0]]}}
  Q5_two_u1s               {"X-variation of the anchors": ["<1e-12", "<1e-12"], "[A56, Asol]": "<1e-12", "anchors vs D56, D_sol, S, Δ (max commutator)": "<1e-12", "centraliser of {S, Δ}: dim, derived dim": [47, 45], "anchors in that so(5,5) (relative residual)": ["<1e-10", "<1e-10"], "torus sl(2): commutant dim, derived dim": [4, 3], "e of the torus sl(2): ρ-residual (outside ρ(gl(8)))": 0.288675, "Weyl: W D56 W⁻¹ + D_sol, W A56 W⁻¹ − A56, W Asol W⁻¹ − Asol, WᵀΩW − Ω": ["<1e-10", "<1e-10", "<1e-10", "<1e-10"], "joint charges √2·(q12, q78) on the 56": [[[-1.0, -1.0], 2], [[-1.0, 0.0], 8], [[-1.0, 1.0], 2], [[0.0, -1.0], 8], [[0.0, 0.0], 16], [[0.0, 1.0], 8], [[1.0, -1.0], 2], [[1.0, 0.0], 8], [[1.0, 1.0], 2]]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  computed  PASS Q1_the_gradings_are_diagonal_sl8_scalings_of_the_planes_12_and_78_the_anchors_their_rotations_and_X_is_a_dyonic_so62_with_odd_plane_78
  computed  PASS Q2_six_pieces_are_electric_magnetic_times_three_blocks_and_locality_decides_consistency_on_all_32_classes
  computed  PASS Q3_wick_rotated_radii_reach_exactly_the_four_so62_classes_never_the_so8_or_split_signature_so44_twins
  computed  PASS Q4_the_radius_flow_is_a_frame_change_and_its_limits_form_a_four_sector_fan_single_piece_sectors_S_and_Delta_rays
  computed  PASS Q5_the_two_u1s_are_gauge_commuting_plane_rotations_inside_so55_fixed_by_the_torus_weyl_element_that_swaps_the_gradings
  argument  ARG  flat_weighted_timed
  argument  ARG  alternative_signatures
  argument  ARG  scope
VERDICT: the 56 is Λ²8 ⊕ Λ²8*; X is a dyonic so(6,2) on 8 = 2 + 4 + 2 (odd plane (7,8)); the two gradings scale the planes (1,2) and (7,8), the two U(1)s rotate them; the radius flow is a frame change with a four-sector cascade fan of contractions; Wick-rotated radii reach only the four so(6,2) classes, never so(8) or the split-signature so(4,4); the torus SL(2) swaps the gradings and fixes both U(1)s.
RESULT_HASH 3acc9c2a78325f30
s1268: 5 computed, 2 receipt, 3 argument, 0 failed
