Belief State Representations in Transformer Models on Nonergodic Data

We present Markov Chain Lock (MCL) watermarking, a cryptographically secure framework for authenticating LLM outputs. MCL constrains token generation to follow a secret Markov chain over SHA-256 vocabulary partitions. Using doubly stochastic transition matrices, we prove four theoretical guarantees: (1) exponentially decaying false positive rates via Hoeffding bounds, (2) graceful degradation under adversarial modification with closed-form expected scores, (3) information-theoretic security without key access, and (4) bounded quality loss via KL divergence. Experiments on 173 Wikipedia prompts using Llama-3.2-3B demonstrate that the optimal 7-state soft cycle configuration achieves 100\% detection, 0\% FPR, and perplexity 4.20. Robustness testing confirms detection above 96\% even with 30\% word replacement. The framework enables $O(n)$ model-free detection, addressing EU AI Act Article 50 requirements. Code available at \url{https://github.com/ChenghengLi/MCLW}

This project prototypes an embedded off-switch for AI accelerators. The security block requires periodic cryptographic authorization to operate: the chip generates a nonce, an external authority signs it, and the chip verifies the signature before granting time-limited permission. Without valid authorization, outputs are gated to zero. The design was implemented in HardCaml and validated in simulation.

We design and simulate a "border patrol" device for generating cryptographic evidence of data traffic entering and leaving an AI cluster, while eliminating the specific analog and steganographic side-channels that post-hoc verification can not close. The device eliminates the need for any mutually trusted logic, while still meeting the security needs of the prover and verifier.