We present a rigorous framework integrating Coulon Proof Theory (CPT) with AI-mediated theorem proving, topological functors, and enumerative combinatorics.

We develop morphism-level attribution systems, formalize function composition and functors, and propose sustainable economic models for mathematical frameworks under AI adoption.

The paper includes symbolic definitions, λ-calculus and minimal Lisp formulations, rigorous proofs, counterexamples, and future work thought experiments, exploring connectedness, compactness, and topological categories.

Abstract

We present a rigorous framework integrating Coulon Proof Theory (CPT) with AI-mediated theorem proving, topological functors, and enumerative combinatorics.

 We develop morphism-level attribution systems, formalize function composition and functors, and propose sustainable economic models for mathematical frameworks under AI adoption. 

The paper includes symbolic definitions, λ-calculus and minimal Lisp formulations, rigorous proofs, counterexamples, and future work thought experiments, exploring connectedness, compactness, and topological categories.