bmv_clause_holds

This module is a field-by-field non-circularity audit of rs_quantum_gravity_master_unconditional. A referee objection is that witness slots of shape $\Sigma(P:\mathrm{Prop}), P$ can be filled by $\langle\mathrm{True},\mathrm{trivial}\rangle$, so the master theorem is only as strong as the concrete propositions in those slots. After M3 the BMV slot is no longer definitional True; it carries a named positivity proposition.

Upstream, bmv_positive_unconditional is defined to be exactly that carried proposition, and bmv_positive_unconditional_proven discharges it by the pure two-qubit entropy theorem (pure_two_qubit_entropy_positive_unconditional). The audit theorem here simply re-exports that fact under the audit naming, so a reader can see the clause holds with no master hypothesis in the dependency cone.

One-line term proof: apply MasterTheorem.bmv_positive_unconditional_proven. That upstream theorem is itself the identification of the carried BMV proposition with the already-proved pure two-qubit entropy/concurrence positivity result. No local tactics or extra hypotheses.

Closes the BMV field of the non-circularity audit: together with the T0–T8 and cost-uniqueness carried clauses, it shows the master conjunction is assembled from independently proved, non-self-referential atoms rather than placeholders. The module header records that after M1–M3 these three clauses are genuine carried content, so non-circularity of the master statement follows. No further downstream edges are recorded on this declaration; its role is the audit disclosure itself, feeding the sibling conjunctions that assert all carried clauses hold.