CAT'S THEORY: Triadic Invariant Collapse and the Binary Structure of Intent

Coty Austin Trout

Published Dec 14, 2025• 0 citations

Abstract

This paper isolates and formalizes a single foundational mechanism: collapse as a lawful consequence of CAT’S Theory’s triadic invariant. We present a compact definition of Triadic Invariant Collapse in discrete and continuous (field-theoretic) form, and show that a purely continuous Intent field is insufficient to account for thresholded instantiation. We therefore formalize Intent bifurcation as a dual operator consisting of a continuous directional component and an irreducible binary commitment gate. This binary gate renders collapse, localization, phase transition, and inverse reconstruction (ORE) well-posed. We derive immediate corollaries concerning locality/globality of collapse, clarify the role of observation as additive rather than causal, and state falsifiable constraints implied by the collapse law. This work builds upon the CAT’S Theory corpus archived on Zenodo (see References) and isolates collapse as a distinct invariant-level mechanism.

DOI: 10.5281/zenodo.17926396

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