s1291 — the massless vector sector of F0 carries the STU period matrix
  Q1_torus_neutral_eight               {"dim W": 8, "rank Ω|W": 8, "s preserves W (max residual)": "<1e-12", "T0 field vectors in W": "<1e-12", "dim E∩W, dim K∩W": [4, 4]}
  Q2_tensor_structure_and_even_frame   {"basis orthonormal": "<1e-12", "max ‖Aₖ|W − σ_z(slot k)‖, ‖ûₖ|W − σ_x(slot k)‖": ["<1e-12", "<1e-12"], "Ω|W − (±)ε⊗ε⊗ε, sign": ["<1e-12", 1], "projector onto E∩W − projector onto the even states": "<1e-12"}
  Q3_closed_form                       {"max ‖M|W − m(τ₁)⊗m(τ₂)⊗m(τ₃)‖ (6 points)": "<1e-12", "max ‖𝒩_house − 𝒩_STU(τ)‖ on the four even fields": "<1e-12", "symplectic consistency": "<1e-10", "τ at o": ["1j"]}
  Q4_Z_and_the_flats                   {"Z in the even-state basis: |coefficients|, common sign (overall basis sign is a convention), residual": [[0.5, 0.5, 0.5, 0.5], true, "<1e-12"], "four-form flat: τₖ = i e^{−2sₖ}, 𝒩 diagonal, diag = −i·exp(−2χᵢ·s) (max deviation, 5 points)": "<1e-12", "radius flat: |τₖ| = 1 and 𝒩_Z = tanh(2Σs) − i sech(2Σs) from the tensor formula (max deviation, 5 points)": "<1e-12"}
  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_d1405_maps_npz
  receipt   PASS s1283_results_construction_and_machinery
  receipt   PASS s1284_results_face_and_twist_definitions
  receipt   PASS s1286_results_neutral_count_machinery
  receipt   PASS s1290_results_kinetic_matrix_machinery
  computed  PASS Q1_the_T0_neutral_subspace_W_is_eight_dimensional_symplectic_s_invariant_and_splits_four_plus_four
  computed  PASS Q2_W_is_the_222_of_sl2_cubed_with_Omega_eps_cubed_and_the_parity_even_states_are_exactly_the_electric_fields
  computed  PASS Q3_M_on_W_is_the_tensor_product_of_three_plane_matrices_and_the_massless_kinetic_matrix_is_the_STU_period_matrix_in_tau
  computed  PASS Q4_Z_is_half_the_sum_of_the_even_fields_up_to_the_basis_sign_and_the_s1290_flat_laws_follow_from_the_tensor_formula
  argument  ARG  reading
  argument  ARG  scope
VERDICT: on F0 the four massless vectors and their duals form the (2,2,2) of sl(2,ℝ)³ with the parity-even states electric; M|W = m(τ₁)⊗m(τ₂)⊗m(τ₃), so their kinetic matrix (ε and θ) is the STU period matrix in τₖ = (sinh 2sₖ sin φₖ + i)/(cosh 2sₖ + sinh 2sₖ cos φₖ); Z = ±½ Σ(even fields); s1290's flat laws follow.
RESULT_HASH 65a8d1bae166bd5b
s1291: 4 computed, 8 receipt, 2 argument, 0 failed
