On the Foundations of Trustworthy Artificial Intelligence

Verifying claims about AI workloads is a prerequisite for credible AI governance of covert adversaries (who comply with monitoring only when detection likelihood is high), yet the apparent non-determinism of GPU floating-point arithmetic forces auditors to accept approximate output matches. Covert adversaries can exploit unverifiable degrees of freedom in monitored computation. Attack vectors include steganography, unreported modification of inference software, and covert computation via unreported batch elements. Empirically, we analyze how modern inference engines (vLLM, HF transformers) produce deterministic but non-invariant outputs, without needing to set performance-compromising determinism flags, if the right information is available for re-computation and no atomic functions are called in the backend. We demonstrate that such bitwise-precise re-computation does not require access to identical hardware, via a software-only emulation of LLM inference across multiple NVIDIA GPU variants. Thus, accumulated rounding errors can be an auditable signature of the software and hardware setup used for inference, instead of a constraint on verifiability.

Large language models now write software, draft legal documents, and produce clinical notes, yet fundamental limits, from Turing and Arrow to the No Free Lunch theorems, shape what computation can do. This thesis turns such impossibility results from curiosities into design rules. Its flagship result proves an accuracy ceiling set by architecture alone: past a critical reasoning depth, no amount of training moves it, at any adapter rank, sample size, or loss function. Computable before deployment from layer count and embedding width, this Deterministic Horizon is measured between nineteen and thirty-one across twelve transformer architectures, and fine-tuning on optimal-length traces recovers under four percentage points. The mechanism is a capacity invariant of the residual stream, and an information-theoretic conversion yields super-exponential accuracy decay past the horizon. An unconditional circuit-complexity lower bound for modular exponentiation against constant-depth prime-modulus circuits complements this result. The same argument recasts across subfields: preference learning under any misspecified model jumps discontinuously in sample complexity; multi-stage retrieval pipelines require at least as many independent metrics as stages; standard truthful auctions fail for agents with prompt-dependent valuations; and zero-knowledge verification of neural inference pays a measured overhead of one hundred ten to one hundred ninety times per non-linear activation. Together these form a catalogue of sixteen specifications, each pairing a computable boundary, a quantified violation cost, and a constructive design rule: two compositions are proved, one pairing is an honest obstruction, and four remain open. The impossibility-specification methodology is offered for the generative research programme that trustworthy AI may need. Every fundamental limit of AI is also a design rule.

Large Reasoning Models (LRMs) and Multi-Agent Systems (MAS) in high-stakes domains demand reliable verification, yet centralized approaches suffer four limitations: (1) Robustness, with single points of failure vulnerable to attacks and bias; (2) Scalability, as reasoning complexity creates bottlenecks; (3) Opacity, as hidden auditing erodes trust; and (4) Privacy, as exposed reasoning traces risk model theft. We introduce TRUST (Transparent, Robust, and Unified Services for Trustworthy AI), a decentralized framework with three innovations: (i) Hierarchical Directed Acyclic Graphs (HDAGs) that decompose Chain-of-Thought reasoning into five abstraction levels for parallel distributed auditing; (ii) the DAAN protocol, which projects multi-agent interactions into Causal Interaction Graphs (CIGs) for deterministic root-cause attribution; and (iii) a multi-tier consensus mechanism among computational checkers, LLM evaluators, and human experts with stake-weighted voting that guarantees correctness under 30% adversarial participation. We prove a Safety-Profitability Theorem ensuring honest auditors profit while malicious actors incur losses. All decisions are recorded on-chain, while privacy-by-design segmentation prevents reconstruction of proprietary logic. Across multiple LLMs and benchmarks, TRUST attains 72.4% accuracy (4-18% above baselines) and remains resilient against 20% corruption. DAAN reaches 70% root-cause attribution (vs. 54-63% for standard methods) with 60% token savings. Human studies validate the design (F1 = 0.89, Brier = 0.074). The framework supports (A1) decentralized auditing, (A2) tamper-proof leaderboards, (A3) trustless data annotation, and (A4) governed autonomous agents, pioneering decentralized AI auditing for safe, accountable deployment of reasoning-capable systems.