Scope, dependency policy, and debugging

The mathematical correspondence between vertex operator algebras and conformal nets is a substantive analytic and categorical problem. The established CKLW construction starts from a strongly local unitary VOA and produces a conformal net CKLW. Gui's comparison and extension theories supply representation-theoretic bridges under their analytic and positivity hypotheses GuiUnbounded,GuiExtensions,GuiQSystems. These results concern chiral conformal field theory, not a derivation of a gravitational metric.

The supplied preprint .pdf, attributed to OpenAI and dated 25 September 2026, claims that the relevant hypotheses follow for every simple unitary strongly rational complex VOA OpenAI280. Its claim is broader than merely constructing a vacuum net: it includes complete unitarity, integration of modules, complete rationality, sector exhaustion, and an extension correspondence.

This companion does not verify that preprint. Its proved statements instead concern independently defined finite channels, specified observable inclusions, and explicit counterexamples. The source record remains available as context without becoming a hidden premise.

Cheung's supplied manuscripts distinguish observable support, channel equality, reference-preserving recovery, physical access, and separately inherited analytic obligations CheungEn05C,CheungEn07A,CheungEn07B, CheungHawk04A,CheungHawk04B. We cite those distinctions with their supplied identifiers and versions. The results needed in our proofs are restated with complete hypotheses and proved locally.