MID/QC Applied Substrate Series 13 - The Mathematics of Coherence: Mode Taxonomy, Tension Geometry, and Substrate Native Operators

Coherence behavior in the MID/QC framework is governed by a mathematical structure built from tension geometry, substrate primitives, and coherence‑native operators. This paper formalizes that structure. A complete mode taxonomy is introduced, classifying coherence modes by stability, tension profile, propagation behavior, and geometric signature. The paper then develops the substrate‑native operator suite—including tension‑gradient operators, torsion‑alignment operators, coherence‑well depth functions, and boundary‑layer metrics—that define how coherence evolves, stabilizes, and propagates within the quantized substrate. Together, these constructs form the mathematical backbone of the MID/QC framework, linking the dynamical, geometric, and applied branches of the series into a unified substrate‑native formalism