{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:O5B37EQY3SYBNDVP5ZESI6GJSL","short_pith_number":"pith:O5B37EQY","schema_version":"1.0","canonical_sha256":"7743bf9218dcb0168eafee492478c992e6e7d9c18c4bd55dd6ab923b83a08db9","source":{"kind":"arxiv","id":"2408.04453","version":1},"attestation_state":"computed","paper":{"title":"Rational Curves on Real Classical Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.GR"],"primary_cat":"math.AG","authors_text":"Ke Ye, Zijia Li","submitted_at":"2024-08-08T13:27:42Z","abstract_excerpt":"This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify quadratic rational curves on $\\mathrm{U}_n$, $\\mathrm{O}_n(\\mathbb{R})$, $\\mathrm{O}_{n-1,1}(\\mathbb{R})$ and $\\mathrm{O}_{n-2,2}(\\mathbb{R})$. (ii) We prove a decomposition theorem for rational curves on real classical groups, which can be regarded as a non-commutative generalization of the fundamental theorem of algebra and partial fraction decomposition. (iii) As"},"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":"2408.04453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-08T13:27:42Z","cross_cats_sorted":["cs.SC","math.GR"],"title_canon_sha256":"c6d453137ff5b2307d69f12e780b0c6c89071869327745b5f110413a79542e43","abstract_canon_sha256":"5e841ec859f27d2926402e06c88bba97c8c58faedfb594c5f5e78b04bc766569"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:53:33.502934Z","signature_b64":"MWqE7VYyCB+d8R0rjE38tiBRGQiVWhlCyytDwO3NMzEGF0/Ro1Ny26pFoSYKhSsyVYetSrlyQpx7lzHIcPsOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7743bf9218dcb0168eafee492478c992e6e7d9c18c4bd55dd6ab923b83a08db9","last_reissued_at":"2026-07-05T08:53:33.502568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:53:33.502568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational Curves on Real Classical Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.GR"],"primary_cat":"math.AG","authors_text":"Ke Ye, Zijia Li","submitted_at":"2024-08-08T13:27:42Z","abstract_excerpt":"This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify quadratic rational curves on $\\mathrm{U}_n$, $\\mathrm{O}_n(\\mathbb{R})$, $\\mathrm{O}_{n-1,1}(\\mathbb{R})$ and $\\mathrm{O}_{n-2,2}(\\mathbb{R})$. (ii) We prove a decomposition theorem for rational curves on real classical groups, which can be regarded as a non-commutative generalization of the fundamental theorem of algebra and partial fraction decomposition. (iii) As"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.04453","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.04453/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2408.04453","created_at":"2026-07-05T08:53:33.502623+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.04453v1","created_at":"2026-07-05T08:53:33.502623+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.04453","created_at":"2026-07-05T08:53:33.502623+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5B37EQY3SYB","created_at":"2026-07-05T08:53:33.502623+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5B37EQY3SYBNDVP","created_at":"2026-07-05T08:53:33.502623+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5B37EQY","created_at":"2026-07-05T08:53:33.502623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.10513","citing_title":"Product Of Exponentials (POE) Splines on Lie-Groups: Limitations, Extensions, and Application to SO(3) and SE(3)","ref_index":42,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL","json":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL.json","graph_json":"https://pith.science/api/pith-number/O5B37EQY3SYBNDVP5ZESI6GJSL/graph.json","events_json":"https://pith.science/api/pith-number/O5B37EQY3SYBNDVP5ZESI6GJSL/events.json","paper":"https://pith.science/paper/O5B37EQY"},"agent_actions":{"view_html":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL","download_json":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL.json","view_paper":"https://pith.science/paper/O5B37EQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.04453&json=true","fetch_graph":"https://pith.science/api/pith-number/O5B37EQY3SYBNDVP5ZESI6GJSL/graph.json","fetch_events":"https://pith.science/api/pith-number/O5B37EQY3SYBNDVP5ZESI6GJSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL/action/storage_attestation","attest_author":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL/action/author_attestation","sign_citation":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL/action/citation_signature","submit_replication":"https://pith.science/pith/O5B37EQY3SYBNDVP5ZESI6GJSL/action/replication_record"}},"created_at":"2026-07-05T08:53:33.502623+00:00","updated_at":"2026-07-05T08:53:33.502623+00:00"}