ora-0097
7.2 Coherent persistence
For a chain \(T_0\to T_1\to \cdots \), write \(\alpha _t:u_t^*M_{t+1}\to M_t\). Persistence requires the comparison for a composite presentation extension to agree with the composite of the local comparisons, strictly or up to a declared coherent equivalence.
If every \(\alpha _t\) is conservative on a query family \(\mathcal Q_0\), and conservativity is closed under reindexing and composition, then every answer in \(\mathcal Q_0\) is preserved along every finite continuation of the execution.
The comparison from \(M_n\) to \(M_0\) is the reindexed composite of the \(\alpha _t\). Closure under reindexing and composition makes this composite an equivalence under each observer in \(\mathcal Q_0\).
The proposition is modest but foundational. It states the categorical invariant that an implementation must maintain. Approximate versions need an observer-valued defect calculus and a composition law controlling how errors accumulate.