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 Lₙ = sqrt (gamma) Pₙ, where Pₙ are the orthogonal projectors onto the Frobenius eigenspaces. We prove: (i) off-diagonal sector density-matrix elements rhoₙm (t) (n not equal m) decay exponentially at rate gamma; (ii) in the presence of a sector-mixing perturbation Vₛys, steady-state off-diagonal elements satisfy |rhoₙmˢs| le 2||Vₛys||/sqrt (gamma²+omegaₙm²) ; (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, Pₙ=0), the diagonal sector populations rhoₙn are conserved by the Lindblad evolution, so the EHSCM torsion weights wₙ (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 = cₖappa TH (natural units hbar=kB=1), with cₖappa = 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.