The Theorem of Detection (ToD): A Unified Ontology of Existence as Self-Referential Information

The Theorem of Detection (ToD) is a ZFC-axiomatic, category-theoretic, and operator-theoretic framework asserting that reality is fundamentally informational detection under absolute conservation. It shows that existence is the realization of informational contrast within the undivided Detection Field (\Phi). This continuous, self-referential process is formalized across a Tri-Domain Architecture (Meta, Micro, Macro), providing a unified ontology for all of physics and core mathematics.

The entire ToD system is governed by a singular, non-negotiable principle: the Absolute Conservation of Total Informational Potential (\mathcal{I}_{\text{total}}), which is proven to be the necessary and sufficient condition for a stable, evolving cosmos: \boxed{\frac{d \mathcal{I}_{\text{total}}}{dt} = 0}