Posterior Entrances: Reuse the Information, Preserve the Sampling Law

Recovering an image from incomplete measurements requires useful reconstructions under a finite inference budget. Yet generating posterior samples repeatedly purchases learned-prior information at related states. We ask whether this information can be reused without changing the prescribed sampling transition. Posterior Entrances (PE) couples two operations: certify a retained first-order reference under the current context, then correct its proposal with live queries. A history-conditioned rejection identity preserves the ideal block conditional and finite-horizon state law; a movement-based refresh bound and a sufficient break-even condition account for both avoided anchor work and added correction. Across two trained priors and four model–observation configurations, paired-median fresh-FORS/PE ratios at sixteen sweeps are 1.354–1.369 for total queries and 1.135–1.296 for pipeline time. In the representative profile, the complete query ledger shows a net saving of 80.34 queried states per endpoint and 22.85% of complete pipeline time. Site-resolved diagnostics evaluate 512-endpoint estimates. A separate photographic entrance ensemble, E32, demonstrates fixed-budget reconstruction from missing pixels and spatial averages. The method makes reference lifetime a controllable inference resource while preserving the prescribed transition.