Constraint-Dispersion Unified Framework (CDUFD): Emergent Quantum Mechanics, Gauge Symmetries, Gravity, and Cosmology

V2. 0 We present the Constraint-Dispersion Unified Framework (CDUFD), in which quantum mechanics, gauge symmetries, gravity, and cosmology emerge from non-equilibrium critical dynamics near second-order phase transitions. The framework operates through a dual mechanism. Emergent convergence (Axioms A1–A4) forms a progressive logical cascade that eliminates constructions incapable of self-consistent physical histories, delimiting the space of logically possible universes. Within this space, the meta-dynamics governed by the self-consistency functional creates a continuous habitability gradient around the self-dual critical point lambda = 1/2: all values of lambda in (0, 1) are dynamically accessible, but states closer to 1/2 possess richer capacities for complex structure formation. Empirical anchoring (Axiom A5) locates our universe at lambda = 0. 48, near the peak of this gradient. We introduce the concept of a critical spectrum: a logical cascade of critical points at different energy scales, each responsible for the emergence of specific physical content. The spectrum is bounded by the UV side (onset of emergence) and the IR pole (maximum entropy), and its ordering describes logical dependency rather than chronological sequence. We propose a survivor mechanism based on logical convergence, not temporal selection. Time itself is an emergent property of survivors; it is not a pre-existing stage for selection. The self-dual critical point lambda = 1/2 is the unique dynamical attractor, but no value of lambda in (0, 1) is dynamically forbidden. The quadratic minimum of the self-consistency functional creates a continuous habitability gradient: the closer to 1/2, the richer the emergent structures. Our universe, anchored at lambda = 0. 48, sits near the peak of this gradient. All core derivations have been completed in the supplementary materials: quantum mechanics emergence (Fokker-Planck to Schroedinger, Wallstrom condition, Born rule), gauge field emergence (solution-space reduction to pi₁ non-zero groups, SO (8) triality), and gravitational dynamics (Lovelock uniqueness, Jacobson verification). Remaining open problems are precisely identified.