Claim and exact logical status

XXII-A fixes the faithful-generation target and its non-circularity audit CheungXXIIA. XXII-B distinguishes operational languages and hypothesis statuses CheungXXIIB. XXII-C fixes the process family and the component order CheungXXIIC. XXII-D supplies the separate transport contract and scoped approximation certificates CheungXXIID. XXII-E identifies the additional structures required for dynamics comparison CheungXXIIE.

The assertion under investigation is not

The prospective existence claim concerns a nonempty operational package producing an affine cone representation, followed by a separately justified approximation layer.

Two statements must therefore be separated:

1. Conditional implication. If an admissible domain, representation rule, and the stated selecting properties are supplied, the represented cone is Lorentzian. If compatible finite protocols and estimates are additionally supplied, their operational approximation obeys the displayed certificate.

2. Existence and construction. There actually is a predeclared nonempty operational package on the frozen class satisfying all those hypotheses, with a successful representation rule and compatible protocols.

Theorem thm:assembly and Corollary cor:approximation prove the first statement. Research target target:existence records the second. It remains open in this note.

In particular, the statement “the theorem is unproved because its hypotheses have not been constructed” is inappropriate for the conditional implication. The implication has a proof below. What is unproved is its non-vacuous operational instantiation.

boundary. The Cheung references identify supplied manuscripts or supplied scope passages, not independently verified publications. No documentary relationship is treated as a proof-transfer theorem. The process and channel conventions are supported by OCB,Watrous; the cone classification is attributed directly to Ito and Lourenço ItoLourenco. Local proofs are included for the specific auxiliary statements used here.

No claim about the full series is inferred from an incomplete retrieval inventory. In particular, the identifier En10-A@1 has no mathematical passage supplied for use here. It is not a theorem premise, and no bibliographic metadata or result is invented for it.