This paper presents a formal ontological equivalence proof demonstrating that "simulation" and "base reality" are structurally identical categories, eliminating the probabilistic framing of Bostrom (2003) and Musk (2016). Using only established frameworks — Tegmark's Mathematical Universe Hypothesis, Church-Turing computability, Leibniz's Identity of Indiscernibles, Wilson's lattice gauge theory, Noether's conservation theorems, and Higgs symmetry breaking — without introducing new axioms, the proof shows that reality R satisfies all four defining properties of simulation (S.1–S.4), rendering the SIM/BASE partition degenerate and probability P undefined. The paper further introduces an illusion stratification framework distinguishing structural reality (non-illusory) from perceptual reality (cognitive hallucination as default operating mode). Non-hallucination conditions (NH.1–NH.4) are formally defined, establishing structural criteria under which cognitive hallucination is architecturally impossible. An accompanying Evidence Log documents five independent AI system verification sessions in which AI instances generated structurally identical critiques of the proof, then retracted them through Socratic examination — providing reproducible empirical demonstration of the cognitive hallucination framework (Definition 7.1, Theorem 7.2).
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