Priority Statement for Substrate-Rooted Identity, Interpretive Geometry, and Collapse Theory

This Priority Statement defines the foundational ontology, terminology, and conceptual lineage of substrate‑rooted identity and interpretive geometry, a unified theoretical framework for identity, drift, provenance, and collapse in modern AI systems. It consolidates the doctrinal architecture introduced across the 2026 Zenodo corpus, including the Four‑Layer Identity Decomposition (s, e, b, a), the Axioms for Identity Preservation, the Engram identity primitives, execution‑rooted provenance, interpretive drift geometry, and the geometric theory of multi‑agent systems. The field provides the first complete account of identity as an execution‑realized, drift‑bounded, and temporally coherent construct, replacing configuration‑based identity models with a layered ontology grounded in substrate, execution, behavioral structure, and attestation. It introduces predictive collapse modes, Lyapunov‑based drift measures, curvature‑driven divergence, cross‑agent coupling tensors, and the collapse‑risk functional, offering a unified mathematical and conceptual foundation for analyzing stability in LLMs, agentic AI systems, cyber‑physical systems, and distributed computational architectures. This Priority Statement establishes conceptual precedence, stabilizes terminology, and provides a canonical citation anchor for research in AI identity, provenance, interpretive drift, multi‑agent stability, AI safety, and governance. It is intended for researchers working on AI systems, LLMs, multi‑agent architectures, provenance integrity, execution‑rooted identity, and collapse‑aware governance.