{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZDUCSVX2DHGBO6FIA6EDJLK6NH","short_pith_number":"pith:ZDUCSVX2","schema_version":"1.0","canonical_sha256":"c8e82956fa19cc1778a8078834ad5e69ca22aa8f27a922535f681e7f769d7a3d","source":{"kind":"arxiv","id":"1506.03727","version":3},"attestation_state":"computed","paper":{"title":"Salem numbers and arithmetic hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.GT","authors_text":"John G. Ratcliffe, Steven T. Tschantz, Vincent Emery","submitted_at":"2015-06-11T16:09:00Z","abstract_excerpt":"In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a \"short geodesic conjecture\", and prove its equivalence with \"Lehmer's conjecture\" for Salem numbers."},"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":"1506.03727","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-11T16:09:00Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"f054024c734e7f9b5d796a8a1f2ab46f2c4df9b113ad70a50f22239cdb22c7e3","abstract_canon_sha256":"b1327a676baac7be1489d1d4de7e1e794ee2e5919a01bdd47dbeed6783d1efa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:01.129083Z","signature_b64":"gx6PZC9MBvJmkPb3C6rReGw53UrkRQf/C/BUWypLEvE+Ez+VNEQK4qSZCTy3xDwm4nLmdg9rb8p8O3bqqFViAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8e82956fa19cc1778a8078834ad5e69ca22aa8f27a922535f681e7f769d7a3d","last_reissued_at":"2026-05-18T00:12:01.128479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:01.128479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Salem numbers and arithmetic hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.GT","authors_text":"John G. Ratcliffe, Steven T. Tschantz, Vincent Emery","submitted_at":"2015-06-11T16:09:00Z","abstract_excerpt":"In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a \"short geodesic conjecture\", and prove its equivalence with \"Lehmer's conjecture\" for Salem numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03727","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1506.03727","created_at":"2026-05-18T00:12:01.128580+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03727v3","created_at":"2026-05-18T00:12:01.128580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03727","created_at":"2026-05-18T00:12:01.128580+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDUCSVX2DHGB","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDUCSVX2DHGBO6FI","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDUCSVX2","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH","json":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH.json","graph_json":"https://pith.science/api/pith-number/ZDUCSVX2DHGBO6FIA6EDJLK6NH/graph.json","events_json":"https://pith.science/api/pith-number/ZDUCSVX2DHGBO6FIA6EDJLK6NH/events.json","paper":"https://pith.science/paper/ZDUCSVX2"},"agent_actions":{"view_html":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH","download_json":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH.json","view_paper":"https://pith.science/paper/ZDUCSVX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03727&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDUCSVX2DHGBO6FIA6EDJLK6NH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDUCSVX2DHGBO6FIA6EDJLK6NH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH/action/storage_attestation","attest_author":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH/action/author_attestation","sign_citation":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH/action/citation_signature","submit_replication":"https://pith.science/pith/ZDUCSVX2DHGBO6FIA6EDJLK6NH/action/replication_record"}},"created_at":"2026-05-18T00:12:01.128580+00:00","updated_at":"2026-05-18T00:12:01.128580+00:00"}