Categorical Projection Truncation Law (ΩCPTL)

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This manuscript formalizes the Categorical Projection Truncation Law (\Omega_{\text{CPTL}}). We investigate the systemic vulnerabilities occurring when autonomous, biological, or computational agents bypass real-time empirical signal verification in favor of generalized categorical labeling. We construct a rigorous cybernetic framework utilizing state-space divergence metrics, truncation operators, and Shannon entropy variance equations. Theorems are derived to prove how a priori projection vectors induce false pseudo-equilibrium, generating exponential state divergence and catastrophic system boundary failure. The model is scale-invariant across N-node networks and is validated across 10 distinct cross-domain applications. Strict Popperian falsifiability criteria (F1 and F2) are established.