NEMS Constraints on Black Hole Information Paper 38 of the NEMS Suite

PSC forbids information "lost outside" the universe or true destruction without internal semantic closure. This paper applies NEMS and the hypercomputation taxonomy (Paper 35) to black hole information. We reframe the paradox in terms of record fragments (e.g., outside thermal, infalling, unitarity). We prove: (1) Record consistency (abstract): an information-erasing appearance (two worlds disagree on an observation) implies the semantics is not categorical (multiple world-types; selection is required). Classically (Choice), a selector exists; internal/effective selector is constrained by diagonal barriers (Papers 29/35). (2) No hypercomputing from black holes: under the same barrier assumptions (extensional + nontrivial predicate; anti-decider closure; \hFP), no internal total-effective black-hole decoder can decide a diagonal-capable predicate on the outcome space. Observer-relative records (complementarity) and islands/Page curve are interpreted as closure-driven reassignment; we do not assume any particular QG microphysics. The development is mechanized in Lean 4 as the BlackHoles library in nems-lean, with zero sorry and no custom axioms. Trust boundary. Record-consistency and no-hypercomputing claims are abstract and conditional on the Paper 29/35 barrier hypotheses; we do not assume a specific quantum-gravity completion. Mechanization is nems-lean . See .