s1350 — the Z-quantum selection
  receipt   PASS   filed_d1414_house_frames_npz
  receipt   PASS   filed_chatgpt_d1423_maps_npz
  receipt   PASS   s1346_results_the_orbit_and_its_lambda_squared
  receipt   PASS   s1345_results_lambda0_is_the_chevalley_lattice
  computed  PASS   the_15_and_its_faithful_action_on_V6_reproduce_s1346   [dim e7 ∩ comm(Γ) = 15; rank of the V6 action 15 (s1346 G1/G2)]
  computed  PASS   Z1_on_Lambda0_the_gauging_is_sqrt2_integral_the_registered_Z_is_integral_and_the_Gram_matrix_is_I   [{"sqrt2_X_L_max_dev_from_Z": "< 1e-9", "|X_L| values": [0.0, 0.707106781], "Z_L_max_dev_from_Z": "< 1e-9", "|Z_L| values": [0.0, 1.0], "Gram_at_o_is_I": true, "Z_eq_X(a)": true, "|a|": 1.0}]
  computed  PASS   Z1b_Z_is_X_of_a_unit_charge_vector   [‖Σ aᴹX_M − Z‖ < 1e-9, |a| = 1.000000000]
  computed  PASS   Z2a_stabiliser_dimensions_X4_o10_D56_10_Dsol2_Z7_gauge6   [dims {'X': 4, 'o': 10, 'D56': 10, 'D_sol': 2, 'Z': 7}; 15 ∩ gauge_all28 6]
  computed  PASS   Z2b_X_o_D56_are_compact_and_each_fixes_exactly_the_f6_ray   [{"X": {"dim": 4, "compact": true, "fixed_dim_on_V6": 1, "fixed_set_is_f6_ray": true}, "o": {"dim": 10, "compact": true, "fixed_dim_on_V6": 1, "fixed_set_is_f6_ray": true}, "D56": {"dim": 10, "compact": true, "fixed_dim_on_V6": 1, "fixed_set_is_f6_ray": true}, "D_sol": {"dim": 2, "compact": true, "fixed_dim_on_V6": 2, "fixed_set_is_f6_ray": false}, "Z": {"dim": 7, "compact": false, "fixed_dim_on_V6": 0, "fixed_set_is_f6_ray": false}}; Stab(o) = Stab(D56): True]
  computed  PASS   Z3a_every_census_boost_commutes_with_Gamma_preserves_Omega_and_puts_the_Z_line_on_its_ray_with_lambda2_eta   [37 boosts; max over them of |g⁻¹ẑ − ray p|, |λ² − η(p,p)|, ‖[g, Γ]‖, ‖gᵀΩg − Ω‖: < 1e-8]
  computed  PASS   Z3b_no_single_integrality_condition_selects_lambda2_2   [X-integral at λ² [2, 4]; Z-integral at [2, 6, 8, 10, 14, 20, 22]; Gram-integral at [2, 4] (37 rays)]
  computed  PASS   Z3c_on_the_lambda2_2_orbit_integrality_holds_on_the_Stab_X_planes_and_breaks_on_the_other_six   [rotations at θ = 0.7 keeping X, Z and Gram integral: ['f1f2', 'f1f3', 'f2f3', 'f4f5']; breaking X and Z (Gram kept): ['f1f4', 'f1f5', 'f2f4', 'f2f5', 'f3f4', 'f3f5']]
  computed  PASS   Z4_X_and_Z_integral_together_occur_only_at_lambda2_of_the_form_2m2_and_the_census_finds_only_m_1   [λ² values with √2·X and Z both integral: [2] (all of the form 2m²: True)]
  argument  ARG    Z4_theorem
  argument  ARG    Z2_why_no_symmetry_selects
  argument  ARG    scope
  argument  ARG    reading

Z3 per λ²: {"2": {"rays": 3, "X": 1, "Z": 1, "G": 3}, "4": {"rays": 4, "X": 1, "Z": 0, "G": 4}, "6": {"rays": 3, "X": 0, "Z": 1, "G": 0}, "8": {"rays": 3, "X": 0, "Z": 1, "G": 0}, "10": {"rays": 3, "X": 0, "Z": 1, "G": 0}, "12": {"rays": 3, "X": 0, "Z": 0, "G": 0}, "14": {"rays": 3, "X": 0, "Z": 2, "G": 0}, "16": {"rays": 3, "X": 0, "Z": 0, "G": 0}, "18": {"rays": 3, "X": 0, "Z": 0, "G": 0}, "20": {"rays": 3, "X": 0, "Z": 1, "G": 0}, "22": {"rays": 3, "X": 0, "Z": 1, "G": 0}, "24": {"rays": 3, "X": 0, "Z": 0, "G": 0}}

VERDICT Z-QUANTUM SELECTION: PARTIAL. No registered symmetry picks the point (X, o, D56 all fix the same vacuum axis, which moves with the data); no single integrality condition picks λ² = 2 (X at 4; Z up to 22; Gram at 4); the gauging and the registered Z integral TOGETHER force λ² = 2m² (proof), and only m = 1 occurs on the pure-boost census. On Λ₀, √2·X and Z are integral.
RESULT_HASH 7ec060f5a830512b
s1350: 13 computed/receipt PASS-able, 4 argument, 0 failed
