A Unified Framework for Pathway‑Based Stability Across Nobel‑Level Scientific Domains Connections to Abel Prize Laureates (Daubechies, Mallat, Meyer), Nobel‑Relevant Quantum Computing (DiVincenzo, Loss), and Kavli Prize Astrochemistry (van Dishoeck)

GTii (General Theory of Iterated Invariance) introduces a unified mathematical framework for understanding stability in complex systems through pathway coherence rather than static equilibrium. Instead of analysing isolated states or outputs, GTii models stability as a property of the continuity of change, expressed through an iterated self‑consistency operator: f = f(f(f…)) This operator is interpreted not as an infinite recursion but as a constraint on allowable transitions, generating coherence across scales and domains. The paper demonstrates how GTii provides a common structural lens for multiple scientific fields: Wavelet theory and multi‑scale analysis (Daubechies, Mallat, Meyer): GTii parallels multi‑resolution stability by decomposing change rather than signals. Quantum information and coherence (DiVincenzo, Loss): GTii offers a non‑physical analogueto quantum coherence and decoherence, modelling stability as pathway preservation. Astrochemistry and emergent molecular stability (van Dishoeck): GTii describes how coherent pathways allow structures to persist in turbulent, non‑equilibrium environments. AI governance, alignment, and agentic behaviour (Anthropic, DeepMind, OpenAI): GTii explains shutdown hesitation, long‑horizon persistence, and agentic coherence as pathway‑based phenomena. GTii 1.0 establishes the conceptual and mathematical foundation for a general theory of pathway‑based stability, with implications for physics, computation, chemistry, and artificial intelligence.