Operational Selector Cones for Ancilla Orientation Decomposability, PPT Resources, and Center-Label Access

A transpose-twisted presentation can preserve every single-system positive state while failing under inert extension by a reference system. This paper asks which finite preparation, effect, and reference resources select a common relative ancilla orientation without assuming the completely positive process category in advance. It proves an exact dual-cone selector criterion, gives a product/separable countermodel and a Bell/singlet selector for transpose, establishes a two-sided Schmidt-resource bottleneck, organizes the CP/DEC/POS apparatus hierarchy, and derives a reference-indexed simultaneous-PPT criterion. It also separates count-vector sufficiency from completeness for center-coarse apparatuses and gives an exact classification under an explicitly orientation-separating preparation-effect pair. Exact qutrit and center-count regressions and accepted scoped Lean evidence support named finite statements; no complete formalization, empirical realization, absolute chirality, or external peer review is claimed.