On the Foundations of Trustworthy Artificial Intelligence

We prove that platform-deterministic inference is necessary and sufficient fortrustworthy AI. We formalize this as the Determinism Thesis and introduce trustentropy to quantify the cost of non-determinism, proving that verification failureprobability equals 1 - 2^{-H_T} exactly. We prove a Determinism-VerificationCollapse: verification under determinism requires O(1) hash comparison; without it,the verifier faces an intractable membership problem. IEEE 754 floating-pointarithmetic fundamentally violates the determinism requirement. We resolve this byconstructing a pure integer inference engine that achieves bitwise identical outputacross ARM and x86. In 82 cross-architecture tests on models up to 6.7B parameters,we observe zero hash mismatches. Four geographically distributed nodes produceidentical outputs, verified by 356 on-chain attestation transactions. Every majortrust property of AI systems (fairness, robustness, privacy, safety, alignment)presupposes platform determinism. Our system, 99,000 lines of Rust deployed acrossthree continents, establishes that AI trust is a question of arithmetic.