Lindblad Dynamics and Quantum Zeno Suppression in the PTRH Framework: Closure of Gap G8

Gap G8 of the PTRH/TMRB framework called for a derivation of Zeno suppression of inter-sector transitions from a Lindblad master equation. We provide this derivation. Modelling the horizon geometry as a continuous measurement apparatus for the Z9 Frobenius quantum number, we formulate a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation for the Z9-graded matter density matrix with jump operators L_n = sqrt(gamma) P_n, where P_n are the orthogonal projectors onto the Frobenius eigenspaces. We prove: (i) off-diagonal sector density-matrix elements rho_nm(t) (n not equal m) decay exponentially at rate gamma; (ii) in the presence of a sector-mixing perturbation V_sys, steady-state off-diagonal elements satisfy |rho_nm^ss| le 2||V_sys||/sqrt(gamma^2+omega_nm^2); (iii) in the Zeno limit gamma to infinity the steady state is block-diagonal, reproducing the sector isolation of the Isolated Horizon Conjecture (Paper 13) by an independent dynamical route; (iv) under the sector-diagonal bath coupling of the PTRH model ([H,P_n]=0), the diagonal sector populations rho_nn are conserved by the Lindblad evolution, so the EHSCM torsion weights w_n (Paper 11) are preserved. The decoherence rate gamma is identified with the Hawking temperature via the fluctuation-dissipation theorem in the KMS state of Paper 13: gamma = c_kappa T_H (natural units hbar=k_B=1), with c_kappa = O(1) depending on the torsion spectral weight. Gap G8 is upgraded from [O] to [V]. Combined with Papers 13 (algebraic) and 14 (geometric), this provides the third independent proof of Z9 sector isolation.