Q5 Decoherence as a Unique Attractor of Kernel Dynamics

This Theorem establishes that the coherence decay rate is the unique globally attracting fixed point of a self-consistent kernel-induced dynamical map. The exponential saturation law of T51 emerges as the asymptotic reduction of this fixed-point structure in the strong-suppression regime, rather than being postulated. The kernel-induced map is F (Γcoh): = Γₘax1 − exp (−M (Γcoh) /M₀), where the composite hazard variable M (Γcoh): = Pᵢnst (1 − exp−β/ (γ + Γcoh) ) is self-referential, stronger decoherence suppresses revival, increasing M, increasing decoherence further. Four steps prove the unique attractor: (1) Monotonicity F' (Γcoh) < 0 by explicit sign chain; (2) Existence and uniqueness via IVT on G = F − id with G' < −1; (3) Global convergence via even/odd subsequence monotone convergence; (4) Asymptotic reduction, in the regime β/γ ≫ 1, M (Γcoh) ≈ Pᵢnst and the fixed-point equation reduces to the exponential saturation law Γcoh ≈ Γₘax (1 − e^−Pᵢnst/M₀). Three corollaries: mechanism separation (β = 0 forces Γcoh* = 0, phase instability alone is insufficient) ; universality across Q5 parameter families; saturation bound Γcoh* ≤ Γₘax. The Grumpy Bear Principle provides an informal interpretation of three dynamical regimes: sleeping bear (M ≈ 0, coherent), grumpy bear (instability present but strong revival), and bear claws (M large, fixed point near Γₘax, self-referential lock-in). Status: Fixed-point monotonicity, G' < −1, existence and uniqueness, global convergence, mechanism separation, and saturation bound are all solid by explicit algebraic argument. Asymptotic reduction solid in β/γ ≫ 1 regime, regime validity not yet verified from T17 kernel. Local stability is solid in the perturbative regime. Primary open step: explicit derivation of β from Mₙ, DₙY geometry from T17 kernel generators. All results inherit T17, T29, T33, T35, T50, T51 conditionality. Dependencies: T8, T11, T29, T33, T35, T50, T51.