s1344 — magic 28, the span census (host-stable successor of s1343)
  computed  PASS   expectation_1_block_reproduces_A1741   [|Fix(A^4)| = 45, orbits 13, periods {1: 1, 4: 10, 2: 2} (A1741 §2 house table: 45 / 13 / {1:1, 2:2, 4:10})]
  computed  PASS   carrier_F_d_is_det_formula   [|Fix(A^d)| d=1..4 = [1, 5, 16, 45] vs |2 − tr A^d|]
  computed  PASS   normalizer_contains_minus_I_unit_and_reverser   [28 normalizer elements in |M_ij| ≤ 6: 14 centralizer (units with C² = A: [((-2, 1), (-1, 1)), ((2, -1), (1, -1))]), 14 reversers]
  computed  PASS   normalizer_elements_preserve_Fix_A4   [28 elements × 45 points]
  computed  PASS   W4_is_the_U_invariant_subspace   [U_4 W = W and rank W = 13]
  computed  PASS   linking_form_well_defined_A_invariant_F_unitary_commutes   [b well defined on sampled coset shifts True; A-invariant True; F unitary True; [F, U_4] = 0 True]
  receipt   PASS   s1343_is_the_filed_kernel_this_succeeds
  receipt   PASS   s1212_is_the_filed_kernel_whose_lines_59_to_216_are_copied
  computed  PASS   M1_span_rank_36_orbital_plus_spin_12_coupled_24   [64 generators X⊗s; real rank 36; orbital-only + spin-only rank 12; coupled complement 24]
  computed  PASS   M2_minus_I_is_central_in_the_whole_span   [one Γ̄ involution with 4 odd orbits (the hyperelliptic −I, located by property); max ‖[H, (−I)⊗1]‖ over the 36 basis elements <1e-10]
  computed  PASS   M3_commutant_dim_7_components_8_4_4_4_2_2_2   [commutant dim 7; components [8, 4, 4, 4, 2, 2, 2]; −I parities [1, -1, -1, 1, 1, 1, 1]]
  computed  PASS   M4_thirteen_unions_each_with_a_coupled_scalar_family   [13 unions of components of dim 8; family dims [9, 9, 13, 13, 13, 13, 13, 13, 17, 21, 21, 25, 25]; min max-coupled-fraction 1.000]
  computed  PASS   M5_exactly_two_unions_reach_an_extreme_the_odd_sector_and_one_even_4_2_2   [2 of 13 reach an extreme with a coupled element: [([4, 4], [-1, -1]), ([4, 2, 2], [1, 1, 1])]]
  computed  PASS   M6_both_are_an_orbital_rank_4_projector_times_spin_lying_in_the_span_uncoupled   [for each hit P_S = Π⊗1 with rank Π = 4, P_S ∈ V, coupled part 0: [(True, True, 4), (True, True, 4)]]
  computed  PASS   M6b_STRICT_with_coupling_is_not_met_on_any_union   [unions whose projector lies in V: 2, all with coupled part 0 — a two-eigenvalue H = aP + b(1 − P) is then uncoupled]
  computed  PASS   M7_certificate_lowest_eigenvalue_multiplicity_exactly_8_on_the_odd_sector_with_coupling   [K = projection of the registered generator period grading⊗sx onto the purely coupled part of F_odd (dim 9), both signs; t = 1.5: lowest multiplicity 8, min gap to the 9th 0.5000, overlap with the −I-odd sector 1.000000000, coupled fraction 0.537]
  argument  ARG    scope
  argument  ARG    reading

VERDICT MAGIC-28 SPAN CENSUS: span rank 36 (coupled 24); −I central; algebra components [8,4,4,4,2,2,2]; of 13 component unions of dim 8, 2 reach an extreme with coupling — both an orbital rank-4 projector ⊗ ℂ² already in the span (spin-blind); STRICT with coupling: none. Sums reach WEAK only on orbital four-spaces; the spin coupling never carries the 8.
RESULT_HASH 11527ba0d04508ec
s1344: 16 computed/receipt PASS-able, 2 argument, 0 failed
