{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OXLW2YKWWWGHNN2ILDMUSHOWR7","short_pith_number":"pith:OXLW2YKW","schema_version":"1.0","canonical_sha256":"75d76d6156b58c76b74858d9491dd68fcc24500a36bde0f8fd6667016cdb6745","source":{"kind":"arxiv","id":"1602.05698","version":1},"attestation_state":"computed","paper":{"title":"Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.SI"],"primary_cat":"math.DG","authors_text":"Andrey E. Mironov, Michael (Misha) Bialy","submitted_at":"2016-02-18T07:23:02Z","abstract_excerpt":"We consider a convex curve $\\gamma$ lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the domain bounded by $\\gamma$. We extend the result by S. Bolotin (1992) and get new obstructions on polynomial integrability in terms of the dual curve $\\Gamma$. We follow a method which was introduced by S. Tabachnikov for Outer billiards in the plane and was applied later on in our recent paper to Birkhoff billiards with the help of a new the so called Angular billiard."},"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":"1602.05698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-18T07:23:02Z","cross_cats_sorted":["math.DS","nlin.SI"],"title_canon_sha256":"c7cc286160268920b1c6988cb1a8d1a4b2f0fe87d53f9177aed20fb417524fbd","abstract_canon_sha256":"6c9a70f3a5cd8ec81f8213d73cebe1b19240a3ea4cffe9797aaae0aa7591f619"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.473126Z","signature_b64":"xQNRvrBOtWnBJKwdsX7u1SywEmUzajWcvFOnrp5Yofns/wZ6stHcwE+Ig8nSbRYxLnvuqY7nh0OVqrshaxugBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75d76d6156b58c76b74858d9491dd68fcc24500a36bde0f8fd6667016cdb6745","last_reissued_at":"2026-05-18T01:20:23.472406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.472406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.SI"],"primary_cat":"math.DG","authors_text":"Andrey E. Mironov, Michael (Misha) Bialy","submitted_at":"2016-02-18T07:23:02Z","abstract_excerpt":"We consider a convex curve $\\gamma$ lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the domain bounded by $\\gamma$. We extend the result by S. Bolotin (1992) and get new obstructions on polynomial integrability in terms of the dual curve $\\Gamma$. We follow a method which was introduced by S. Tabachnikov for Outer billiards in the plane and was applied later on in our recent paper to Birkhoff billiards with the help of a new the so called Angular billiard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05698","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":"1602.05698","created_at":"2026-05-18T01:20:23.472502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05698v1","created_at":"2026-05-18T01:20:23.472502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05698","created_at":"2026-05-18T01:20:23.472502+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXLW2YKWWWGH","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXLW2YKWWWGHNN2I","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXLW2YKW","created_at":"2026-05-18T12:30:36.002864+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/OXLW2YKWWWGHNN2ILDMUSHOWR7","json":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7.json","graph_json":"https://pith.science/api/pith-number/OXLW2YKWWWGHNN2ILDMUSHOWR7/graph.json","events_json":"https://pith.science/api/pith-number/OXLW2YKWWWGHNN2ILDMUSHOWR7/events.json","paper":"https://pith.science/paper/OXLW2YKW"},"agent_actions":{"view_html":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7","download_json":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7.json","view_paper":"https://pith.science/paper/OXLW2YKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05698&json=true","fetch_graph":"https://pith.science/api/pith-number/OXLW2YKWWWGHNN2ILDMUSHOWR7/graph.json","fetch_events":"https://pith.science/api/pith-number/OXLW2YKWWWGHNN2ILDMUSHOWR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7/action/storage_attestation","attest_author":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7/action/author_attestation","sign_citation":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7/action/citation_signature","submit_replication":"https://pith.science/pith/OXLW2YKWWWGHNN2ILDMUSHOWR7/action/replication_record"}},"created_at":"2026-05-18T01:20:23.472502+00:00","updated_at":"2026-05-18T01:20:23.472502+00:00"}