{"paper":{"title":"Refraction laws in spatio-temporal media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"math.AP","authors_text":"Cristian E. Guti\\'errez, Eric Stachura","submitted_at":"2026-08-04T17:55:18Z","abstract_excerpt":"We study the time-dependent Maxwell system, formulated in the sense of distributions, for electromagnetic waves propagating through media with temporal and spatial material interfaces. Under explicit trace and regularity assumptions on the permittivity and permeability, we derive the jump conditions produced by temporal discontinuities and by subsequent spatial interfaces. These conditions are used to obtain generalized Snell laws for the wave vectors generated by temporal splitting, reflection, and transmission. We also derive the associated amplitude equations and organize them as a finite-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03995","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03995/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}