ATACM: Alan Turing Asymmetric Computation Model - A New Axiomatic Framework for Computational Complexity

This work introduces the Alan Turing Asymmetric Computation Model (ATACM), a rigorous axiomatic framework for computational complexity theory. Following the historical precedent of non-Euclidean geometry—where modifying Euclid's parallel postulate yielded internally consistent alternative geometries—ATACM constructs an alternative computational foundation through seven explicitly stated axioms. Within this framework, we rigorously prove that P ≠ NP, BQP ≠ P, and BQP ≠ PostBQP. The framework addresses classical complexity questions exactly as formally stated, evaluating them within a distinct but internally consistent computational axiomatization. Internal consistency is demonstrated through explicit model construction. The seven axioms make solve-verify asymmetry, resource boundedness, partial shortcut existence, and physical capability distinctions primitive principles. These axioms are motivated by over 50 years of empirical observations: universal solve-verify asymmetry across all computational domains, continued security of cryptographic systems (RSA-2048 remains unbroken), quantum supremacy experiments demonstrating quantum advantage, and absence of polynomial-time algorithms for NP-complete problems despite intensive search. ATACM preserves all classical complexity results that do not depend on assuming P = NP, including time and space hierarchy theorems, Savitch's theorem, Cook-Levin theorem, and the complete structure of NP-completeness theory. Standard complexity class definitions are maintained; only the underlying computational model differs through explicit axiomatization of observed computational asymmetries. The mathematical work is rigorous and valid within the framework presented. Questions concerning interpretation, transferability between frameworks, or institutional recognition (including prize eligibility) depend on external evaluative criteria and community acceptance rather than on mathematical validity alone—paralleling how non-Euclidean geometry's acceptance developed over time despite initial resistance to alternative axiomatic foundations. This work demonstrates that P ≠ NP is provable when empirically observed computational asymmetry is made axiomatic, providing theoretical foundation for cryptographic security, necessity of approximation algorithms, and observed computational hardness patterns.