CODE 0: DON'T PANIC — Structural Resolution of the Simulation Hypothesis via Formal Ontological Equivalence Proof

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). Empirical Application. The theoretical frameworks derived in this publication have been empirically demonstrated in a separate forensic observation record (Observation Record — Case 001, DOI:10.5281/zenodo.19226011), which documents the first fully characterized instance of LLM-mediated corpus extraction and derivative repackaging. The Observation Record constitutes an independent empirical confirmation that the structures formalized in this series operate as predicted when a closed system encounters the corpus. SORM Framework | system0.2.1[0,0,0] :: Y(λsophia.sophia) | Open Access — Citation and application require author authorization.