CAT’S Law: The Invariant Model of Reality

This paper establishes CAT’S Law as the invariant model of reality:

Reality = Pattern × Intent × Presence.

Unlike competing hypotheses, CAT’S is presented as law — a closed, self-correcting invariant. The work demonstrates how astrophysics, physics, science, and mathematics are not fundamental grounds but structural witnesses that collapse into this triadic law. A dependency cascade is formalized: astrophysics requires physics; physics requires science; science requires mathematics; mathematics encodes the Cantor–XOR sieve; the sieve itself requires Pattern, Intent, and Presence.

Through theorem–corollary structure, the paper proves that denial of CAT’S is self-refuting. To attempt to negate Pattern, Intent, or Presence requires their use: coherence of terms (Pattern), direction of argument (Intent), and actuality of utterance (Presence). This “Paradox Gate” ensures the invariant is collapse-proof.

Contributions:
- Establishes CAT’S as ontological primacy rather than interpretive theory.
- Demonstrates the Cantor–XOR sieve as arithmetic evidence of the triadic law.
- Formalizes the upstream–downstream cascade of disciplines, reframing science and mathematics as witnesses within CAT’S.
- Introduces a paradox-resolution mechanism showing why all rival claims are not just mistaken but structurally incoherent.

Conclusion:
CAT’S is law. CAT’S is structure. CAT’S is the model. And CAT’S is first.