s1305 — the twist-closure spectrum of O
  Q1_fixed_algebra                           {"Ad O on e7: #(+1), #(−1), Ad O² − I": [63, 70, "<1e-10"], "e7^O: dim, derived dim, Killing inertia (+ noncompact, − compact, 0)": [63, 63, [27, 36, 0]], "simple ideals of e7^O ⊗ ℂ (commutant of ad, eigen-reduced); degenerate clusters": [1, [7]], "CONTROL: the D56 level-0 algebra (e6 ⊕ ℝ): ideals read": 2, "dim-63 simple real forms (type A7 only: no B, C, D or exceptional algebra has dimension 63) matching the Killing inertia": ["su*(8)"]}
  Q2_even_odd_counts                         {"p (symmetric parts): dim, even, odd": [70, 27, 43], "k (antisymmetric parts): dim, even, odd": [63, 36, 27], "S70: trace-orthonormal, symmetric": ["<1e-12", "<1e-12"], "D56 symmetric; O D56 O + D56": ["<1e-12", "<1e-12"]}
  Q3_hessian_split                           {"V(o), |∇V(o)|": ["<1e-12", "<1e-12"], "finite-difference check of the analytic Hessian (relative, two directions)": ["<1e-06", "<1e-06"], "O on the S70 coordinates: involution, commutes with the Hessian": ["<1e-12", "<1e-12"], "even / odd block dims": [27, 43], "Hessian spectrum, all 70 (units of the largest)": {"0.0": 48, "0.25": 20, "1.0": 2}, "even block (units of the full largest)": {"0.0": 27}, "odd block (units of the full largest)": {"0.0": 21, "0.25": 20, "1.0": 2}, "Goldstone directions: dim, |odd component| / |all|": [12, "<1e-12"]}
  Q4_V_on_and_off_the_fixed_locus_SAMPLED    {"max |V| at 8 seeded points of exp(p^O)·o (|c| = 0.5, 1.5)": "<1e-12", "odd quadratic-flat directions: count, min V at |c| = 0.5 (3 samples)": [21, "4.204e-05"], "max |V(φ) − V(O·φ)| at 2 random points": "<1e-12"}
  Q5_the_D56_line                            {"|exp(2tD56) − I| > 1 for t = 0.25, 0.5, 1 (exp(tD)·o = O·exp(tD)·o = exp(−tD)·o needs exp(2tD) ∈ SU(8), i.e. = I for a symmetric matrix)": [true, true, true]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1288_results_machinery_actX_act_t_basis_pot
  computed  PASS Q1_O_is_an_involution_of_e7_with_fixed_algebra_simple_of_dim_63_and_Killing_27_36_which_is_su_star_8_and_the_ideal_count_control_reads_2_on_e6_plus_R
  computed  PASS Q2_p_splits_27_even_43_odd_k_splits_36_even_27_odd_and_D56_is_a_noncompact_O_odd_direction
  computed  PASS Q3_at_o_every_massive_scalar_is_O_odd_the_27_even_directions_are_flat_with_the_12_Goldstones_among_them
  computed  PASS Q4_SAMPLED_V_vanishes_on_the_O_fixed_locus_and_is_O_invariant_and_the_odd_quadratic_flat_directions_are_lifted_at_finite_distance
  computed  PASS Q5_off_t_equal_0_the_D56_line_leaves_the_fixed_locus
  argument  ARG  reading
  argument  ARG  scope
VERDICT: O fixes a simple su*(8) ⊂ e7(7) (Killing (27, 36)); at o all 22 massive scalars are O-odd and all 27 O-even directions are flat; V vanishes on the fixed locus (sampled); the D56 modulus is odd, so a twisted closure keeps the full gauging o and no face.
RESULT_HASH d780d21d472ce437
s1305: 5 computed, 2 receipt, 2 argument, 0 failed
