s1345 — the Chevalley question on the A1785 lattices
  receipt   PASS   filed_d1414_house_frames_npz
  receipt   PASS   filed_chatgpt_d1423_maps_npz
  receipt   PASS   s1307_results_house_checks_of_the_lattices
  computed  PASS   F1_the_supplied_integer_basis_is_a_chevalley_system_for_the_minuscule_56_in_lambda0_coordinates   [{"entries": [-1, 0, 1], "diagonal_generators": 7, "cartan_rank": 7, "distinct_weights": 56, "root_vectors": 126, "non_root_vectors": 0, "distinct_roots": 126, "roots_closed_under_negation": true, "string_test": "1512/1512", "coroots_diagonal_24_unit_entries": "126/126"}]
  computed  PASS   F2_C_is_bracket_closed_with_integer_constants_and_has_covolume_one_half_against_the_supplied_span   [C = span_Z{126 E_α, 126 coroots}; 8778 brackets closed, constants integral; covol(C) = 1/2 in span_Z{E_a} units — span_Z{E_a} has index 2 in C (coroots with half-integral coefficients in the 7 diagonal generators: True), the source of A1785 (c)'s half-integral coefficients]
  computed  PASS   F3_the_stabiliser_order_of_lambda0_is_exactly_C   [covol(g_Λ₀) = 1/2 = covol(C), and C ⊆ g_Λ₀ (E_α integer, coroots integer diagonal) — so g_Λ₀ = C: Λ₀ is the minuscule weight lattice of C]
  computed  PASS   F4_lambda0_is_gamma_stable_and_omega_unimodular_and_gamma_normalises_the_order   [{"Q^-1 {B1,B2,O,C56} Q == lane integer generators (<1e-9)": true, "generators integral": true, "Q^T Ω Q == Ω (<1e-9)": true, "det": 1.0, "Ω integral": true, "Γ normalises e7 and preserves span_Z{E_a}": true, "Q E_a Q^-1 spans the house e7": true}]
  computed  PASS   F5_none_of_lambda1_to_lambda16_carries_a_chevalley_order   [covol(g_{Λ_r}) = 2^k, k(r = 1..16) = [54, 87, 108, 121, 128, 140, 145, 146, 143, 150, 152, 147, 153, 151, 144, 129], every one > covol(C) = 2^-1 — a Chevalley order C′ on Λ_r would force covol(g_{Λ_r}) ≤ covol(C′) = covol(C)]
  argument  ARG    F5_invariant
  argument  ARG    F6_scale
  argument  ARG    reading

VERDICT THE CHEVALLEY QUESTION: Λ₀ carries the Chevalley order C of e7(7) (supplied basis = Chevalley system for the minuscule 56; g_Λ₀ = C, covol ½ against span_Z{E_a}; Γ-stable, Ω-unimodular); Λ₁…Λ₁₆ carry none (stabiliser covolumes 2^54…2^153). Exactly one of the seventeen.
RESULT_HASH 65fbf9ced7c99469
s1345: 8 computed/receipt PASS-able, 3 argument, 0 failed
