Dynamical Qutrit Coherence-Cycle Witness from Calibrated Pairwise Visibilities

This preprint introduces a dynamical qutrit coherence-cycle witness based on calibrated pairwise visibility measurements in a three-path interferometer. The central idea is that pairwise visibility data contain a geometry of normalized qutrit coherences that is not captured by scalar coherence measures alone. For nonzero path populations, the population-calibrated two-path visibility equals the normalized off-diagonal coherence of the reduced path qutrit. The squared normalized coherences define the cycle expression Scyc = kappa_12^2 + kappa_23^2 - kappa_13^2. Classical jointly diagonalizable overlap geometries obey the boundary Scyc <= 1. A statistically certified value Scyc > 1 therefore indicates a nonclassical cyclic arrangement of pair coherences, rather than merely a large amount of coherence. The paper proves the physical qutrit range Scyc <= 5/4, gives explicit positive semidefinite qutrit examples with equal scalar coherence but different cycle geometry, constructs a completely positive random-unitary dephasing model with time-dependent geometry windows, and formulates a finite-data certification protocol including calibration and covariance propagation. The static overlap-cycle inequality is imported from prior overlap-cycle work; the new contribution is its calibrated realization as a path-qutrit coherence-geometry witness. The proposed witness is intended as a measurement-efficient diagnostic of normalized coherence geometry in multipath interferometry and open qutrit dynamics. It is not a full state-tomography method and does not by itself constitute a complete contextuality experiment; stronger interpretations require the additional operational assumptions stated in the manuscript.