s1256 — Cl(4,4) on the vector eight; the signature splits; the golden vacuum; the operator census
  vacuum      {"Peirce identification residual": "<1e-12", "so(4,4) on the six golden points": "<1e-12", "invariant symmetric forms (number, signature)": {"P12": [1, [4, 4]], "P13": [1, [4, 4]], "P23": [1, [4, 4]]}, "golden boost on the eights (scale, residual, non-scalar part)": {"P12": [1.27201965, "<1e-12", "<1e-12"], "P13": [1.0, "<1e-12", "<1e-12"], "P23": [0.786151378, "<1e-12", "<1e-12"]}, "[golden boost, so(4,4)]": "<1e-10"}
  clifford44  {"γ(v) maps P′12 ↔ P′23 (diagonal blocks)": "<1e-12", "anticommutator − G·I": "<1e-12", "G eigenvalues": [-0.5, -0.5, -0.5, -0.5, 0.5, 0.5, 0.5, 0.5], "G so(4,4)-invariant": "<1e-12", "normalised squares": [-1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0], "Clifford words span": 256, "chirality on P′12 / P′23 (mean, mean, residual)": [1.0, -1.0, 2.6645352591003757e-15]}
  splits      {"frame split": {"U (1,3)": {"squares": [1.0, -1.0, -1.0, -1.0], "dim": 16, "trace-form signature": [6, 10]}, "U⊥ (3,1)": {"squares": [1.0, 1.0, 1.0, -1.0], "dim": 16, "trace-form signature": [10, 6]}, "cross anticommutator": "<1e-10", "together span": 256}, "random rotated split": {"U (1,3)": {"squares": [1.0, -1.0, -1.0, -1.0], "dim": 16, "trace-form signature": [6, 10]}, "U⊥ (3,1)": {"squares": [1.0, 1.0, 1.0, -1.0], "dim": 16, "trace-form signature": [10, 6]}, "cross anticommutator": "<1e-10", "together span": 256}}
  cone_carrier {"outside W ⊕ P′12": "<1e-12", "component in V = P′13": "<1e-12", "component in P′23": "<1e-12", "outside W alone": 0.682465188, "outside P′12 alone": 0.710002818}
  operators   {"dim so(4,4) ∩ gauge(28)": 4, "dim so(4,4) ∩ Levi(16)": 4, "T_a inside so(4,4) ∩ gauge (rel residual)": "<1e-10", "orbit ranks on the split family": {"so(4,4) at the frame split": [16, 28], "so(4,4) at the random split": [16, 28], "so(4,4) ∩ gauge at the frame split": [4, 4], "so(4,4) ∩ gauge at the random split": [4, 4]}, "single gauge generators preserving V": 0, "discrete operators": {"O": {"preserves V": false}, "C56": {"preserves V": true, "G-isometry": "<1e-10", "identity on V": "1.906e+00", "moves the random split": 3.147638649}, "CP": {"preserves V": false}, "cycle": {"preserves V": false}, "A13": {"preserves V": true, "G-isometry": "<1e-10", "identity on V": "2.000e+00", "moves the random split": 2.684472369}, "golden boost": {"preserves V": true, "G-isometry": "<1e-10", "identity on V": "<1e-10", "moves the random split": 0.0}}, "K preserves V": false}
  receipt   PASS filed_d1412_house_frames_npz
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_chatgpt_d1410_maps_npz
  receipt   PASS s1253_results_hold_the_golden_frame_on_the_pointed_shell
  computed  PASS P2_so44_fixes_every_golden_point_each_eight_has_one_invariant_44_form_and_the_golden_boost_is_1_on_the_vector_eight_and_sqrt_phi_inverse_on_the_spinor_eights
  computed  PASS P3_the_c_isotope_product_of_the_vector_eight_on_the_two_spinor_eights_is_Cl44_with_the_sqrt_phi_eight_and_the_inverse_eight_as_its_chiral_halves
  computed  PASS P4_every_signature_split_of_the_vector_eight_gives_Cl13_as_M2H_and_Cl31_as_M4R_graded_commuting_and_jointly_Cl44
  argument  ARG  clifford_types
  computed  PASS P5_the_records_13_cone_carrier_lives_in_the_diagonal_plus_the_sqrt_phi_spinor_eight_not_in_the_vector_eight
  computed  PASS P6_so44_moves_splits_transitively_but_the_gauge_part_is_the_four_dim_torus_with_orbit_rank_4_C56_and_A13_move_splits_and_O_CP_cycle_K_leave_the_vector_eight
  argument  ARG  what_a_and_b_say
  argument  ARG  scope
VERDICT the c-isotope product makes the golden weight-1 eight the vector space of Cl(4,4) with the √φ and 1/√φ eights as its chiral halves; every (1,3)+(3,1) split gives Cl(1,3) ≅ M₂(ℍ) ⊗̂ Cl(3,1) ≅ M₄(ℝ) and shares the golden vacuum; the record's (1,3) cone carrier lies in the diagonal ⊕ the √φ eight; so(4,4) moves splits transitively but the gauge moves only the 4-dim torus slice, leaving a 12-dim non-gauge family; C56 and A13 also connect splits.
RESULT_HASH f246916e14deede7
s1256: 5 computed, 5 receipt, 3 argument, 0 failed
