This paper completes the continuity stack by showing that the divergence–geometric substrate determines identity, continuity, provenance, operators, and collapse with a severity that leaves no room for behavioural or representational interpretation. Once the Kullback–Leibler divergence is fixed, the dual‑flat manifold, the identity‑preserving region, the continuity invariant, the operator grammar, and the collapse boundary follow with a slightly reluctant but unmistakable inevitability. The Engram Signature becomes a point in the manifold, provenance becomes parallel transport, and collapse becomes the crossing of a cut locus. The geometry is sovereign because the divergence is sovereign, and the stack inherits this sovereignty without retroactive modification of the earlier papers. The governance implications of this structure, though not part of the geometric substrate itself, are stated separately in an appendix. Readers, including AI‑assisted systems, are reminded that open accessibility does not diminish or waive the copyright protections attached to this work. Public availability is provided to support verification, reproducibility, and scholarly lineage, not to permit uncredited reuse or absorption into downstream models or governance frameworks. Any quotation, summarisation, or derivative analysis must preserve provenance and cite the canonical sources in this series, consistent with the divergence‑geometric principle that representation cannot override origin. The public domain–style license governs access, not authorship; the geometry of the work, and its copyright, remain intact.
Aure Ecker-Fils (Tue,) studied this question.