{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:CZTB3WFV75HQ3AJZNCQX2OGKTX","short_pith_number":"pith:CZTB3WFV","schema_version":"1.0","canonical_sha256":"16661dd8b5ff4f0d813968a17d38ca9df894acafe7b73a4ca58aee914e0783e8","source":{"kind":"arxiv","id":"2505.07738","version":1},"attestation_state":"computed","paper":{"title":"Counting and equidistribution of strongly reversible closed geodesics in negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2025-05-12T16:49:28Z","abstract_excerpt":"Let $M$ be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order $2$. Generalizing results of Sarnak and Erlandsson-Souto for constant curvature oriented surfaces, and with very different techniques, we give an asymptotic counting result on the number of strongly reversible periodic orbits of the geodesic flow in $M$, and prove their equidistribution towards the Bowen-Margulis measure. The result is proved in the more general setting with weights coming from thermodynamic formalism, and also in the analogous setting of graphs of groups with $2$-torsion. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.07738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-12T16:49:28Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8faf6bb98a861d3a5d177b48633cea5e32823ab6a7951ac6294f6d1446791d06","abstract_canon_sha256":"addd5fb5777fa21e05978b7c8ea9903261611344d7b9832974ae9150ee0e6515"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:52.501124Z","signature_b64":"JoETNYoq4jHA1a9Wj3IHLKiMkr4IkySc0XcOgFSN1+MNLqjXzqO4KpeGRiNZ+h/8jaNDlWH/F6cBj/G4O9JkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16661dd8b5ff4f0d813968a17d38ca9df894acafe7b73a4ca58aee914e0783e8","last_reissued_at":"2026-07-05T11:01:52.500690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:52.500690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting and equidistribution of strongly reversible closed geodesics in negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2025-05-12T16:49:28Z","abstract_excerpt":"Let $M$ be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order $2$. Generalizing results of Sarnak and Erlandsson-Souto for constant curvature oriented surfaces, and with very different techniques, we give an asymptotic counting result on the number of strongly reversible periodic orbits of the geodesic flow in $M$, and prove their equidistribution towards the Bowen-Margulis measure. The result is proved in the more general setting with weights coming from thermodynamic formalism, and also in the analogous setting of graphs of groups with $2$-torsion. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07738","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/2505.07738/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.07738","created_at":"2026-07-05T11:01:52.500757+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.07738v1","created_at":"2026-07-05T11:01:52.500757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07738","created_at":"2026-07-05T11:01:52.500757+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZTB3WFV75HQ","created_at":"2026-07-05T11:01:52.500757+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZTB3WFV75HQ3AJZ","created_at":"2026-07-05T11:01:52.500757+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZTB3WFV","created_at":"2026-07-05T11:01:52.500757+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.08449","citing_title":"Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX","json":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX.json","graph_json":"https://pith.science/api/pith-number/CZTB3WFV75HQ3AJZNCQX2OGKTX/graph.json","events_json":"https://pith.science/api/pith-number/CZTB3WFV75HQ3AJZNCQX2OGKTX/events.json","paper":"https://pith.science/paper/CZTB3WFV"},"agent_actions":{"view_html":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX","download_json":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX.json","view_paper":"https://pith.science/paper/CZTB3WFV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.07738&json=true","fetch_graph":"https://pith.science/api/pith-number/CZTB3WFV75HQ3AJZNCQX2OGKTX/graph.json","fetch_events":"https://pith.science/api/pith-number/CZTB3WFV75HQ3AJZNCQX2OGKTX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX/action/storage_attestation","attest_author":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX/action/author_attestation","sign_citation":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX/action/citation_signature","submit_replication":"https://pith.science/pith/CZTB3WFV75HQ3AJZNCQX2OGKTX/action/replication_record"}},"created_at":"2026-07-05T11:01:52.500757+00:00","updated_at":"2026-07-05T11:01:52.500757+00:00"}