Paper 116A: Dynamic Admissibility and Organizer Stability Gate Evolution, Hysteresis, and Rotation Stability Transitions

Paper 116A upgrades the organizer primitive introduced in Paper 116 by allowing the admissibility gate g(x,t)∈[0,1]g(\mathbf{x},t)\in[0,1]g(x,t)∈[0,1] to evolve in time under a declared, bounded update rule. The licensed transport current remains J=g J0\mathbf{J}=g\,\mathbf{J}_0J=gJ0, so rotational structure can still be injected geometrically through gate gradients, but the core question becomes stability: when does gate-injected rotation persist as an organizer under feedback, and when is it transient? The paper defines a minimal admissibility-update class ∂tg=F(g,Ω,Π,H)\partial_t g=\mathcal{F}(g,\Omega,\Pi,\mathcal{H})∂tg=F(g,Ω,Π,H) based on declared diagnostics—swirl magnitude Ω=∥∇×J∥\Omega=\|\nabla\times\mathbf{J}\|Ω=∥∇×J∥ and throughput Π=∥J∥\Pi=\|\mathbf{J}\|Π=∥J∥—and an explicitly bounded history state H\mathcal{H}H. Organizer claims are made only through preregistered decision objects (thresholds, persistence windows, and fraction-of-region criteria), producing contract-defined regimes (transient, marginal, locked) and a governed hysteresis test under parameter rollback. A clean-control simulation protocol is specified to isolate gate-gradient effects, enforce boundedness, audit limiter dominance, and rule out hidden sources or boundary injection. The result is an audit-stable stability layer for dynamic admissibility: a reusable framework for organizer persistence and hysteresis that preserves the inherited no-free-energy posture and avoids force-law or Navier–Stokes equivalence claims.