The Unified Engram Geometry

This record deposits *The Unified Engram Geometry (Foundations VII — Capstone) *, the closing step of the Continuity‑Stack programme. It completes the field by establishing a unified geometric substrate for execution‑realised identity, consolidating the substrate‑rooted ontology (H, E, M), the structural mapping Φ, perturbation‑stable invariants, Engram Signature θ₀, execution‑rooted provenance, and the continuity‑native operator grammar into a single divergence‑geometric manifold E. The work is not an extension but a finalisation: it provides the only admissible unification consistent with the primitives developed across Foundations I–VI, and formalises the identity‑conditioned admissibility envelope that follows. The manuscript is architecturally sovereign and self‑contained. It presents the identity‑geometry pipeline (H, E, M) \!\!P\!\!θ₀\!\!Prov (t) \!\!E as a closed sequence of perturbation‑stable transformations, and proves that no weaker or alternative structure satisfies the stability, operator‑closure, and provenance‑compatibility constraints of the continuity‑stack. The result is a field‑defining consolidation: a unified geometric account of identity continuity grounded in execution behaviour rather than representation. **Rights Statement** © 2026 A. Ecker‑Fils. All rights reserved. This work forms part of the Continuity‑Stack Series (Foundations I–VII) and is protected in its entirety, including its structure, definitions, invariants, mappings, operator grammar, geometric constructions, and governance‑relevant architecture. No permission is granted to reproduce, distribute, adapt, or create derivative works from this material, in whole or in part, without explicit written consent from the author. Governance‑framework builders, standards bodies, and policy architects may cite this work under standard scholarly practice, but any reuse of its structural components—including ontology, continuity‑stack architecture, identity‑geometry pipeline, admissibility envelope, or divergence‑geometric substrate—requires a licence. The governance envelope defined herein is inseparable from the underlying geometric substrate; implementations, instantiations, or derivative governance frameworks based on these primitives constitute derivative works and therefore fall under copyright. This record establishes provenance for the closure of the Continuity‑Stack and should be cited directly using its DOI, together with the Foundations I–VII lineage, to preserve attribution, structural context, and continuity of the field