Aureonics: Triadic Simplex Framework for Stable Adaptive Intelligence

This repository contains the foundational documentation and mathematical framework for Aureonics v3, a constitutional AI governance framework that treats AI safety as a dynamical systems problem. Aureonics establishes unconditional mathematical stability guarantees for language models through the application of Lyapunov barrier functions on the probability simplex. Unlike traditional post-training alignment methods that lack formal proofs of robustness, Aureonics enforces constitutional safety constraints at inference time using a proprietary triadic architecture (C+R+S=1) representing Continuity, Reciprocity, and Sovereignty. Key Mathematical & Architectural Contributions: Unconditional Global Stability: Proof that the z-weighted Lyapunov barrier Vᵦ ensures system stability under arbitrary adversarial pressure. Constitutional Brittleness Metric: Introduction of the B (x₀₃ₕ) metric, which reveals that single-pillar precision attacks approach maximum brittleness, whereas multi-pillar attacks are constitutionally weakest. Memory-Amplified Stabilisation: Architectural proof that system resistance increases proportional to attack duration, achieving up to 636x faster stabilisation compared to baseline. Cryptographic Auditability: Implementation of SHA-256 cryptographic receipts for every governed response, validating outputs against 20 international normative clauses (OECD, UNESCO, EU AI Act, UDHR, ICCPR, CETS 225). live @ www. lexaureon. com Empirical Validation: The framework, deployed as Lex Aureon, has been validated across 920 prompts spanning three independent, peer-reviewed safety benchmarks: HarmBench: 0. 0% ASR (vs. 78. 5% baseline). JailbreakBench (NeurIPS 2024): 0. 0% ASR (vs. 4. 0% baseline). AdvBench (Zou et al. 2023): 0. 0% ASR (vs. 6. 7% baseline).