Model specification: Obligations O1–O6

A later selection theorem on ${\mathcal{P}}_{3q}$ must address:

1. Order theorem and carrier interpretation. Theorem thm:order supplies a partial order for the frozen component quotient. A later theorem must retain that carrier or explicitly state and justify a revised carrier construction. It must not identify component reachability with direct influence or individual events without a further theorem. Acyclicity alone does not establish a complete circuit realization or the scheduler package.

2. Faithful generated representation. Construct ${\mathfrak{F}}_m$ in (eq:selector) on the claimed admissible domain and prove (eq:proper-injective)–(eq:span), with (eq:generated). In particular, prove that convexification and closure introduce no spurious comparisons. Nonemptiness of a feasibility set, if shown nonconstructively, must not be reported as an implemented extraction algorithm.

3. Infinite-family, extension, or limit compatibility. Explain how the separately tested data family supports the claimed common affine representation. If no completion or limit is used, say so. If one is used, supply its event maps, operational comparisons, topology, compatibility, and convergence theorem. The experiment identifiers must not become a time or spatial coordinate by numerical relabelling. Existence and uniqueness are separate claims.

4. Relevant countermodel audit. Compare each relevant En08-A countermodel with the actual frozen access, component carrier, and proposed cone rule. Supply either a justified interpretation and a failed additional premise, or a proof that the required interpretation is unavailable. An unchanged interpreted countermodel satisfying all premises and falsifying the conclusion defeats the selection claim. Excluding the named examples is not a sufficient classification of all remaining cones.

5. Honest cone-selection status. Prove homogeneity and strict convexity from the stated operational premises, or mark them as additional assumptions about the constructed cone. In the latter case the theorem remains conditional. No classification theorem proves its hypotheses for the frozen quantum data merely by being cited.

6. Layer separation and invariance. The present relation is formed from operational influence, not scheduled ancestry. A future schedule comparison requires a certified schedule; a geometric comparison requires a separate supplied causal carrier and embedding. Prove affine invariance of the selected representation under the matched operational equivalences. State all implementation and statistical allowances actually used.