s1289 — house checks of A1779
  Q1_mass_product_law            {"χ columns (sorted)": [[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]], "sampled ∏μᵢ (5 points)": [1.791882, 0.40495, 1.095651, 0.504796, 0.856358], "max relative |∏μᵢ·4∏cos²δ − 1| and pair split": "<1e-10", "∏μᵢ ≥ 1/4 at every sample": true}
  Q2_D56_ray                     {"a = 0.1": [0.631734, 0.631734, 0.631734], "a = 0.25": [1.837113, 1.837113, 1.837113], "a = 0.5": [26.625278, 26.625278, 26.625278]}
  Q3_chamber_involution          {"exp(πJ) − h (SO(8))": "<1e-10", "exp(πρ(J)) − diag(Λ²h, Λ²h)": "<1e-10", "house P − lane P56": "<1e-12", "P² − I, PᵀΩP − Ω, P normalises e7": ["<1e-12", "<1e-12", "<1e-12"], "[P, Aₖ] (k = 1, 2, 3)": "<1e-12", "chamber H = .3A₁ − .2A₂ + .1A₃: H ↦, face ↦, twist ↦": ["+", "+", "−"], "min Frobenius distance to the five s1286 elements": 9.797959}
  Q4_neutral_fermion_split       {"twist-neutral (gravitini, spin-½) — s1286 count": [6, 26], "u_of residual (twist, J)": ["<1e-10", "<1e-10"], "P8² ∓ I (best sign), sign": ["<1e-10", "+"], "P8 t₈ P8⁻¹ + t₈": "<1e-10", "|tr P8|: lane, house": [0.0, 0.0], "neutral 8: dim, split of P8": [6, {"classes": [3, 3], "leak": "<1e-10"}], "neutral 56: dim, split of Λ³P8": [26, {"classes": [13, 13], "leak": "<1e-10"}]}
  Q5_surviving_gauge_image       {"face algebra dim; P-invariant part dim": [13, 6], "P-invariant part: max bracket": "<1e-10", "compact part acting on each P-half of the neutral 8 / 56 (norm)": ["<1e-08", "<1e-08"], "even neutral dims (8, 56)": [3, 13]}
  Q6_su3_su2_centralisers        {"compact gauge algebra dim": 16, "centraliser of T₁: dim, derived dim": [10, 8], "centraliser of T₁, T₂: dim, derived dim": [6, 3], "Z − ½(T₁ + T₂ + T₃ + T₄)": "<1e-12", "derived(T₁) spans the lane su(3)": "<1e-10"}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS filed_chatgpt_d1417_maps_npz
  receipt   PASS filed_chatgpt_d1419_maps_npz
  receipt   PASS s1283_results_construction_and_machinery
  receipt   PASS s1284_results_face_and_twist_definitions
  receipt   PASS s1286_results_neutral_count_machinery
  computed  PASS Q1_the_spin32_mass_product_is_one_over_four_prod_cos2_delta_on_F0
  computed  PASS Q2_on_the_D56_ray_all_eight_spin32_m2_equal_half_cosh_cubed_4a
  computed  PASS Q3_the_house_built_involution_equals_the_lane_P56_is_compact_E7_and_keeps_the_chamber_face_while_inverting_its_twist
  computed  PASS Q4_the_spinor_lift_inverts_the_twist_and_splits_the_6_plus_26_neutral_fermions_3_3_and_13_13
  computed  PASS Q5_the_P_invariant_gauge_image_is_an_abelian_R6_acting_trivially_on_the_kept_neutral_fermions
  computed  PASS Q6_the_centraliser_of_T1_in_the_compact_gauge_algebra_has_derived_su3_and_of_T1_T2_derived_su2_and_Z_is_half_the_torus_sum
  argument  ARG  reading
  argument  ARG  scope
VERDICT: A1779 confirmed where checkable in house — mass product law, D56 ray, the new chamber involution (built from h ∈ SO(8); keeps the face, inverts the twist), its 3/3 and 13/13 split of the neutral fermions, a surviving abelian R⁶ that acts trivially on them (charged chiral index zero), and su(3) / su(2) as torus centralisers.
RESULT_HASH d431cebed76b6715
s1289: 6 computed, 7 receipt, 2 argument, 0 failed
