{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GO5QIKZLKRDEIACFK7XGX6FMDE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"599c42f41d39cac9df6f91eede46faceadf32f7b810ecad42dfde28608a9198f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-03T16:51:23Z","title_canon_sha256":"6dfee1409543870a63e362b41754f978386a14a27d40cb25d5fa4ffdc953968b"},"schema_version":"1.0","source":{"id":"1110.0415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0415","created_at":"2026-05-18T04:11:49Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0415v1","created_at":"2026-05-18T04:11:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0415","created_at":"2026-05-18T04:11:49Z"},{"alias_kind":"pith_short_12","alias_value":"GO5QIKZLKRDE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GO5QIKZLKRDEIACF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GO5QIKZL","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:1fb97c5ad1c4d515f16de16b1b52797aa77fb327a8af2e7925e5bfde4bfd82f2","target":"graph","created_at":"2026-05-18T04:11:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $D$ be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in $D.$ This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobi's proof of Poncelet's theorem by means of elliptic functions.","authors_text":"Daniel Pecker","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-03T16:51:23Z","title":"Poncelet's theorem and Billiard knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0415","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83890275655b8d0d239276b52a3dd436151ce5beb6e3c4e3593a9426b039c11c","target":"record","created_at":"2026-05-18T04:11:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"599c42f41d39cac9df6f91eede46faceadf32f7b810ecad42dfde28608a9198f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-03T16:51:23Z","title_canon_sha256":"6dfee1409543870a63e362b41754f978386a14a27d40cb25d5fa4ffdc953968b"},"schema_version":"1.0","source":{"id":"1110.0415","kind":"arxiv","version":1}},"canonical_sha256":"33bb042b2b544644004557ee6bf8ac193628c8c544ba9b50e8ebffb9809a1e32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33bb042b2b544644004557ee6bf8ac193628c8c544ba9b50e8ebffb9809a1e32","first_computed_at":"2026-05-18T04:11:49.997717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:49.997717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mEq5X/N48/Y81jFJHT+d2ph517igX3wiHWBM9mNXkp17yN+vyOZ31RYCjIpobGFtMtlc0whjrks9vXC838JoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:49.998273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83890275655b8d0d239276b52a3dd436151ce5beb6e3c4e3593a9426b039c11c","sha256:1fb97c5ad1c4d515f16de16b1b52797aa77fb327a8af2e7925e5bfde4bfd82f2"],"state_sha256":"49bc47d3929a2e1359965d20b3ef83591d818902e9a69eee1f230909c305bf42"}