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Point: Self-Referential Structure

DOI: 10.5281/zenodo.18879768

Establishes that category theory's compositional grammar is the least fixed point of the meta-rule producing structure-preserving maps. A reflexive object D ≅ [D, D] emerges from iterating the internal hom, taking the ω-colimit, and applying the Lambek isomorphism, modeling untyped lambda calculus without external enumeration. The monograph spans seven interconnected sections covering foundational category theory derivation, fixed-point identification, computational evidence, adjunction properties, methodological convergence, and dimensionality relationships. Formal verification uses Lean 4 (42 files, zero gaps, zero custom axioms).

Category TheoryFixed PointLambek LemmaReflexive ObjectLambda CalculusLean 4Formal Verification