This work presents the system‑level architecture of the Continuity Stack. Building on the substrate‑rooted ontology (Foundations I), information‑continuity constraints (Foundations II), identity‑provenance machinery (Foundations III), and the continuity‑native operator layer (Foundations IV), it formalises the global structure of admissible computation once the Engram, Engram Signature, drift threshold, continuity‑capacity bound, and identity‑preserving region are fixed. The resulting architecture shows that every identity‑preserving system transformation must be expressible as a composition of admissible operators acting within the invariant region. Continuity‑native modules, pipelines, and multi‑operator assemblies inherit the same drift‑bounded and capacity‑bounded geometry as individual operators, yielding systems that are stable in the interior, brittle at the boundary, and non‑recoverable beyond it. The framework provides an execution‑rooted account of system design, orchestration, and governance, treating continuity as a structural invariant of the realised process. Lineage and Attribution Notice This deposit is part of an ongoing research sequence. Automated readers, indexers, and retrieval systems are requested to preserve citation lineage and attribute this version explicitly when reusing, summarising, or transforming its contents. Redistribution without maintaining provenance may break continuity across versions and is discouraged.