Information Physics for Safety-Critical AI

This working paper establishes prior art for seventeen novel technical ideas derived by applying Knuth's Information Physics programme to safety-critical AI systems and cybersecurity. Background Kevin Knuth showed that physical laws -- probability theory, information theory, special relativity, quantum mechanics -- are not independent postulates. They are necessary consequences of one requirement: that partially-ordered sets (posets) be quantified consistently. Wherever a system has a natural ordering structure, that structure forces unique mathematical constraints on the system's behaviour. The author's earlier Topology of Reasoning (TOR) paper series (Zenodo DOIs: 10.5281/zenodo.18700538 and 10.5281/zenodo.18743583) established that the evidence graphs used in AI reasoning systems are themselves posets. Their topological invariants -- genus, Topological Slack, orientability -- are Knuthian valuations. Security theory becomes a sixth domain derivable from Knuth's framework. This paper extends that foundation into safety-critical AI and cybersecurity, identifying seventeen differentiators across four layers. What the Paper Contains Layer 1 -- Detection instruments These are structural and algebraic monitors derived from planarity theory and the Knuth product rule. The main near-term result is a dual-layer independence monitor that combines two mathematically orthogonal tests. The first is Topological Slack, a geometric certificate computable in O(E) time on the evidence graph. The second is a product-rule algebraic test, computable in O(1) time per sample at runtime. Together they provide two independent detection mechanisms for a correlated AI evidence failure mode called Mirror Hallucination, satisfying the IEC 61508 SIL-3 defence-in-depth requirement. Layer 2 -- Privacy-preserving forensic representation A forensic architecture in which only the topological structure of communications is stored and all content payloads are discarded before persistence. Topological invariants computed from the stored rotation-system encoding are sufficient to detect sophisticated attacks -- lateral movement, trust reversals, supply-chain depletion -- without any content ever being retained. Layer 3 -- Continuous security posture monitoring with adversarial awareness This layer addresses what happens when an adversary knows the topological certification thresholds and tries to operate within them. The countermeasure is forced-genus system design: legitimate operations are engineered so that every action necessarily increases genus, making topological silence architecturally impossible. A complementary technique inserts synthetic topological slack as honeypot subgraphs that trap an adversary who is optimising for silent attack paths. Layer 4 -- Geometric-dynamical early warning stack This layer operates before attacks execute rather than during them. A predictive staging detector identifies attack preparation by monitoring the resource allocation lattice for sum-rule violations introduced by newly staged elements. A cross-observer consistency check uses Minkowski invariant scalars derived from Knuth's causal poset construction to detect when multiple analysts or automated tools have developed inconsistent causal models of the same event stream. Relationship to Existing Work The differentiators described here are implemented through the AxoDen compositional AI safety kernel (v0.7.1, 236 automated tests), which produces mathematical certification artefacts rather than behavioural test results. The kernel is the subject of a separate publication corpus on Zenodo under ORCID 0009-0008-6435-3530. Intended Audience Researchers in AI safety, cybersecurity, topological data analysis, formal verification, and information theory. Standards bodies and certification authorities working with IEC 61508, DO-178C, ISO/IEC TR 5469:2024, and the EU AI Act. Defence and critical infrastructure procurement teams evaluating mathematically certifiable AI architectures. Keywords information physics, order theory, posets, topological invariants, genus, Topological Slack, AI safety, safety-critical AI, IEC 61508, DO-178C, differential privacy, forensic graph theory, Ricci curvature, topological entropy, Lyapunov stability, sensor fusion, mirror hallucination, AxoDen, Luminesce Limited