Abstract

We give a self-contained operational companion to the supplied OpenAI preprint Strongly rational unitary vertex operator algebras and conformal nets, dated 25 September 2026. The preprint's strongly rational correspondence and finite-index extension claims are recorded, not independently verified and not used as premises of the operational results.

For independently declared finite sector labels and finite channel interfaces, we prove an exact complete-complement recovery theorem, a tensor-free snapshot–channel comparison, and a simultaneous three-correlation half-diamond certificate. Its statistical, calibration, and channel-transfer allowances are separately typed; channel transfer is added outside the square root. The certificate can be attached to a declared finite encoding in a named sector, but does not certify that the encoding realizes that sector or that the apparatus implements the associated conformal net.

Explicit counterexamples separate commuting channels from commuting observable algebras, common-domain field commutation from strong commutation, sector data from recovery and entropy histories, and one preserved observable from full-code recovery. Extension and energy claims are treated by an explicit record-only nonidentification criterion rather than by universal impossibility assertions.

All seven stages of the proposed comparison are addressed. The remaining characteristic-map, endpoint, and physical-identification obligations are stated without being discharged. No gravitational dictionary, Page curve, spacetime emergence, or inherited characteristic quantum coefficient is constructed.