The Axiomatic Foundation and Operative Mathematical Forms of Triadic Coherence Invariants (TCI) in CAT'S Theory: A Master Index

This document serves as the formal ontological registry for the core mathematical principles of CAT'S Theory (Crystalline/Superfluid Aetheric Topological Structures Theory). It provides a master index of the primary algebraic, topological, and Lagrangian forms derived from the theory's foundational axiom: the Triadic Coherence Invariant (Reality = Pattern Intent Presence). This index is presented to establish, prove, and solidify that all subsequent derivations, formulations, and dynamic simulations are operative expressions of this irreducible ontological bedrock. No derived form, regardless of complexity or physical scale, can replace, override, or supersede the triadic requirement for persistence; all valid operational forms must logically and topologically simplify back to the unified Triadic Coherence baseline.