s1115 — P1 sector decomposition (independent fusion-path build)
  n= 3 dim=  3 braid-rel 2.4e-16 · Var(all)=0.3906 · Var_τ(P_τRP_τ)=0.490881 · dims (1,τ)=(1,2) · ⟨R²⟩₁=0.3455 ⟨R²⟩_τ=0.5773 · τ ρⁿ phase +1.00×2π/5
  n= 4 dim=  5 braid-rel 3.1e-16 · Var(all)=0.3090 · Var_τ(P_τRP_τ)=0.264663 · dims (1,τ)=(2,3) · ⟨R²⟩₁=0.3455 ⟨R²⟩_τ=0.3652 · τ ρⁿ phase -1.00×2π/5
  n= 5 dim=  8 braid-rel 3.5e-16 · Var(all)=0.5013 · Var_τ(P_τRP_τ)=0.500000 · dims (1,τ)=(3,5) · ⟨R²⟩₁=0.5318 ⟨R²⟩_τ=0.5000 · τ ρⁿ phase +2.00×2π/5
  n= 6 dim= 13 braid-rel 3.5e-16 · Var(all)=0.5279 · Var_τ(P_τRP_τ)=0.562500 lane 0.562500 Δ=+0.0e+00 · dims (1,τ)=(5,8) · ⟨R²⟩₁=0.4382 ⟨R²⟩_τ=0.5625 · τ ρⁿ phase +0.00×2π/5
  n= 7 dim= 21 braid-rel 3.5e-16 · Var(all)=0.4711 · Var_τ(P_τRP_τ)=0.463532 lane 0.463532 Δ=-1.6e-07 · dims (1,τ)=(8,13) · ⟨R²⟩₁=0.4807 ⟨R²⟩_τ=0.4689 · τ ρⁿ phase -2.00×2π/5
  n= 8 dim= 34 braid-rel 3.5e-16 · Var(all)=0.4903 · Var_τ(P_τRP_τ)=0.491859 lane 0.491859 Δ=+2.5e-08 · dims (1,τ)=(13,21) · ⟨R²⟩₁=0.4881 ⟨R²⟩_τ=0.4926 · τ ρⁿ phase +1.00×2π/5
  n= 9 dim= 55 braid-rel 3.5e-16 · Var(all)=0.5082 · Var_τ(P_τRP_τ)=0.511115 lane 0.511115 Δ=-1.4e-07 · dims (1,τ)=(21,34) · ⟨R²⟩₁=0.5000 ⟨R²⟩_τ=0.5119 · τ ρⁿ phase -1.00×2π/5
  n=10 dim= 89 braid-rel 3.5e-16 · Var(all)=0.4967 · Var_τ(P_τRP_τ)=0.500000 lane 0.500000 Δ=+0.0e+00 · dims (1,τ)=(34,55) · ⟨R²⟩₁=0.4881 ⟨R²⟩_τ=0.5000 · τ ρⁿ phase +2.00×2π/5
  [PASS] braid relations hold to 1e-12 for n=3..10
  [PASS] VALIDATION: house τ-sector variances of P_τ R_n P_τ match the lane's c1116 values to 1e-5 for n=6..10 (independent construction)
  [PASS] ribbon identity: τ-sector ρ_nⁿ phase = (1−n)·(4π/5) mod 2π for n=6..10 (c1112: 0, −2, +1, −1, +2 × 2π/5)

  THRESHOLD TEST — does any sector quantity switch between n=7 and n=8?
    Var̂ all-charge n=3..10: +0.391 +0.309 +0.501 +0.528 +0.471 +0.490 +0.508 +0.497   window-match: False
    Var_τ (lane obj) n=3..10: +0.491 +0.265 +0.500 +0.562 +0.464 +0.492 +0.511 +0.500   window-match: False
    ⟨R²⟩ charge-1  n=3..10: +0.345 +0.345 +0.532 +0.438 +0.481 +0.488 +0.500 +0.488   window-match: False
    ⟨R²⟩ charge-τ  n=3..10: +0.577 +0.365 +0.500 +0.562 +0.469 +0.493 +0.512 +0.500   window-match: False
    ⟨R⟩ charge-1   n=3..10: -0.588 -0.000 -0.317 +0.000 -0.073 -0.045 +0.000 -0.028   window-match: False
    ⟨R⟩ charge-τ   n=3..10: -0.294 +0.317 +0.000 -0.000 +0.073 -0.028 +0.028 +0.000   window-match: False
    deficit (data) n=3..10: -0.013 -0.029 -0.000 -0.101 -0.109 -0.009 -0.007 +0.015
  [PASS] NO sector quantity reproduces the window (on 6,7 / off ≥8): none ⇒ the charge filtration does NOT thresholds at n=8
    corr(deficit, Var̂ all-charge) over n=6..10 = +0.02
    corr(deficit, Var_τ (lane obj)) over n=6..10 = -0.13
    corr(deficit, ⟨R²⟩ charge-1) over n=6..10 = +0.69
    corr(deficit, ⟨R²⟩ charge-τ) over n=6..10 = -0.17
    corr(deficit, ⟨R⟩ charge-1) over n=6..10 = +0.25
    corr(deficit, ⟨R⟩ charge-τ) over n=6..10 = -0.55

VERDICT
  Independent fusion-path build REPRODUCES the lane's annular sector (P_τ-projected variances to 1e-5, ribbon identity exact) — c1112/c1116 are
  house-confirmed from scratch. Sector decomposition by total charge (the registered filtration of the Fibonacci annulus) shows NO
  threshold at n=8 in any sector quantity: the second-moment profile is flat (0.46–0.56) while the data drop 10× between n=7 and 8.
  SCOPED NO-GO: the P1 support cannot come from the charge/through-string filtration of the τ-strand annulus either. What is left
  is exactly what A1545 named — an n-LOCAL projector (support built in by hand = not a derivation) or an annular→depth
  intertwiner that is NOT rotation-invariant. Lens verdict: P1 is not a framing object of the τ annulus at all; the hexagon/
  heptagon locality points to the CELL GEOMETRY (the packing of 6 and 7 cells around a centre — coordination), i.e. the same
  writhe/packing sector as ⁶⁴Ge, not the twist sector. Route: retype P1's reopen class from 'annular' to 'packing' (PI-gated).

s1115: ALL CHECKS PASS
