Self-Awareness as a Resource: Hierarchies of Internal Self-Knowledge, Selector Necessity, and Limits of Introspective Optimality Paper 33 of the NEMS Suite

Papers 26–32 developed a unified toolkit for diagonal self-reference (Paper 26), closure audits and no-free-bits (Paper 27), stratified representability and diagonal closure (Paper 28), strength-ordered barrier schemas (Paper 29), self-trust incompleteness (Paper 30), social verification protocols and diversity necessity (Paper 31), and self-improvement under diagonal constraints (Paper 32). The present paper develops the remaining abstract pillar: limits of self-awareness. We formalize self-awareness as an internal certification capacity over classes of self-claims, and prove three theorem families: (i) a self-awareness hierarchy with strict separations: some claim classes admit total internal certification while richer classes do not under diagonal capability; (ii) a selector necessity theorem for self-model multiplicity: when multiple observationally indistinguishable self-consistent self-model fixed points exist, identifying "the actual self" cannot be decided from world-types and requires symmetry-breaking selection, which becomes non-total-effective in diagonal-capable regimes; and (iii) an introspective optimality barrier: no diagonal-capable agent can totally certify nontrivial extensional "rightness of decision" predicates in full generality, though stratified positive results exist on restricted fragments. The development is mechanized in Lean 4 as the SelfAwareness library in nems-lean, with zero sorry and no custom axioms. Trust boundary. Self-awareness hierarchies, selector necessity, and introspective barriers are strength-indexed and assume the diagonal/closure premises stated in each theorem; they are not blanket claims about consciousness. Mechanization is nems-lean . See .