{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DRLS67RLBS625Q3OS3BA4YFCJF","short_pith_number":"pith:DRLS67RL","schema_version":"1.0","canonical_sha256":"1c572f7e2b0cbdaec36e96c20e60a2496677bd99b603a3445109d8d5481ebcc5","source":{"kind":"arxiv","id":"1308.3904","version":2},"attestation_state":"computed","paper":{"title":"The existence of two closed characteristics on every compact star-shaped hypersurface in ${\\bf R}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Hui Liu, Yiming Long","submitted_at":"2013-08-19T00:51:03Z","abstract_excerpt":"Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in ${\\bf R}^4$. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et al."},"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":"1308.3904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-19T00:51:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"53b8889dfb5d2ca521c24cbc7ddc1669f8bbdb29be814030c727adea48de8b4a","abstract_canon_sha256":"125a02afe4f26bda45706cd540461f6a9e7e0c51ebf7fafde0cda1f84678cbe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:26.097039Z","signature_b64":"6bH2lCVtHxLHKMxAS5mfZlXFrG5MMOc52gRIDut1gmkZloelJl1gj+5tN/zo8JvYAaGukOBdzy7M5ZhUsWIPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c572f7e2b0cbdaec36e96c20e60a2496677bd99b603a3445109d8d5481ebcc5","last_reissued_at":"2026-05-18T02:48:26.096584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:26.096584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of two closed characteristics on every compact star-shaped hypersurface in ${\\bf R}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Hui Liu, Yiming Long","submitted_at":"2013-08-19T00:51:03Z","abstract_excerpt":"Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in ${\\bf R}^4$. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3904","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":""},"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":"1308.3904","created_at":"2026-05-18T02:48:26.096645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3904v2","created_at":"2026-05-18T02:48:26.096645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3904","created_at":"2026-05-18T02:48:26.096645+00:00"},{"alias_kind":"pith_short_12","alias_value":"DRLS67RLBS62","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DRLS67RLBS625Q3O","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DRLS67RL","created_at":"2026-05-18T12:27:43.054852+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/DRLS67RLBS625Q3OS3BA4YFCJF","json":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF.json","graph_json":"https://pith.science/api/pith-number/DRLS67RLBS625Q3OS3BA4YFCJF/graph.json","events_json":"https://pith.science/api/pith-number/DRLS67RLBS625Q3OS3BA4YFCJF/events.json","paper":"https://pith.science/paper/DRLS67RL"},"agent_actions":{"view_html":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF","download_json":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF.json","view_paper":"https://pith.science/paper/DRLS67RL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3904&json=true","fetch_graph":"https://pith.science/api/pith-number/DRLS67RLBS625Q3OS3BA4YFCJF/graph.json","fetch_events":"https://pith.science/api/pith-number/DRLS67RLBS625Q3OS3BA4YFCJF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF/action/storage_attestation","attest_author":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF/action/author_attestation","sign_citation":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF/action/citation_signature","submit_replication":"https://pith.science/pith/DRLS67RLBS625Q3OS3BA4YFCJF/action/replication_record"}},"created_at":"2026-05-18T02:48:26.096645+00:00","updated_at":"2026-05-18T02:48:26.096645+00:00"}