Mathematical Principles of Cyber Endogenous Safety and Security

Abstract

Global cyber defense still relies heavily on prior-knowledge-based techniques such as vulnerability patching, signature matching, and perimeter isolation, which are inadequate for unknown threats arising from persistent APTs, weaponized zero-day vulnerabilities, supply-chain infiltration, and AI-automated attacks. This limitation is partly rooted in inherent contradictions of the von Neumann architecture, as well as fundamental theoretical boundaries implied by Gödel's incompleteness theorem, Rice’s undecidability theorem, and Goodhart’s law. To break this dilemma, a scientific pathway of "breakthrough in cognitive foundations-construction of a theoretical framework- mathematical properties and proofs" is followed. A relatively complete system of mathematical principles is proposed for cyber endogenous safety and security (CESS). First, the axioms and theorems (the true relatively axiom, the DVR intersection theorem, the existence theorem of CESS, etc.) are originally proposed, providing theoretical foundations and design criteria for constructing CESS system. Second, mathematical properties are proposed and proved, consolidating the theoretical foundation of CESS and verifying the scientific soundness and feasibility of the DHR architecture. Furthermore, we integrate previously dispersed axioms, theorems, mechanisms, and mathematical properties into a relatively complete theoretical system, helping advance CESS from an "effective defense technology" toward a "systematic axiomatic framework", and exploring a potential paradigm shift for cybersecurity from the "art of confrontation" toward the "science of construction".