s1134 — replication carrier census

PART A — FUSION COUNT (Hom endpoint: real components of J₃(𝕆_s) = 3 diag + 3×8 off-diag = 27; indexing: A689 B map)
  J12: 2 components used of 8 → ['e0', 'e7']
  J13: 8 components used of 8 → ['e0', 'e1', 'e2', 'e3', 'e4', 'e5', 'e6', 'e7']
  J23: 8 components used of 8 → ['e0', 'e1', 'e2', 'e3', 'e4', 'e5', 'e6', 'e7']
  one generation: 18 of 24 off-diagonal real dims (Higgs 2 + fermions 16); three generations of fermions: 48; plus one Higgs plane: 50
  [PASS] J₁₃ and J₂₃ are each FULLY occupied by one generation (8/8) — no spare block dimension for a second generation
  [PASS] three generations need 3×16 = 48 fermion components > 24 off-diagonal dims (> 27 total): the replication map cannot land in ONE J₃(𝕆_s)
  ⇒ the codomain of 𝒪_rep must be a carrier of dimension ≥ 50 (48 + Higgs plane); J₃ ⊗ ℝ³ (81) is the smallest registered tensor candidate; the 56 of E₇₍₇₎ (App H) is the smallest registered non-tensor one

PART B — SLOT COLLISION: the Peirce swaps R_ij(π/2) (s1133) act on the A689 block assignment
  generation swap (1↔2) R₁₂:
    J12 (Higgs)                → J12 (Higgs)                (sign -1)
    J13 (Q, L)                 → J23 (u^c d^c e^c ν^c)      (sign +1)
    J23 (u^c d^c e^c ν^c)      → J13 (Q, L)                 (sign -1)
  generation swap (2↔3) R₂₃:
    J12 (Higgs)                → J13 (Q, L)                 (sign +1)
    J13 (Q, L)                 → J12 (Higgs)                (sign -1)
    J23 (u^c d^c e^c ν^c)      → J23 (u^c d^c e^c ν^c)      (sign -1)
  [PASS] (1↔2) exchanges the LEFT-fermion block J₁₃ with the RIGHT-fermion block J₂₃ (Q,L ↔ u^c,d^c,…)
  [PASS] (2↔3) exchanges the HIGGS block J₁₂ with the left-fermion block J₁₃
  blocks moved by each idempotent permutation: {(0, 1, 2): 0, (0, 2, 1): 2, (1, 0, 2): 2, (1, 2, 0): 3, (2, 0, 1): 3, (2, 1, 0): 2}
  [PASS] every non-identity generation permutation moves ≥ 2 of the 3 field blocks: 'generations = f_i' AND 'fields = P_ij' cannot coexist on one J₃ with the generation action by Peirce permutation (naive replication DEAD)

PART C — TENSOR ROUTE: Y_f = L_{h_f} ⊗ D̂_f with D̂ in the s954 naturality-cut family (all polynomials in M)
  spec |M| = [1.61803398875, 1.0, 0.61803398875] (φ, 1, φ⁻¹ — the J_vac spectrum)
  [PASS] spec |M| = {φ, 1, φ⁻¹} = spec J_vac (relative 1e-12): the coincidence D1230 hands the lane is real
  [PASS] D̂(A,B,C) reconstructed from the |M| eigenprojectors equals s954's D_vis = [[C−B,0,B],[0,A,0],[B,0,C]] (relative 1e-12)
  max |[Y_u, Y_d]| over 200 random (A,B,C)_u, (A,B,C)_d pairs: 0.00e+00
  [PASS] [Y_u, Y_d] = 0 for EVERY pair in the naturality-cut family (absolute ≤ 1e-12): the tensor route is ALIGNED, V = I — the spectral coincidence buys no frame
  [PASS] relative frame U_uᵀU_d is a signed permutation (|entries| ∈ {0,1}): no mixing angle exists in this class
  [PASS] control: a generic symmetric D_d OUTSIDE the family does not commute with D̂_u — non-alignment requires leaving the naturality-cut family (the A1471 premise), as Paper 3 states

VERDICT (typing, no number): the replication map cannot be an endomorphism of one J₃ (count), cannot be 'one channel per
  idempotent' on the same J₃ (slot collision), and cannot be 'field channel ⊗ A1471 generation family' (aligned). Its codomain
  is a bigger registered carrier and its generation operators must sit outside the naturality-cut family. These three
  closures are the house's ACCEPTANCE TEST for the D1230 W1 return: a positive build must name which of the three it evades.

RESULT: ALL GATES PASS
