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s1212 — MAGIC 28: existence census of a non-scalar coupling splitting the d = 4 return block 8 + 18 (R189 call 5)
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carrier: {"G_order": 45, "d": 4, "det_B": -45, "n_orbits": 13, "period_histogram": {"1": 1, "2": 2, "4": 10}}
normalizer (box 6): 28 elements (14 centralizer, 14 reversers); units C² = A: [((-2, 1), (-1, 1)), ((2, -1), (1, -1))]; image Γ̄ order 8, abelian False, exponent 2 False
linking-form F on W_4: eigen-phases (units of π/2): [0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3] · F⁴ = 1 on W: True
ENUMERATION LOCK 5048a05f0504587c: 64 operators X ⊗ s
  ORBITAL-ONLY       n =  15  STRICT 2  WEAK 6  (CLUSTER, reported only: 6)   partitions 12+14×2 · 2+4+20×1 · 4+18+4×4 · 4+22×2 · 8+18×2 · 8+8+10×4
  ORBITAL⊗SPIN       n =  45  STRICT 0  WEAK 0  (CLUSTER, reported only: 0)   partitions 10+2+1+1+2+10×3 · 13+13×18 · 4+18+4×12 · 9+8+9×12
  SCALAR (excluded)  n =   1  STRICT 0  WEAK 0  (CLUSTER, reported only: 0)   partitions 26×1
  SPIN-ONLY          n =   3  STRICT 0  WEAK 0  (CLUSTER, reported only: 0)   partitions 13+13×3
  expectation (5) — ORBITAL-ONLY STRICT/WEAK hits: 6 [('Gamma[3] sym', [8, 18]), ('Gamma[4] sym', [8, 8, 10]), ('Gamma[7] sym', [8, 8, 10]), ('F^1 herm', [8, 8, 10]), ('F^2 herm', [8, 18]), ('F^3 herm', [8, 8, 10])]
    frozen-criterion λ scan (800 points): λ giving exactly 2, 8, 20, 28 below 30 → []

  LOWER BLOCKS for Gamma[3] sym via M = [[-3, 1], [-1, 0]]: odd/even orbits per d = d1 0/1 · d2 0/3 · d3 2/4 · d4 4/9 · d5 12/13 · d6 26/32
    odd_low_small                      all-boundaries<60 [2, 8, 12, 20, 28, 46]  frozen-criterion<130 [2, 8, 20, 46, 96]  lowest 1.619034
    odd_low_lambda_min_eps4_over_3     all-boundaries<60 [4, 6, 12, 20, 28, 46]  frozen-criterion<130 [4, 96]  lowest 1.618034
    even_low_small                     all-boundaries<60 [2, 8, 16, 20, 38, 46]  frozen-criterion<130 [2, 8, 20, 46, 96]  lowest 1.617034
    even_low_lambda_min_eps4_over_3    all-boundaries<60 [2, 8, 16, 34, 38, 46]  frozen-criterion<130 [16, 96]  lowest -13.708204

  LOSS CONDITION FIRED → MISSING OBJECT: a Hermitian orbital–spin coupling on W_4 ⊗ C² OUTSIDE span{Γ̄, period grading, linking-form F} ⊗ {σx, σy, σz}, whose extreme eigenspace is 8-dimensional — equivalently, an intertwiner from a registered isotype (Peirce/Fano, 𝒪 support) into W_4 that the corpus does not supply (A1741 §14 P3(a)).

VERDICT d = 4 block (45 points, 13 orbits, 26 states): 64 single-term couplings enumerated (lock 5048a05f0504587c); ORBITAL⊗SPIN STRICT/WEAK hits 0; ORBITAL-ONLY hits 6; Γ̄ order 8 (abelian False); loss condition FIRED
RESULT_HASH 81eec00eb588846e
s1212: 14 computed PASS-able, 4 argument, 0 failed
