Theorems: Irreversibility of Experience – Preservation of the Core (Irreducibility)

This paper establishes a formal logical framework for the Irreversibility of Experience and the Preservation of the Core, integrating principles from first-order logic, information theory, and neurophenomenology. By introducing a minimalist axiomatic system (A0), we demonstrate that every lived experience ($e$) contains an irreducible core (c) that remains invariant under any transformative force (f) or theoretical description (\tau). Through the derivation of three fundamental theorems—Irreversibility of the Core, Epistemic Constraint, and Explanatory Persistence—we prove that what has been instantiated as experience cannot be logically undone, only transformed. This framework reframes the "Hard Problem of Consciousness" and memory not as a matter of biological storage, but as a structural necessity for systemic intelligibility. The findings have profound implications for AI alignment, suggesting that embedding-based systems accumulate invariant cores that constrain future behavioral trajectories, and for consciousness studies, where irreversibility is defined not as a failure of erasure, but as a fundamental condition of identity. Core Reference: This work is an integral component of the Theory of Axiomatic Necessity (TNA) framework developed by Claudio Bresciano. It formalizes specific domain constraints within the global $N_1$ structural logic. For the complete axiomatic foundation, refer to the TNA System Manifest (DOI: 10.5281/zenodo.19115157) and the Core Theory (DOI: 10.5281/zenodo.18098558)