Closed timelike curves (CTCs) and time-travel scenarios are constrained by NEMS when framed as record dynamics with a feedback operator. This paper applies the Closure calculus (Paper 27) and the hypercomputation taxonomy (Paper 35) to admissible time travel. We model evolution as a feedback operator on histories; self-consistent loops are fixed points modulo observational equivalence (Deutsch, Novikov self-consistency). We prove: (1) Record non-overwrite: overwriting stable records forces non-categoricity (multiple world-types), hence selection is required; a selector exists classically, while internal total-effective selection is constrained by the diagonal barrier. (2) Selection barrier for chronology: under diagonal capability (extensional + nontrivial predicate; anti-decider closure;), selecting among consistent loops cannot be total-effective internally (Paper 29 barrier). (3) Taxonomy: contradiction vs. fixed-point selection vs. branching; closure-compliant options only. The development is mechanized in Lean 4 as the ChronologyUnderClosure library in nems-lean, with zero sorry and no custom axioms. Trust boundary. Chronology constraints assume the feedback/record model, PSC/stable-records posture, and Paper 29 diagonal hypotheses where invoked; the taxonomy organizes escape routes rather than ruling out all CTC mathematics. Mechanization is nems-lean. See.
Nova Spivack (Sun,) studied this question.