{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SHIQR4YEBMUZNHISLCXEW6ZTNY","short_pith_number":"pith:SHIQR4YE","schema_version":"1.0","canonical_sha256":"91d108f3040b29969d1258ae4b7b336e1caf27add81e09e2f8d86488e9995ca1","source":{"kind":"arxiv","id":"1712.00880","version":2},"attestation_state":"computed","paper":{"title":"Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dimitrios Chatzakos, Dmitry Frolenkov, Giacomo Cherubini, Niko Laaksonen, Olga Balkanova","submitted_at":"2017-12-04T02:28:13Z","abstract_excerpt":"For $\\Gamma$ a cofinite Kleinian group acting on $\\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\\Gamma \\backslash \\mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics) on $M$. Let $E_{\\Gamma}(X)$ be the error in the counting of prime geodesics with length at most $\\log X$. For the Picard manifold, $\\Gamma=\\mathrm{PSL}(2,\\mathbb{Z}[i])$, we improve the classical bound of Sarnak, $E_{\\Gamma}(X)=O(X^{5/3+\\epsilon})$, to $E_{\\Gamma}(X)=O(X^{13/8+\\epsilon})$. In the process we obtain a mean subconvexity estimate for the Rankin"},"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":"1712.00880","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-04T02:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"1bdc462a1f30eec24cceedac44d57ddad37519051b5d8e1dd48e2965852ce3fb","abstract_canon_sha256":"18995a96a0c65d3c7e4c82859e69133da61cd639032a8f83283dc6ff044fdcc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:50.314153Z","signature_b64":"TVS9X8k3RcY2lYskldAO/NZAsX6OsIE41zbKrMzkzkMdR3PsZjC8uqwxJBOS+7L/379JdDflvISlXpQLIZxCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91d108f3040b29969d1258ae4b7b336e1caf27add81e09e2f8d86488e9995ca1","last_reissued_at":"2026-05-18T00:07:50.313479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:50.313479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dimitrios Chatzakos, Dmitry Frolenkov, Giacomo Cherubini, Niko Laaksonen, Olga Balkanova","submitted_at":"2017-12-04T02:28:13Z","abstract_excerpt":"For $\\Gamma$ a cofinite Kleinian group acting on $\\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\\Gamma \\backslash \\mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics) on $M$. Let $E_{\\Gamma}(X)$ be the error in the counting of prime geodesics with length at most $\\log X$. For the Picard manifold, $\\Gamma=\\mathrm{PSL}(2,\\mathbb{Z}[i])$, we improve the classical bound of Sarnak, $E_{\\Gamma}(X)=O(X^{5/3+\\epsilon})$, to $E_{\\Gamma}(X)=O(X^{13/8+\\epsilon})$. In the process we obtain a mean subconvexity estimate for the Rankin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00880","kind":"arxiv","version":2},"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":"1712.00880","created_at":"2026-05-18T00:07:50.313594+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00880v2","created_at":"2026-05-18T00:07:50.313594+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00880","created_at":"2026-05-18T00:07:50.313594+00:00"},{"alias_kind":"pith_short_12","alias_value":"SHIQR4YEBMUZ","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SHIQR4YEBMUZNHIS","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SHIQR4YE","created_at":"2026-05-18T12:31:43.269735+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/SHIQR4YEBMUZNHISLCXEW6ZTNY","json":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY.json","graph_json":"https://pith.science/api/pith-number/SHIQR4YEBMUZNHISLCXEW6ZTNY/graph.json","events_json":"https://pith.science/api/pith-number/SHIQR4YEBMUZNHISLCXEW6ZTNY/events.json","paper":"https://pith.science/paper/SHIQR4YE"},"agent_actions":{"view_html":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY","download_json":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY.json","view_paper":"https://pith.science/paper/SHIQR4YE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00880&json=true","fetch_graph":"https://pith.science/api/pith-number/SHIQR4YEBMUZNHISLCXEW6ZTNY/graph.json","fetch_events":"https://pith.science/api/pith-number/SHIQR4YEBMUZNHISLCXEW6ZTNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY/action/storage_attestation","attest_author":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY/action/author_attestation","sign_citation":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY/action/citation_signature","submit_replication":"https://pith.science/pith/SHIQR4YEBMUZNHISLCXEW6ZTNY/action/replication_record"}},"created_at":"2026-05-18T00:07:50.313594+00:00","updated_at":"2026-05-18T00:07:50.313594+00:00"}