Formal verification demonstrates closure without semantic collapse in nontrivial reflexive systems, highlighting mathematical boundaries on complete internal self-representation.
Key Points
Unify foundational results from preceding work into the Reflexive Closure Theorem to establish the structural boundaries of self-representation in nontrivial reflexive systems.
Constructed a formal mathematical unification of precursor proofs regarding internal self-theories and syntactic exhaustion.
Machine-checked all formal proofs in Lean 4 within the reflexive-closure-lean library, utilizing zero custom axioms and zero unproven placeholders ('sorry').
Formally proved that a nontrivial reflexive system can execute self-return and partial self-articulation with a semantic remainder, but cannot fully coincide with its own complete internal semantic image.
Verified that complete self-exhaustion and total self-coincidence are logically impossible within nontrivial reflexive frameworks.