Spin-Universal Kryukov Intertwining Angle and the Krein–Fermi–Dirac Identity for Gravitational Decoherence Corrections

We prove three exact results for gravitational decoherence in the two-level Bogoliubov truncation of the Minkowski vacuum, extending the Krein-space framework of Paper I to fields of arbitrary spin. Lemma (No-go): The naive kernel Tr(ρ dR²_Krein) is identically equal to 1/4 for any T∈SO(2) and any state ρ, showing that second moments of the boost generator are blind to Krein corrections. Theorem A (Spin universality): The Bogoliubov thermal factor |β_s/α_s|² = e^{−2πωL} is independent of spin s via the Bisognano–Wichmann theorem. Consequently, the Kryukov intertwining angle λ* = (2/π)arctan(e^{−πωL}) is universal for all free Wightman fields in 3+1 Minkowski spacetime, within the two-level truncation. The result is exact for spin-1/2 (Dirac) fields and approximate for bosonic fields. Theorem B (Krein–Fermi–Dirac identity): The J-negative sector weight δ = Tr(P₋ ρ_trunc) equals the Fermi–Dirac occupation number at the Unruh temperature T_U = 1/(2πL): δ(ω,L) = e^{−2πωL}/(1+e^{−2πωL}) = n_F(ω,T_U). This identity is exact for spin-1/2 fields. Theorem C (Coherence Squaring): The interference visibility satisfies V_Krein = V²_QM, a quadratic suppression providing a falsifiable signature for Pikovski-type gravitational decoherence experiments. Paper II of the Scale-Dependent Categorical Quantum Gravity (SDCQG) Programme. Companion paper: Paper I (10.5281/zenodo.18876992, 2026).