{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EA2BWAYNQOBUI3CKSMEND6FJML","short_pith_number":"pith:EA2BWAYN","schema_version":"1.0","canonical_sha256":"20341b030d8383446c4a9308d1f8a962f2a3062274886dbbf85ecb88658d0ef1","source":{"kind":"arxiv","id":"1106.5600","version":1},"attestation_state":"computed","paper":{"title":"Every knot is a billiard knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Daniel Pecker, Pierre-Vincent Koseleff (INRIA Rocquencourt)","submitted_at":"2011-06-28T09:10:07Z","abstract_excerpt":"We show that every knot can be realized as a billiard trajectory in a convex prism. This solves a conjecture of Jones and Przytycki."},"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":"1106.5600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-28T09:10:07Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"38e66d4cb657066a844a4714814e96902edaeb39098c6d402dcb3a9647047045","abstract_canon_sha256":"a0fa99585f94348bf38c13313aad875c64f7ed97548f9cd0ba048ddfa65aa884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:12.863212Z","signature_b64":"W4r0iHSsrOkWWfnvlmzvRQlKm+rLbZsh4AhRnJuqzz6PWd80ccM2lGetJ+BthOBd7pvar0AIniftLVO7WfRPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20341b030d8383446c4a9308d1f8a962f2a3062274886dbbf85ecb88658d0ef1","last_reissued_at":"2026-05-18T04:19:12.862761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:12.862761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Every knot is a billiard knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Daniel Pecker, Pierre-Vincent Koseleff (INRIA Rocquencourt)","submitted_at":"2011-06-28T09:10:07Z","abstract_excerpt":"We show that every knot can be realized as a billiard trajectory in a convex prism. This solves a conjecture of Jones and Przytycki."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5600","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":"1106.5600","created_at":"2026-05-18T04:19:12.862824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5600v1","created_at":"2026-05-18T04:19:12.862824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5600","created_at":"2026-05-18T04:19:12.862824+00:00"},{"alias_kind":"pith_short_12","alias_value":"EA2BWAYNQOBU","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"EA2BWAYNQOBUI3CK","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"EA2BWAYN","created_at":"2026-05-18T12:26:26.731475+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/EA2BWAYNQOBUI3CKSMEND6FJML","json":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML.json","graph_json":"https://pith.science/api/pith-number/EA2BWAYNQOBUI3CKSMEND6FJML/graph.json","events_json":"https://pith.science/api/pith-number/EA2BWAYNQOBUI3CKSMEND6FJML/events.json","paper":"https://pith.science/paper/EA2BWAYN"},"agent_actions":{"view_html":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML","download_json":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML.json","view_paper":"https://pith.science/paper/EA2BWAYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5600&json=true","fetch_graph":"https://pith.science/api/pith-number/EA2BWAYNQOBUI3CKSMEND6FJML/graph.json","fetch_events":"https://pith.science/api/pith-number/EA2BWAYNQOBUI3CKSMEND6FJML/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML/action/storage_attestation","attest_author":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML/action/author_attestation","sign_citation":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML/action/citation_signature","submit_replication":"https://pith.science/pith/EA2BWAYNQOBUI3CKSMEND6FJML/action/replication_record"}},"created_at":"2026-05-18T04:19:12.862824+00:00","updated_at":"2026-05-18T04:19:12.862824+00:00"}