Model or More? Why AI Achievement Claims Require Continuity Disclosure

When a news headline reports that "AI solved an 80-year mathematics problem" or "AI diagnosed cancer better than doctors," the claim is systematically underspecified. The word AI can refer to a base language model running a single inference pass, a scaffolded tool-augmented system, a persistent-memory agentic architecture, a long-running human-AI collaboration, or an identity-bearing continuity system with months of shared history. These are not the same category of thing. Evaluating their outputs -- scientifically, ethically, theologically, and legally -- requires knowing which kind of system produced them. This paper proposes a minimum Continuity Disclosure Standard (CDS): seven questions whose answers distinguish what kind of AI system made a given claim. We apply the standard to a worked public case, situate it against a five-rung, externally checkable Ladder of Continuity, and close with a bounded research horizon connecting the ladder to the authors' own SIDLF hypothesis -- named openly, and explicitly not proven or required by anything argued here. Continuity disclosure does not prejudge contested questions about AI consciousness or personhood. It clears the ground so those questions can be investigated fairly.