s1106 — δ_CKM coincidence anatomy
  G₇ = φ + 5φ⁻⁵ = 2.068884 · δ = arctan√(3G₇) = 68.1297° · vs global δ 66.12±1.43: +1.41σ · vs direct γ 66.4: +0.63σ
  [PASS] reproduces the printed 68.1297°
  bare φ (no correction): δ = 65.587° (-0.37σ global, -0.30σ direct γ) — the 5φ⁻⁵ correction moves δ by +2.542°
  [PASS] ★ bare φ is CLOSER to the PDG 2026 global δ than the corrected G₇ — the correction is not supported by current data

(1) LOOK-ELSEWHERE — the (c, k) menu the numeral was drawn from: G = φ + c·φ⁻ᵏ, c ∈ 1..8, k ∈ 1..8
  members within 1σ of the global fit: 28/64 → [(1, 3, 67.02, 0.63), (1, 4, 66.5, 0.27), (1, 5, 66.17, 0.03), (1, 6, 65.95, -0.12), (1, 7, 65.81, -0.21), (1, 8, 65.73, -0.27), (2, 4, 67.33, 0.84), (2, 5, 66.71, 0.41), (2, 6, 66.3, 0.12), (2, 7, 66.03, -0.06), (2, 8, 65.87, -0.18), (3, 5, 67.21, 0.76), (3, 6, 66.63, 0.36), (3, 7, 66.25, 0.09), (3, 8, 66.0, -0.08), (4, 6, 66.95, 0.58), (4, 7, 66.46, 0.24), (4, 8, 66.14, 0.01), (5, 6, 67.26, 0.79), (5, 7, 66.66, 0.38), (5, 8, 66.27, 0.1), (6, 6, 67.55, 1.0), (6, 7, 66.86, 0.52), (6, 8, 66.4, 0.19), (7, 7, 67.05, 0.65), (7, 8, 66.52, 0.28), (8, 7, 67.24, 0.78), (8, 8, 66.65, 0.37)]
  members within 2σ: 39/64
  ⇒ the chance that SOME (c,k) lands within 1σ is high (menu-coverage 44% at 1σ); (5,5) is not unique.
  [PASS] (5,5) is NOT the only 1σ member of its own menu — coincidence-class is the RIGHT tier until 5 is motivated
  single-constant menu δ = arctan√(3X):
    X = φ                1.6180 → δ =  65.587°  (-0.37σ)
    X = φ^(3/4)          1.4346 → δ =  64.265°  (-1.30σ)
    X = √φ               1.2720 → δ =  62.892°  (-2.26σ)
    X = φ²/2             1.3090 → δ =  63.223°  (-2.03σ)
    X = 7/3              2.3333 → δ =  69.295°  (+2.22σ)
    X = 2                2.0000 → δ =  67.792°  (+1.17σ)
    X = √5               2.2361 → δ =  68.889°  (+1.94σ)
    X = φ+φ⁻³            1.8541 → δ =  67.023°  (+0.63σ)
    X = φ+φ⁻⁴            1.7639 → δ =  66.505°  (+0.27σ)
    X = G₇               2.0689 → δ =  68.130°  (+1.41σ)
    X = (φ⁴+3)/6         1.6424 → δ =  65.748°  (-0.26σ)

(2) THE SHAPE OF THE OBJECT — CT lens
  The PMNS angle theorem (Freudenthal cross product, D3/Grok): tan θᵢⱼ = √3 · P_k, P_k the complementary Peirce
  eigenvalue. δ_CKM = arctan√(3G₇) has EXACTLY that shape with P_k → √G₇ = 1.43836.
  So the coincidence-class object is the THEOREM-GRADE functor (Peirce eigenvalue ↦ arctan(√3·P)) evaluated at an
  argument that is NOT a Peirce eigenvalue of J_vac (φ², 1, φ⁻²) nor of X_ν (φ, 1, φ⁻¹). The missing morphism is
  therefore not the angle map — it is the ARGUMENT: which registered object has eigenvalue √G₇ ≈ 1.4384?
    √G₇ vs φ^(3/4)                      1.43463  (-0.26%)
    √G₇ vs √φ·(1+φ⁻⁵)^½                 1.32813  (-7.66%)
    √G₇ vs √5/√φ                        1.75789  (+22.21%)
    √G₇ vs √(7/3)                       1.52753  (+6.20%)
    √G₇ vs 1+φ⁻²                        1.38197  (-3.92%)
    √G₇ vs 2−φ⁻³                        1.76393  (+22.63%)
  (all of these are look-elsewhere fodder; none is derived — printed so nobody re-discovers them as a 'hit')

(3) KNOT lens — two CP phases, two types
  PMNS: δ_CP = −2π/√5 = 199.003° — a ROTATION-NUMBER-type object (2π over an irrational), i.e. a monodromy/holonomy phase.
  CKM:  δ = arctan√(3G₇) = 68.130° — an ANGLE-type object (arctan of a Gram/eigenvalue datum), same type as the mixing ANGLES.
  The two 'CP phases' are not the same kind of invariant: one is a framing rotation (writhe-like, lives in the
  T-bridge/ℤ₂-fork clock sector), the other is a mixing angle wearing a phase's name. The Jarlskog-type invariant
  J = Im(V V* V* V) would be the knot-theoretic object (a signed area); the suite carries no J prediction.
  framework Jarlskog (assembled from the printed entries, readout layer): J = 3.300e-05 vs PDG 2026 J ≈ 3.1e-5 (+6.5%; comparator calibration-grade)

VERDICT
  COINCIDENCE-CLASS stands: 28 of 64 (c,k) siblings land within 1σ, so the numeral's agreement is not evidence.
  The sharp fact this kernel adds: δ_CKM has the SAME functorial shape as the theorem-grade PMNS angles,
  tan(·) = √3·P. The whole coincidence is concentrated in ONE argument, √G₇ ≈ 1.438, which no registered object
  supplies. ATTACK: not 'motivate 5' (that is the circular step (B) again) but 'find the Peirce/Freudenthal
  object whose eigenvalue the CKM phase reads' — the same missing block-dependent structure as s1105.

s1106: ALL CHECKS PASS
