Relational Anchors for Quantum Subsystem Identification: Minimal Separation and Robust Rigidity

Operational data can be complete inside a chosen subsystem frame while leaving the frame itself non-unique. A previous finite certification construction exhibits this phenomenon explicitly: an unpartitioned three-qubit Pauli presentation supports three inequivalent finest full tensor frames even though its generated observable algebra is all of M_8( C). We ask what additional information can select one frame without treating that information as merely another unlabelled control direction. We introduce relational anchors: gauge-equivariant constraints on a finite refinement poset of direction-generated frames. A general finite-poset theorem characterizes exact anchor collapse and turns target certification into a hitting-set problem, while global frame identification becomes a test-cover problem. In the three-qubit presentation we enumerate the complete nontrivial full witness poset, prove that one two-direction locality anchor separates all three finest frames, and determine exactly twelve single anchors of this type that pass the full-poset test. For robustness, exact support is replaced by conditional-expectation signatures, yielding a sharp γ/2 separation criterion. We prove a zero-radius result for the exact witness poset under unrestricted raw perturbations and derive a sharp projective Pauli decoding radius. Six Hamiltonian-derivation squares reconstruct the projective Pauli geometry. A residual synchronization analysis separates ordinary graph cycles from gauge-invariant parity constraints, and four atomic Jordan–Lie anchors are necessary and sufficient, within the declared anchor class, to reduce the remaining scale and sign freedom to Clifford gauge. An explicit relative-defect rigidity modulus and a protocol-conditioned end-to-end error certificate are obtained. The result does not claim that probabilities alone determine a physical tensor-product structure. Rather, unpartitioned process data together with a finite relational anchor package robustly identify a subsystem frame up to the declared gauge.