Admissible Continuation: Closure-Compatible Burden-Bearing Constraints on System Evolution

We formalize the bridge between closure-compatible determinacy and admissible continuation. The NEMS program establishes that load-bearing determinacy must be internally realized; the present paper asks what this implies for the evolution of systems over time. We introduce an abstract ContinuationSystem comprising states, records, time, and an update structure, and define the properties ClosureCompatible and BurdenBearing. We prove the Closure-Compatible Continuation Theorem: a system that is both closure-compatible and burden-bearing has admissible continuation. This formalizes Meta-Principle 7 of Paper 82 : closure and continuation are coupled. All results are machine-checked in Lean 4 in the AdmissibleContinuation library of nems-lean, with zero sorry and zero custom axioms. Trust boundary. The AdmissibleContinuation library is machine-checked in nems-lean . The main theorem is definitional given AdmissibleContinuation as conjunction; rich continuation theory remains in ViableContinuation (Papers 71–72); see .