{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PW42GFBG6NWIYZZMS25AWLIGWZ","short_pith_number":"pith:PW42GFBG","schema_version":"1.0","canonical_sha256":"7db9a31426f36c8c672c96ba0b2d06b66cef037a74fda8cf9e5a237624d536f9","source":{"kind":"arxiv","id":"2403.06626","version":2},"attestation_state":"computed","paper":{"title":"The Prime Geodesic Theorem for the Picard Orbifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ikuya Kaneko","submitted_at":"2024-03-11T11:35:12Z","abstract_excerpt":"We establish the prime geodesic theorem for the Picard orbifold $\\mathrm{PSL}_{2}(\\mathbb{Z}[i]) \\backslash \\mathbb{H}^{3}$, wherein the error term shrinks proportionally to improvements in the subconvex exponent for quadratic Dirichlet $L$-functions over $\\mathbb{Q}(i)$. Our result sheds light on a venerable conjecture by attaining an unconditional exponent of $1.483$ and a conditionally superior exponent of $1.425$ under the generalised Lindel\\\"{o}f hypothesis. The argument synthesises, among other elements, the complete resolution of Koyama's (2001) mean Lindel\\\"{o}f hypothesis over $\\mathb"},"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":"2403.06626","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-03-11T11:35:12Z","cross_cats_sorted":[],"title_canon_sha256":"f5020fb4246d2029af97ad5ab3b7d256b260d9047e7fc5475aba1f63bfc514f2","abstract_canon_sha256":"0fa9989b970142469c13dbfe4a216df3a1f63b70c93ce4b3c8582f3d898cfcd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:44.727808Z","signature_b64":"2nRKTsjfC04WgU6zUeD+yV7wSUXAvcvD1woeu9KjdBDmCBT9Nm9jWlMD6flXbOyjqhfnXZnQAyTjMja9UfotBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7db9a31426f36c8c672c96ba0b2d06b66cef037a74fda8cf9e5a237624d536f9","last_reissued_at":"2026-07-05T09:59:44.727443Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:44.727443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Prime Geodesic Theorem for the Picard Orbifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ikuya Kaneko","submitted_at":"2024-03-11T11:35:12Z","abstract_excerpt":"We establish the prime geodesic theorem for the Picard orbifold $\\mathrm{PSL}_{2}(\\mathbb{Z}[i]) \\backslash \\mathbb{H}^{3}$, wherein the error term shrinks proportionally to improvements in the subconvex exponent for quadratic Dirichlet $L$-functions over $\\mathbb{Q}(i)$. Our result sheds light on a venerable conjecture by attaining an unconditional exponent of $1.483$ and a conditionally superior exponent of $1.425$ under the generalised Lindel\\\"{o}f hypothesis. The argument synthesises, among other elements, the complete resolution of Koyama's (2001) mean Lindel\\\"{o}f hypothesis over $\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06626","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.06626/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":"2403.06626","created_at":"2026-07-05T09:59:44.727505+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.06626v2","created_at":"2026-07-05T09:59:44.727505+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06626","created_at":"2026-07-05T09:59:44.727505+00:00"},{"alias_kind":"pith_short_12","alias_value":"PW42GFBG6NWI","created_at":"2026-07-05T09:59:44.727505+00:00"},{"alias_kind":"pith_short_16","alias_value":"PW42GFBG6NWIYZZM","created_at":"2026-07-05T09:59:44.727505+00:00"},{"alias_kind":"pith_short_8","alias_value":"PW42GFBG","created_at":"2026-07-05T09:59:44.727505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.17753","citing_title":"The hyperbolic lattice counting problem in large dimensions","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ","json":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ.json","graph_json":"https://pith.science/api/pith-number/PW42GFBG6NWIYZZMS25AWLIGWZ/graph.json","events_json":"https://pith.science/api/pith-number/PW42GFBG6NWIYZZMS25AWLIGWZ/events.json","paper":"https://pith.science/paper/PW42GFBG"},"agent_actions":{"view_html":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ","download_json":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ.json","view_paper":"https://pith.science/paper/PW42GFBG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.06626&json=true","fetch_graph":"https://pith.science/api/pith-number/PW42GFBG6NWIYZZMS25AWLIGWZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PW42GFBG6NWIYZZMS25AWLIGWZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ/action/storage_attestation","attest_author":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ/action/author_attestation","sign_citation":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ/action/citation_signature","submit_replication":"https://pith.science/pith/PW42GFBG6NWIYZZMS25AWLIGWZ/action/replication_record"}},"created_at":"2026-07-05T09:59:44.727505+00:00","updated_at":"2026-07-05T09:59:44.727505+00:00"}