ora-0099
7.4 Presentation invariance
The same world may be revealed in different orders, by different generators, or at different granularities. A persistent learner should not confuse these encodings with different worlds.
Let \(F:\mathbf{Pres}\simeq \mathbf{Pres}'\) be an equivalence of presentation protocols and let the induced hypothesis fibrations, query families, and probe categories be pseudonaturally equivalent. A UOCL algorithm is presentation invariant along \(F\) when its probe, selection, and repair rules are equivariant under these equivalences and the resulting executions correspond up to coherent observational equivalence.
Under the hypotheses of the definition, every execution over \(\mathbf{Pres}\) transports to an observationally equivalent execution over \(\mathbf{Pres}'\). Behavioral stabilization and conservative persistence are preserved.
Transport each state and comparison through the pseudonatural equivalence. Equivariance transports the selected probes, lifts, and repairs, while coherence identifies transported composites. The query equivalence preserves answers and therefore preserves both stabilization and conservativity.
This is the online form of Kan invariance at the algorithmic level. Kan invariance of isolated constructions is necessary but not sufficient: the selection and repair mechanisms must also respect the change of presentation.