{"paper":{"title":"Prime scattering geodesic theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.NT","authors_text":"Punya Plaban Satpathy, Sudhir Pujahari","submitted_at":"2025-05-08T06:18:13Z","abstract_excerpt":"The modular surface, given by the quotient $\\mathcal{M} = \\Ha/\\text{PSL}(2,\\Z)$, can be partitioned into a compact subset $\\Mm$ and an open neighborhood of the unique cusp in $\\mathcal{M}$. We consider scattering geodesics in $\\mathcal{M}$, first introduced by Victor Guillemin in \\cite{Guillemin1976-xr} for hyperbolic surfaces with cusps. These are geodesics in $\\mathcal{M}$ that lie in $\\mathcal{M} \\setminus \\Mm$ for both large positive and negative times. Associated with such a scattering geodesic in $\\mathcal{M}$, a finite \\textit{sojourn time} is defined in \\cite{Guillemin1976-xr}. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04973","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/2505.04973/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"}