Continuity Is the Self A Computational Axiomatic Framework for Consciousness and Personal Identity

The questions of personal identity, consciousness essence, and the boundary between self-continuation and replication have long been central puzzles in philosophy, neuroscience, and artificial intelligence (AI). Existing theories often rely on ambiguous metaphysical concepts or fragmented logic, failing to provide a unified and falsifiable explanatory system. This paper proposes a minimal, physicalist computational axiomatic framework to redefine the core propositions of self and consciousness: