A Minimal Axiomatisation of Identity Continuity

Identity continuity for synthetic entities is often treated implicitly and implemented through mechanisms that depend on naming conventions, storage artefacts, or provenance structures. These approaches do not provide the structural conditions under which identity‑equivalence and identity‑continuity can be meaningfully asserted. This paper introduces SEBA, a minimal axiomatisation of identity continuity based on substrate independence, execution binding, behavioural invariance, and attestation. The axioms define the class of SEBA‑admissible identity models and supply a meta‑theoretical framework for analysing identity relations in evolving systems. Canonical examples and counterexamples illustrate the scope and necessity of the axioms, and an independence and minimality analysis establishes the structural adequacy of the kernel. The SEBA framework is domain‑agnostic and is intended as a foundational layer for future extensions.