Two separate existence obligations

On a scheduler-comparable branch, let $\mathfrak{U}$ be a declared common operational model universe, let $C(D)$ express the class restrictions, and let

express the actual additional assumptions for a fixed proposed extraction rule $\mathfrak{E}$. The desired joint admissible set is

The two distinct requirements are

Equation (eq:nonvacuity) needs an admissible witness or an existence theorem. Equation (eq:additional-content) needs a scheduler model failing a stated additional restriction or assumption. Neither is established for a cone-selecting candidate here.

This formulation includes class restrictions in the additional-content audit. It does not require every $H_j$ separately to be independent of $\mathsf{S}$. A repeated scheduler condition may be restated for readability, but must be marked as baseline rather than credited as new cone-selecting content.

For a general process matrix with no declared complete dependency schedule, $\mathsf{S}(D)$ is not silently assigned a meaning. A corresponding branch must state its own operational premises and how the scheduler obstruction is compared with them. Rejecting all scheduler models merely by changing language is not a construction of a successful operational extraction.