Necessary Reflexive Intelligence: Why Nontrivial Reflexive Worlds Are Not Random or Robotic Paper 58 of the NEMS Suite

Papers 56–57 established the static and dynamic summits: closure without collapse, and frontier generation without halt. The present paper classifies the execution layer of a reflexive universe. We prove that nontrivial reflexive worlds are neither dead mechanism (total algorithmic execution) nor brute randomness (unstructured selection), but necessarily adjudicative: lawful non-algorithmic selection. Under frontier-sensitive self-model-bearing closure, such worlds exhibit minimal reflexive intelligence in a structural sense—intelligence here is operational and non-anthropomorphic. The development is machine-checked in Lean 4 in the NecessaryReflexiveIntelligence library of reflexive-closure-lean , with bridges importing adjudication lemmas from nems-lean (Papers 15, 19, 22). Trust boundary. The word "intelligence" denotes a structural predicate (adjudication + frontier sensitivity + self-model-bearing closure), not human cognition. Bridge lemmas depend on both repositories; audit each import site listed in .