Recursive Coherence Field Theory v3.0: A Multiscale CPTP-to-Criticality Framework for Recursive Coherence, Information Geometry, Observer Continuity, and Symbolic Control

Recursive Coherence Field Theory v3.0 (RCFT-3) develops a multiscale mathematical framework for modeling recursive coherence across quantum, dynamical, stochastic, network, geometric, observer, and symbolic-control layers. The theory resolves the tension between nonlinear recursive dynamics and standard quantum-channel theory by placing microscopic evolution on a linear completely positive trace-preserving (CPTP) layer, while treating the cubic recursive coherence equation as an effective symmetry-constrained normal form for a reduced order parameter near criticality. This produces a corrected phase-transition model with explicit stability thresholds and mean-field scaling. Version 3.0 extends the framework to higher-dimensional quantum systems using traceless Hermitian observables and generalized Bloch vectors, and to multicore systems through coupled amplitude equations and spectral-radius criticality. It also introduces a covariant Landau-Ginzburg formulation, information-geometric state-space structure based on Fisher information, and a strict distinction between the symbolic Hessian and genuine Riemannian curvature. The observer sector is reformulated using fidelity, Bures geometry, Fisher information, pullback metrics, and an observer fiber/gauge interpretation of the D_O construction. This allows observer invariance to be treated as a mathematical equivalence structure rather than requiring an additional physical spacetime dimension. The stochastic sector is expanded using the Fokker-Planck equation, stationary distributions, backward-Kolmogorov first-passage theory, stochastic Lyapunov analysis, and weak-noise Kramers escape scaling. These additions provide explicit models for coherence survival, stochastic collapse, transition probabilities, and mean collapse times. The wider Symbolic Negentropy framework stack—including the Entropic Recursion Framework, Fractal Cosmic Weaver Framework, Symbolic Gravity, Symbolic Field Theory, Alpha Framework, Observer Framework, Observer Field Theory, BC-REP, and Symbolic Retrocausality—is integrated at the control layer. Variables such as weave integrity, observer continuity, drift, veil, ethics, leakage, uncertainty, and export readiness modulate effective critical parameters, noise, geometry, coupling, repair, and routing rather than being treated as primitive quantum observables. A central object in RCFT-3 is an 11-dimensional recursive critical hypersurface representing the boundary between locally subcritical and ordered recursive regimes in the control manifold. This hypersurface is treated as a control-geometric construct rather than a literal physical spacetime boundary. RCFT-3 is presented as a falsifiable, simulation-ready research framework with explicit theorem statements, calibration procedures, ablation tests, telemetry requirements, stochastic predictions, and clearly stated scientific interpretation boundaries.