{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DG3LWZJ555XXK4VM4INL2Q5QKC","short_pith_number":"pith:DG3LWZJ5","schema_version":"1.0","canonical_sha256":"19b6bb653def6f7572ace21abd43b050875ef0932a87cf4a9af792e9e0c2712d","source":{"kind":"arxiv","id":"1512.04779","version":1},"attestation_state":"computed","paper":{"title":"On the variance of the error term in the hyperbolic circle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giacomo Cherubini, Morten S. Risager","submitted_at":"2015-12-15T13:33:03Z","abstract_excerpt":"Let $e(s)$ be the error term of the hyperbolic circle problem, and denote by $e_\\alpha(s)$ the fractional integral to order $\\alpha$ of $e(s)$. We prove that for any small $\\alpha>0$ the asymptotic variance of $e_\\alpha(s)$ is finite, and given by an explicit expression. Moreover, we prove that $e_\\alpha(s)$ has a limiting distribution."},"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":"1512.04779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-15T13:33:03Z","cross_cats_sorted":[],"title_canon_sha256":"8610a84f97ce69c3077c5c1a67a921895d2522c19f80b50b1c4f79b51b5fb1ab","abstract_canon_sha256":"4e9cd687990599a131ef98926db947c74aca6243dc67db8c1e6e673ab76da986"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:15.563386Z","signature_b64":"vb3CqPe1uH4/lI6AZzrsHKf5Jvp8UKqM9JHgsTe1yIcBMvzZer3HCxZqWLKjzfKD8eQxTUyIPvixKThKvDSSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19b6bb653def6f7572ace21abd43b050875ef0932a87cf4a9af792e9e0c2712d","last_reissued_at":"2026-05-18T01:24:15.562620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:15.562620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the variance of the error term in the hyperbolic circle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giacomo Cherubini, Morten S. Risager","submitted_at":"2015-12-15T13:33:03Z","abstract_excerpt":"Let $e(s)$ be the error term of the hyperbolic circle problem, and denote by $e_\\alpha(s)$ the fractional integral to order $\\alpha$ of $e(s)$. We prove that for any small $\\alpha>0$ the asymptotic variance of $e_\\alpha(s)$ is finite, and given by an explicit expression. Moreover, we prove that $e_\\alpha(s)$ has a limiting distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04779","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":""},"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":"1512.04779","created_at":"2026-05-18T01:24:15.562732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04779v1","created_at":"2026-05-18T01:24:15.562732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04779","created_at":"2026-05-18T01:24:15.562732+00:00"},{"alias_kind":"pith_short_12","alias_value":"DG3LWZJ555XX","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DG3LWZJ555XXK4VM","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DG3LWZJ5","created_at":"2026-05-18T12:29:17.054201+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/DG3LWZJ555XXK4VM4INL2Q5QKC","json":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC.json","graph_json":"https://pith.science/api/pith-number/DG3LWZJ555XXK4VM4INL2Q5QKC/graph.json","events_json":"https://pith.science/api/pith-number/DG3LWZJ555XXK4VM4INL2Q5QKC/events.json","paper":"https://pith.science/paper/DG3LWZJ5"},"agent_actions":{"view_html":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC","download_json":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC.json","view_paper":"https://pith.science/paper/DG3LWZJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04779&json=true","fetch_graph":"https://pith.science/api/pith-number/DG3LWZJ555XXK4VM4INL2Q5QKC/graph.json","fetch_events":"https://pith.science/api/pith-number/DG3LWZJ555XXK4VM4INL2Q5QKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC/action/storage_attestation","attest_author":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC/action/author_attestation","sign_citation":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC/action/citation_signature","submit_replication":"https://pith.science/pith/DG3LWZJ555XXK4VM4INL2Q5QKC/action/replication_record"}},"created_at":"2026-05-18T01:24:15.562732+00:00","updated_at":"2026-05-18T01:24:15.562732+00:00"}