Universal Theory of Constrained Possibility (UTCP)

The Universal Theory of Constrained Possibility (UTCP) is a structural framework for analyzing persistence under perturbation. Rather than proposing an ontology, UTCP specifies the minimal constraint architecture required for a system to continue navigating possibility space without collapse. It identifies three independent constraint services — Indicative (availability or floor), Relational (coherent coupling), and Semantic (temporal coherence) — whose multiplicative interaction defines admissibility. Reduction to fewer than three axes fails to discriminate principal continuation failure modes, establishing triadic minimality as a diagnostic requirement.

The Coalescence Gradient (CG) extends UTCP to regimes of increasing recursion, branching, and internal constraint accessibility, with particular relevance to consciousness modeling. Within the CG, systems are described in a derived manifold defined by Scope (branching breadth), Fidelity (discrimination resolution), and Stability (margin above collapse threshold). Movement along this gradient is continuous but may exhibit discrete stabilization thresholds as new constraint capacities become reliably maintained. Consciousness is thus modeled not as a binary property but as a scalable position within a constraint-governed manifold.

The CG M10 formalism describes the geometric and dynamical structure produced when triadic constraint minimality operates recursively. The system begins with the three services defined by UTCP.

Indicative maintains persistence and availability of state. Relational governs interaction and transformation among states. Semantic preserves interpretation and trace across time. Interactions among these services produce nine functional roles forming a three by three constraint lattice:

Persistence, Availability, Signal

Coupling, Transformation, Flux

Sensation, Interpretation, Trace

These nine roles define the spatial coordinates of a constraint space.