Back to Research

Reflexive Compression Boundaries in Graded Categories

DOI: 10.5281/zenodo.18917019

Decomposes the complexity of self-referential computation into three independent gaps: naming, construction, and depth transfer. Proves that naming and fixed-point construction close from the categorical structure of a reflexive object D ≅ [D,D] alone, while depth transfer reduces to a growth gap hypothesis independent of the categorical axioms. The anti-compression theorem shows the three conditions are jointly unsatisfiable. A non-uniformity theorem separates denotational from computational models. As a bridge result, Markov's principle at polynomial bounds is equivalent to P = NP. Formalized in Lean 4 with 93 files, zero sorry, zero Classical.choice.

Category TheoryComputational ComplexityReflexive ObjectsFormal VerificationLean 4P vs NP