s1105 — CKM first row: Route A vs Route B anatomy, selection cost, and the replacement functor
  Route A: θ_C = arctan(φ⁻³) − arctan(α/π) → |V_us| = 0.22749  (+3.74σ vs PDG 2026)  [LOADS α — fenced object]
  Route B: sin θ₁₂ᴾᴹᴺˢ/√6, framework angle 33.488° → 0.22526  (+1.11σ)
  Route B on the MEASURED angle 33.76° → 0.22687  (+3.01σ)  [Rev32.1 'measured-angle readout']
  [PASS] Route A value reproduces the printed 0.22749
  [PASS] Route B value reproduces the printed 0.22526/0.22527
  [PASS] Route A is worse than Route B against PDG 2026 (the selection was real, and it was by data)

(1) THE SIBLING MENU — what the row could have been, from registered objects only
  candidate                                   value       σ
  sinθ₁₂/√6  (Route B)                      0.22526   +1.11
  sinθ₁₂/√5                                 0.24676  +26.41
  sinθ₁₂/√7                                 0.20855  -18.55
  sinθ₁₂/√8                                 0.19508  -34.39
  sinθ₁₂·φ⁻²                                0.21075  -15.95
  sinθ₁₂·φ⁻¹/√2                             0.24113  +19.79
  tanθ₁₂/3                                  0.22053   -4.45
  tanθ₁₂/√8                                 0.23391  +11.29
  tanθ₁₂·φ⁻³                                0.15618  -80.15
  sin(arctan φ⁻³)  (Route A, α off)         0.22975   +6.40
  Route A (with α)                          0.22749   +3.74
  φ⁻³                                       0.23607  +13.83
  1/(φ+3)                                   0.21654   -9.14
  sinθ₁₂/√(φ²+1)                            0.29008  +77.37
  members within 1σ/2σ/3σ of PDG 2026: 0/1/1 of 14
  SELECTION COST of picking one by data: log₂(14) = 3.81 bits (declared menu; the true menu the authors faced was ≥2 = 1 bit)
  [PASS] Route B is the best member of the declared menu (the data-selection picked the optimum, as data-selection does)

(2) THE FUNCTOR THAT WOULD REPLACE THE DATA — CT lens
  Route B's weight 1/√6 = 1/√(3!) = 1/√|S₃| (s499). Categorical shape: |V_us|² = sin²θ₁₂ / |S₃| is the
  Peirce-triality (S₃) ORBIT AVERAGE of the solar-angle datum — a functor F: PMNS-angle → CKM-element,
  F(θ) = sinθ/√|S₃|. If F is a functor it is UNIFORM: the same rule must send θ₂₃ᴾᴹᴺˢ to |V_cb|.
  test: F(θ₂₃ᴾᴹᴺˢ = arcsin√(7/16)) = 0.2700 vs |V_cb| = 0.0407 → ratio 6.63×
  [PASS] uniform S₃-orbit-average functor FAILS on |V_cb| (>2× off) — Route B's 1/√6 is ROW-SPECIFIC, not functorial
  what |V_cb| actually carries: 1/(9√7) — the √7 is DET-7 (same object as sin²θ₂₃ = 7/16); the 9 is underived.
  so the second row's weight is 1/(9√7) = 0.04200; first row's is 1/√6. Two rows, two unrelated weights ⇒ no functor yet.

(3) KNOT lens — where the route bit lives
  The first row is a ℤ₂ choice (A|B) fixed by data; Paper 3 §retier calls this the override. In the braid
  reading (KNOT_BRAID_PROGRAM P1: mixing = image of a B₃ word under B₃→PSL(2,ℤ)→S₃), Route A and Route B are
  two different WORDS with the same closure — the choice is a FRAMING datum, exactly the class the knot type
  does not fix (OPEN_ITEMS: 'absolute scale and generation order are framing/orientation data').
  AVENUE: the S₃ = B₃/⟨σᵢ²⟩ quotient makes 1/√|S₃| a PLANCHEREL weight of the trivial S₃-isotype. A derivation
  of Route B = 'the first row is the trivial-isotype projection of the solar datum' would need the SAME
  projection to give |V_cb| — it does not (2). So the honest avenue is narrower: derive WHY the (1,2) block
  averages over S₃ while the (2,3) block carries 1/(9√7). That is a Peirce-block-dependent weight — a
  natural transformation, not a functor. Name that object and Route B stops being a selection.

VERDICT
  LOADED is the right tier. Route A also loads α (fenced) — it was never a clean sibling. The selection cost is
  ≥1 bit (≈3.8 against the declared menu). The replacement structure is NOT the naive S₃-average functor
  (fails |V_cb| by 6.6×); it is a block-dependent weight (1/√6 on J₁₂, 1/(9√7) on J₂₃) whose rule is the
  missing object. ATTACK: derive the two weights from ONE rule (Peirce block ↔ S₃ isotype ↔ DET-7), then
  Route B is forced and the 9 in 9√7 falls out with it — two rows for one derivation.

s1105: ALL CHECKS PASS
