s1162 — |V_us| closed form (S302.8) + exact-asymmetric R₂ audit (S302.9)

(A) |V_us| FROM THE CLOSED FORM — the kernel line the print is corrected from
  tan θ₁₂ = √3/φ²        = 0.661584538
  θ₁₂ = arctan(√3/φ²)     = 33.488005°   (print: 33.4880°)
  sin²θ₁₂                 = 0.304442  = 3/(3+φ⁴) = 0.304442
  |V_us| = sin θ₁₂/√6      = 0.225256056   (print: 0.225256)
  vs PDG 2026 0.22431 ± 0.00085: +0.42%  ·  +1.113σ   (print: +1.11σ)
  [PASS] sin²θ₁₂ from arctan equals the closed form 3/(3+φ⁴) to 1e-12
  [PASS] |V_us| rounds to 0.225256 (six decimals) — the S302.8 print
  [PASS] θ₁₂ rounds to 33.4880° (four decimals) — the S302.8 print
  [PASS] σ vs PDG 2026 rounds to +1.11 — unchanged from Rev32.5
  the Rev32.5 print 0.225247 = sin(33.4865°)/√6 — no angle in the chain; 33.4877° − arctan(√3/φ²) = -0.0003°
  [PASS] 0.225247 is NOT the closed form (differs by > 5 ppm)
  [PASS] 33.4877° is NOT arctan(√3/φ²) (differs by > 1e-4°)
  shift 0.225247 → 0.225256: 40 ppm; no tier moves
  corollaries (unchanged in print): |V_cb| = 1/(9√7) = 0.041996 · |V_ub| = |V_us||V_cb|/√6 = 0.0038620 (print 0.003862) · |V_ud| = √(1−|V_us|²−|V_ub|²) = 0.974292 (print 0.97429)
  [PASS] |V_ub| corollary rounds to 0.003862
  [PASS] |V_ud| corollary rounds to 0.97429

(B) THE R₂ ROW (22b) WITH THE EXACT ASYMMETRIC NuFIT 6.1 ERRORS — supersedes s1104 as certificate
  R₂ = 1/(φ⁴−1) = 0.17082 · R₂² = 0.02918
  without SK-ATM: Δm²₃ₗ = 2.521e-03 (+2.600e-05 −1.800e-05) · ratio 0.02990 · floor √ratio = 0.17291 (+0.00124 −0.00145)
      R₂ − floor = -0.00209 (-1.21%) → 1.436σ below (downward floor error)
      m₁ at which the floor is 2σ above R₂: 0.86 meV
  with SK-ATM   : Δm²₃ₗ = 2.511e-03 (+2.100e-05 −2.000e-05) · ratio 0.03002 · floor √ratio = 0.17325 (+0.00128 −0.00136)
      R₂ − floor = -0.00243 (-1.40%) → 1.789σ below (downward floor error)
      m₁ at which the floor is 2σ above R₂: 0.51 meV
  [PASS] z without SK-ATM = 1.436 rounds to 1.44 (print lower bound)
  [PASS] z with SK-ATM = 1.789 rounds to 1.79 (print upper bound)
  [PASS] R₂ below BOTH floors (edge target, m₁>0 only widens the gap)
  [PASS] floor with SK-ATM prints as 0.17325 (p5)
  [PASS] m₁ at −2σ = 0.86 meV without SK-ATM / 0.51 meV with — p5 prints the pair as '0.51/0.86' (WITH/without order; the sentence's earlier 'without / with' order is reversed for this pair → retitle in tex)
  [PASS] |z| < 2σ in both datasets — NOT refuted; NOT a hit
  s1104 v1 certificate said −1.04σ with a SYMMETRIC 1.35% calibration-grade error — that certificate is RETIRED by this line.

(C) LOOK-ELSEWHERE — the same 20-member menu as s1104, coverage restricted to local bands
  menu: 20 numbers · tolerance ±2% (log-space, disjoint upper bound) · hits within 2% of the floor: ['R_2']
  coverage full range [9.71e-06, 0.62]: 7.23%  (20 members)
  coverage local band [0.1, 0.3]: 10.92%  (members ['R_2', 'φ^-3', 'φ^-4'])
  coverage local band [0.15, 0.2]: 13.90%  (members ['R_2'])
  [PASS] local-band look-elsewhere prints as 10.9–13.9% (p5)
  [PASS] R₂ is the only menu member within 2% of the floor

VERDICT
  (A) The closed form prints |V_us| = 0.225256 (θ₁₂ = 33.4880°), +1.11σ vs PDG 2026. The six Rev32.5 sites
      that print 0.225247 / 33.4877° are corrected FROM THIS LINE (S302.8); σ, |V_ub|, |V_ud| and every tier unchanged.
  (B) R₂ = 0.17082 sits 1.44–1.79σ below the m₁=0 NO floor (without / with SK-ATM) under the exact asymmetric errors,
      local-band look-elsewhere 10.9–13.9%. The 22b print stands; s1104's −1.04σ certificate is superseded here.

s1162: ALL CHECKS PASS
