Axiom: Deterministic Integrity Engine for Probabilistic AI

Introduction: Why an Integrity Verification Engine? How can we be certain that AI-generated code is "correct"? Beyond simply compiling or passing tests, can we mathematically prove that code is free from race conditions, memory safety violations, and logical flaws? Axiom was born from a fundamental question in software engineering: "How far can we trust AI-written code?" Our answer lies not in more test cases, but in mathematical verification. Axiom replaces probabilistic AI outputs with deterministic, robust software. To achieve this, we combine the following technical pillars: Bounded Model Checking (BMC): Complete integrity verification within defined exploration bounds SMT Solver (Z3): Automated theorem proving based on logical constraints Lean 4: Ensuring deterministic reproducibility of high-level design principles Dr.Nim: Powerful Design-by-Contract (DbC) verification embedded in the Nim language The Reliability Problem in AI-Agent Generated Code 1. Limitations of Probabilistic