Conditioning Is Not Control: Scientific Endpoint Controllability for Tensor-Conditioned Generative Models

Property-conditioned generators are increasingly used for scientific inverse design, but a conditioning variable need not be an action that controls the requested physical response. We formalize scientific endpoint controllability for tensor-valued targets by composing a generator with an independently specified scientific evaluator and quotienting physically equivalent $\mathrm{SO}(3)$ representatives. This formulation separates three notions that are often conflated: structural recoverability, conditioning-path visibility, and local endpoint reachability; direct target tracking further requires local inverse-action calibration. On a matched clamped-piezoelectric benchmark, tensor orbits are strongly recoverable from structure (CEITNet proper-orbit cosine 0.883), yet conditioning interventions reveal a distinct actuation geometry: scalar conditioning is locally rank one, whereas full-tensor routes expose roughly twelve numerically visible directions while concentrating most response energy in about two stable-rank directions. Common-noise swaps further show that a nonzero field response can remain nearly orthogonal to the requested correction. Independently, response-state analysis shows that endpoint specification materially changes the target, while DFPT separates many-mode lattice dynamics from the pointwise Born-charge-visible response channel. These results provide a mechanism-level diagnostic criterion for locating which stage limits endpoint control despite condition responsiveness.