Coherence as a Mathematical Object

Traditional theories define truth via correspondence, pragmatics, or coherence. This preprint paper argues that coherence is not merely one rival theory but the structural precondition enabling correspondence and pragmatic success. Coherence is formalized across three interconnected levels: epistemic (mutual justification among beliefs), ontological (invariant relational structures constituting identity), and dynamical (stability under recursive transformation). Objectivity emerges as invariance across coherent systems, exemplified by the Cartesian cogito. Sustained coherence under indefinite iteration requires a scale-invariant self-consistency. This can be illustratively modeled by the golden ratio ϕ as an extremal fixed point that maximizes stability in recursive dynamics. This yields a fractal attractor space of maximally coherent trajectories (a formalized model of recursive stability), offering a unified lens for understanding truth, identity, and reality as dynamically stabilized invariants.