A calibration-invariant fringe offset in published Wigner tomograms: evidence for the Maslov quarter-turn and a three-platform classification of interference topology

Interference fringes in the Wigner function of a cubic-phase bosonic state are the phase-space image of a fold caustic: semiclassically the fringe zeros satisfy a chord-area law A_n = πℏ(n − δ) with δ = 1/4, the offset being the Maslov phase of the fold. The offset δ is dimensionless and invariant under all linear distortions of the tomogram axes, so linear calibration errors can neither fake nor destroy it. Reanalyzing the published cubic-phase-state tomogram of Eriksson et al. (Nat. Commun. 15, 2512, 2024), the fully calibration-invariant fit gives a chord-area slope of 3.04 ± 0.49 (predicted π) and δ = 0.34 ± 0.35, consistent with the fold value 1/4; anchoring the vertex to the paper's calibrated theory map sharpens this to δ = 0.30 ± 0.20 (statistical). To my knowledge this is the first extraction of this observable from quantum-state tomography data. Two public control datasets complete a three-way classification: mechanical cat states (Bild et al., Science 380, 274, 2023) show the two-branch chord signatures a two-sided fringe train, pooled offset sum δ+ + δ− = 0.94 ± 0.13 against the chord invariant 1, carrier phases clustering at parity values, and no fold-like chirp and GKP lattice states (Brock et al., Nature 641, 612–618, 2025) pass the no-fold control with exactly periodic zeros (pooled spacing ratio 1.000 ± 0.007). Also included: an exact rigid-shift theorem for finite squeezing, a reconstruction background systematic present in every dataset examined, and the use of GKP lattices as built-in phase-space rulers. All results use only public data; analysis code and numerical results are deposited alongside the note.