Phase-Mediated Attractor Dynamics (PMAD)

Phase-Mediated Attractor Dynamics (PMAD) is a minimal axiomatic framework in which relative phase structure—rather than spatial adjacency—organizes long-time coherent behavior in driven many-body systems. Grounded in four axioms (Phase Primacy, Attractor Determinism, Stability over Symmetry, and Ubiquitous Resonance), PMAD derives spacetime geometry and quantum probability from a single underlying object: the long-time phase-overlap functional $\langle e^{i(\phi_i - \phi_j)} \rangle_T$. The effective spacetime metric emerges as the Hessian of the phase variance, while the Born rule arises as its weak-drive, stationary-phase limit. Projection onto observable submanifolds further induces persistent effective force terms arising from phase-space incompleteness, wherein stiff hidden-sector attractors renormalize visible dynamics. Wilsonian renormalization group flow applied to the attractor stability manifold yields an analytic estimate of attractor dimensionality, with UV and IR fixed points corresponding to full phase manifold preservation and complete phase-space contraction, respectively. These results are empirically validated through an untuned operational pipeline applied without parameter adjustment to solar wind plasma, coronal EUV emission, pulsar timing residuals, black hole accretion noise, and Floquet lattice simulations, recovering a consistent negative-Lyapunov stability signature across all systems. Hardware validation on IBM Sherbrooke confirms that the mechanism requires global phase coherence, consistent with PMAD predictions. We conclude that conventional spacetime assumptions are not a necessary organizing principle for driven dynamics; rather, classical geometry and quantum probability emerge as complementary reductions of phase-dynamical averaging.