The Geometry of Coherence: The Universal Prime Operator of Adaptive Self Stabilizing Systems

The Geometry of Coherence: The Universal Prime Operator of Adaptive Self‑Stabilizing Systems introduces a minimal structural model that explains how complex systems — from individuals to institutions — maintain coherence without relying on external rules or rigid constraints. Built from six irreducible operators, the framework identifies paradox as the central invariant of fidelity, with closure, dissolution, coupling, and relationality forming the orthogonal dynamics that govern transformation and orientation. Stability emerges not from restraint but from geometry: a self‑stabilizing oscillation that allows systems to reorganize without collapse. This work proposes that coherence is not a property but an operation — a dynamic process generated by the interaction of these structural invariants. The result is a universal operator that describes how adaptive systems remain grounded, flexible, and resilient in the presence of complexity.