s1346 — the Z quantum on the Chevalley orbit of Λ₀
  receipt   PASS   filed_d1414_house_frames_npz
  receipt   PASS   filed_chatgpt_d1423_maps_npz
  receipt   PASS   s1311_results_lambda_squared_2_on_the_seventeen
  receipt   PASS   s1345_results_lambda0_is_the_chevalley_lattice
  computed  PASS   G1_e7_cap_comm_gamma_is_15_dimensional_and_generates_from_Z_the_rational_six_space_V6   [{"Q_orthogonal": true, "dim_e7_cap_comm_Gamma": 15, "dim_module_from_Z": 6, "module_is_span_f": true, "Z_parallel_f6": true, "Lambda_r_cap_V6_is_Z6_on_f_all_17": true, "f_norms2": [2, 2, 2, 2, 2, 2]}]
  computed  PASS   G2_the_action_is_faithful_so51_preserving_exactly_one_form_eta_lorentzian_and_euclidean_on_the_Z_line   [{"restricted_action_rank": 15, "V6_invariant": true, "invariant_symmetric_forms": 1, "eta_is_2diag(-1^5,+1)": true, "eta_on_Z_line_equals_Euclidean": true}]
  computed  PASS   G3_three_boosted_chevalley_lattices_have_lambda_squared_6_4_8   [p = [1, 0, 0, 0, 0, 2]: λ² = 6.000000000 = η(p,p) = 6; p = [1, 1, 0, 0, 0, 2]: λ² = 4.000000000 = η(p,p) = 4; p = [2, 1, 0, 0, 0, 3]: λ² = 8.000000000 = η(p,p) = 8 — each g commutes with Γ and preserves Ω; g⁻¹ẑ lies on the ray of p]
  computed  PASS   G4_lambda_squared_takes_every_even_value_2_to_24_and_never_less_than_2   [η = 2·diag(−1⁵, +1) is even on ℤ⁶, so λ² = η(p,p) ∈ 2ℤ_{>0} (min 2, at p = f6: Λ₀ itself); primitive witnesses for λ² = 2..24: {2: [0, 0, 0, 0, 0, 1], 4: [0, 0, 0, 1, 1, 2], 6: [0, 0, 0, 0, 1, 2], 8: [0, 0, 0, 1, 2, 3], 10: [0, 0, 0, 0, 2, 3], 12: [0, 0, 0, 1, 3, 4], 14: [0, 0, 0, 0, 3, 4], 16: [0, 0, 0, 0, 1, 3], 18: [0, 1, 1, 1, 2, 4], 20: [0, 0, 1, 1, 2, 4], 22: [0, 0, 0, 1, 2, 4], 24: [0, 0, 0, 2, 3, 5]}]
  argument  ARG    G_transitivity
  argument  ARG    reading

VERDICT THE Z QUANTUM: on the Chevalley orbit of Λ₀ under E7 ∩ Comm(Γ) (one A1785 class) the Z line is rational on the rational rays of an so(5,1) hyperboloid and λ² = η(p,p) takes every even value ≥ 2 (boosts exhibited at 6, 4, 8). s1311's λ² = 2 is the minimum, attained at Λ₀; not a lattice invariant.
RESULT_HASH 2ca3845370279e43
s1346: 8 computed/receipt PASS-able, 2 argument, 0 failed
