Oracles as External Selectors: NEMS Constraints on Hypercomputation and Physical Computability Paper 35 of the NEMS Suite

Hypercomputers and oracle machines are well-defined as abstract mathematical models, but their physical realizability in a PSC universe with stable records and diagonal capability is sharply constrained by NEMS. This paper delivers three headline results. (1) Oracle-as-Selector Theorem (Closure): Any oracle that decides a predicate not determined by the observational quotient is formally an external selector injecting free bits unless its provenance is internalized. (2) No Internal Hypercomputer Theorem (SelectorStrength): In a diagonal-capable PSC universe with stable records, no total-effective internal procedure can decide halting or record-truth-like predicates; a "halting oracle machine" cannot be physically realized as an internal device. (3) Hypercomputation Taxonomy: Any hypercomputer claim forces at least one escape regime: non–diagonal-capable fragment, unstable records, non-extensional predicate, non-total or non-effective selection, or PSC violation (external runner). The taxonomy serves as an audit tool for exotic proposals (CTCs, Malament–Hogarth spacetimes, black-hole decoders). Papers 36 (Chronology Under Closure) and 37 (Black Hole Information) will apply this machinery. The companion Lean library Hypercomputation/ in nems-lean formalizes the oracle-audit interface, the no-internal-hypercomputer theorem, and the premise-failure taxonomy, with halting and record-truth instances (0 sorry). Trust boundary. Oracle-as-selector and no-internal-hypercomputer claims are conditional on PSC, stable records, and diagonal capability as formalized; the taxonomy lists premise-failure escapes rather than one-size-fits-all bans. Mechanization is nems-lean . See .