Physics-Constrained Generative Inference of Sub-Crystal Electromagnetic Shower Structure in a Segmented Calorimeter

The finite transverse granularity of a segmented electromagnetic calorimeter fundamentally limits the precision with which the observables of a shower can be reconstructed, among them its position, its lateral profile, and the direction of the incident particle. We show that a substantial fraction of the information suppressed by the segmentation can be inferred under physical constraints, and that it propagates to downstream physics quantities. The reconstruction is cast as an inverse problem and solved with a generative model constrained by the low-order spatial moments of the shower, driving the solution toward physically consistent energy distributions rather than image similarity alone. Using the undoped CsI calorimeter of the KOTO experiment as a reference system, the reconstruction reduces the per-event residual of these moments with respect to the truth-level reference by roughly 40-62% in a representative 1 GeV bin. The inferred morphology also generalizes beyond the training objective: on a $K_{L}\to\pi^{0}\nu\bar\nu$ Monte Carlo sample it improves the reconstruction of the photon incident angle, a quantity never used during training, and of the $\pi^{0}$ decay vertex. These results indicate that finite segmentation is better viewed as a limit on what a calorimeter measures directly than as an absolute limit on the physics information it retains, with the recoverable fraction depending on the observable and growing with the shower energy.