Law-Sector Decoherence in de Sitter Space: A Recursion-Constrained Determination of Coupling Scale

We connect Fibonacci Causal Loop Theory (FCLT) depth-2 recursion to a minimal open-system model of law-sector decoherence in de Sitter space (Clark 2026). The recursion eigenstructure defines orthogonal φ- and ψ-sectors, with ψ = −1/φ furnishing a decaying mode. Exact coefficient-space orthogonality ⟨v_φ, v_ψ⟩ = 1 + φψ = 0 (Vieta's formulas) provides the sector basis underlying Clark's direct-sum assumption. A transfer-matrix formulation makes the two-sector decomposition explicit. The invariant I = ln|φ/ψ| = 2 ln φ and the influence-functional normalisation Γ(t) ∝ (Δg̃)²/2 together fix the minimal positive branch: (Δg̃)² = ln φ ≈ 0.481, yielding decoherence timescale τ_d = 1/[(ln φ)H] ≈ 2.08/H. Two independent arguments confirm this branch: (1) the trace condition absorbs one factor of ln φ from the invariant; (2) only the ψ-mode decoheres, with decay rate (ln φ)H per e-fold. The same ψ-mode structure fixes the bispectrum shape function F(k) = k^(−φ⁻⁷), φ⁻⁷ ≈ 0.03444, already confirmed at 0.16σ as the CMB spectral tilt (Planck 2018). A self-contained derivation of (1−nₛ) = φ⁻⁷ is provided in Appendix A. Four falsifiable predictions are pre-registered per FCLT Protocol V3: (1) (Δg̃)² = ln φ ≈ 0.481; (2) ω = H/φ ≈ 0.618H; (3) F(k) = k^(−φ⁻⁷); (4) m₁/m₂ = φ² ≈ 2.618. The framework constrains but does not derive the full influence functional, does not resolve α-vacuum ambiguities, and does not include infrared logarithmic corrections. Three open calculations are explicitly named.