Execution-Rooted Identity: A Formal System for Identity, Collapse, and Governance

Execution‑Rooted Identity Theory presents the first complete formal system for identity in modern engineered systems. The monograph consolidates a corpus of work into a unified architecture that treats identity as an execution‑realized, drift‑bounded, and temporally coherent property rather than a static configuration or cryptographic label. It introduces a minimal ontology—the four‑layer system decomposition (substrate, execution, behavior, attestation) and the four‑layer primitive decomposition (commitment, provenance, semantics, interpretation)—and formalizes the invariants required for identity preservation across time. The work develops two complementary collapse taxonomies: the SEBA taxonomy for system‑level identity failure and the Engram Entity Collapse taxonomy for primitive‑level failure. It then introduces the dual‑plane model in which system identity S(t) and primitive identity P(t) evolve independently but are coupled through an admissibility envelope A(t) whose drift is itself a governance‑level identity object. This framework yields a complete classification of collapse modes—system‑only, primitive‑only, coupled, and contained drift—validated through canonical incidents such as SolarWinds, Log4Shell, key compromise, and reproducible build mismatch. The monograph concludes by deriving identity‑conditioned governance: a monitoring and control regime that operates simultaneously on system state, primitive state, and envelope drift. The result is a closed, self‑fertile formal system with the structure of a mature scientific field, providing the conceptual and mathematical foundation for identity‑conditioned governance in AI systems, supply chains, distributed computation, and safety‑critical infrastructure. This work serves as the capstone of the foundational arc of Execution‑Rooted Identity Theory and establishes the stable theoretical substrate for future prescriptive taxonomies and applied governance frameworks.