Finite-pulse reconstruction of relative quantum contexts: Calibrated inversion and fit-free composition tests

Two labelled rank-one quantum measurement contexts can have identical static transition probabilities while differing in their relative complex realization. This preprint studies reconstruction in a specified one-system access model with state preparation, context readout, and independently calibrated projector-phase controls. It gives a finite-pulse extraction of fourth-order Bargmann invariants, constructive reconstruction of the relative unitary matrix modulo row and column phases, a common-unitary completion condition, stability bounds, and a fit-free four-setting composition identity. Combined with simultaneous finite-sample confidence regions, the latter yields a conservative level-alpha rejection rule for the stated stable-control model class. Numerical evidence is synthetic and limitations, blind spots, and unequal hardware access in comparisons are reported explicitly.