Hypothesis and non-circularity audit

A proposed solution must satisfy the following acceptance conditions.

1. One model and one relation. Freeze the process class, admissible data, intervention access, equivalences, and extraction rule. State whether the represented relation is scheduled ancestry, direct influence, or a declared order constructed from influence. A state-positivity cone is not an operational event cone without an order-identification theorem.

2. Genuine additional content. Include class restrictions in the hypothesis ledger. In a common operational language, their conjunction with $\mathsf{H}$ must contain content not forced by $\mathsf{S}$. This does not require every individual $H_j$ to be independent of $\mathsf{S}$, but it excludes a package that merely renames it.

3. Non-vacuity and countermodel exclusion. Exhibit admissible data satisfying the complete package. For each relevant En08-A countermodel, identify and justify the failed class restriction or hypothesis. An unchanged countermodel satisfying all proposed premises defeats the proposed conclusion.

4. Honest use of classification. Homogeneity and strict convexity may be proved from operational data, or they may be explicitly assumed as properties of the extracted cone. In the latter case, the result is conditional on those assumptions. The classification theorem does not discharge their operational derivation.

5. Generation, faithfulness, and invariance. Prove (eq:faithful)–(eq:generated), including the absence of spurious comparisons introduced by convexification or closure. The same declared data, up to the permitted relabellings, must give affinely isomorphic representations. The input must not prescribe the cone whose extraction is claimed.

6. Limits and evidence. If a completion or refinement is used, give its comparison maps, topology, compatibility, and convergence theorem. A finite list of universally quantified structural hypotheses is not automatically a finite empirical certificate. Statistical records require their own coverage and implementation allowances.

Externally supplied correlations are permissible operational inputs, but their preparation and access model must be declared. A static entanglement table does not by itself provide intervention access or a temporal influence relation. Likewise, a quantum comb's declared slot ordering must not be misreported as an ordering derived from its outcome probabilities CDP,OCB,Beckman.