A Calculus of Intelligence: Frontier, Adjudication, and Self-Modeling in Reflexive Systems Paper 59 of the NEMS Suite

Paper 58 established that nontrivial reflexive worlds are necessarily adjudicative and exhibit minimal reflexive intelligence under frontier-sensitive self-model-bearing closure. The present paper provides a formal calculus of intelligence: intelligence levels coincide with the chooser hierarchy; without frontier, there is no nontrivial intelligence; frontier-bearing reflexive systems admit precise intelligence levels; and distributed diversity strictly amplifies certified intelligence coverage. We prove the central theorem: terminal reflexive completion implies no minimal reflexive intelligence. The development is machine-checked in Lean 4 in the CalculusOfIntelligence library of reflexive-closure-lean . Trust boundary. "Intelligence levels" are bookkeeping over Paper 58's chooser hierarchy; distributed-acceleration claims lean on Paper 31 via an explicit Lean bridge. See .