Fractional Evolution on Anatomy-Derived Aortic Branch Graphs: Multiresolution Geometry, Observation Leakage, and Controlled Off-Grid Joint Identifiability

A fractional graph-evolution model is formulated on a surface-derived thoracic-aortic branch tree and evaluated through multiresolution geometry and controlled joint-parameter experiments. A checksum-tracked source audit separates three model-specific MRI collections from a shared nominal wall surface and confirms that no validated MRI–STL transformation is available. The surface pipeline yields five terminal openings, three junctions, seven semantic branches, refined cross-sections, and an unapproved same-source candidate. Consequently, the instantiated operator is dimensionless and geometry normalized, rather than a calibrated pressure–flow operator. Graphs with 50, 100, 200, and 400 nodes preserve topology; relative to the internal 400-node discretization, the 200-node graph has a 9.20% 95th-percentile discrepancy in the first 12 positive eigenvalues and a 7.58° maximum principal angle for the first 10 modal subspaces. The analysis establishes a Caputo-consistent control-volume reduction, finite-horizon well-posedness for bounded forcing, non-normal augmented dynamics, observation leakage, finite-band phase conditions, and residual power-law stability. In 810 off-grid synthetic experiments, seven parameters are estimated jointly with repeated noise, multistart optimization, profile likelihood, and held-out testing. The median fractional-order error is 0.001304 and the median held-out complex NRMSE is 0.01086. The results support controlled synthetic practical identifiability on a shared nominal anatomy, not measured hemodynamic calibration or physiological-memory identification.