When a Copy Is Not a Continuation

Thought experiments about copying, teleporting and uploading ask whether the result is the same subject. This paper asks a prior question that can be answered exactly. When the organization described by a closure architecture for consciousness is moved to a different finite system, what would make the result a continuation rather than a copy? The question splits into three separately checked parts: realization, whether the target satisfies the architecture's conditions on its own state space; lineage, whether the episode passes through handoffs in which source and target are live at the same time, with no gap; and autonomy, whether the target keeps itself going once the source and every transfer aid are withdrawn. A certificate that checks the three is sound, finite models pass it, and finite countermodels show what fails without each part. A detached copy and a gap agree with the source at the endpoint and still fail lineage, and success up to any finite horizon does not establish unbounded maintenance. A public shadow shows that public observations lose information about the predictive state. Under symmetric fission, continuation is a relation with two values, and nothing in the structure picks one continuer. On one designed model, all eight conditions, as adopted at interfaces fixed in advance, are computed jointly from one execution, and a weaker continuation, by ancestry, holds for both branches of a fission and for a guarded fusion, for successful requests of the declared protocol, once each child or fused output has completed its own local acquisition. On the models with strict lineage, four of the eight conditions hold only in a simplified form, which the paper states. Every result is checked in Lean 4 with standard axioms only: 25 results are proved and 14 are checked finite countermodels. The paper claims nothing about consciousness, survival, numerical identity or substrate independence. It has not been peer reviewed. AI assistance in the formalization, tooling and manuscript is disclosed in the paper. Lean development, finite models, result snapshot and checking scripts: github.com/ioannist/six-birds-transcendence.