{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FAKI52YO4R6GEL2XYBFKAPKFDR","short_pith_number":"pith:FAKI52YO","schema_version":"1.0","canonical_sha256":"28148eeb0ee47c622f57c04aa03d451c686c68f69fa233e7b6dc4fc31c4241c9","source":{"kind":"arxiv","id":"1010.3160","version":1},"attestation_state":"computed","paper":{"title":"Special symplectic Lie groups and hypersymplectic Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.QA","math.SG"],"primary_cat":"math-ph","authors_text":"Chengming Bai, Xiang Ni","submitted_at":"2010-10-15T13:32:24Z","abstract_excerpt":"A special symplectic Lie group is a triple $(G,\\omega,\\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\\nabla$. In this paper starting from a special symplectic Lie group we show how to ``deform\" the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure $\\nabla$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider t"},"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":"1010.3160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-15T13:32:24Z","cross_cats_sorted":["math.DG","math.MP","math.QA","math.SG"],"title_canon_sha256":"87d32370c4c0957e5f807bbc8f82abe62d6ff1fcd162c2863a4e548e8ac2d442","abstract_canon_sha256":"bca8064ef5895d50ef988b644013477152a133cd725b3cc165b2ed430c09d3dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:17.593822Z","signature_b64":"zIIKzmFvRYij7fiQFPjF/0uZfyTftgpAyTFW3TyzEdbqZlhzH5isKefJrZyZYsbRm4ATrT+dDsuAl+78G0QFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28148eeb0ee47c622f57c04aa03d451c686c68f69fa233e7b6dc4fc31c4241c9","last_reissued_at":"2026-05-18T04:39:17.591414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:17.591414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special symplectic Lie groups and hypersymplectic Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.QA","math.SG"],"primary_cat":"math-ph","authors_text":"Chengming Bai, Xiang Ni","submitted_at":"2010-10-15T13:32:24Z","abstract_excerpt":"A special symplectic Lie group is a triple $(G,\\omega,\\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\\nabla$. In this paper starting from a special symplectic Lie group we show how to ``deform\" the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure $\\nabla$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3160","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":"1010.3160","created_at":"2026-05-18T04:39:17.591569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.3160v1","created_at":"2026-05-18T04:39:17.591569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3160","created_at":"2026-05-18T04:39:17.591569+00:00"},{"alias_kind":"pith_short_12","alias_value":"FAKI52YO4R6G","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"FAKI52YO4R6GEL2X","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"FAKI52YO","created_at":"2026-05-18T12:26:06.534383+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/FAKI52YO4R6GEL2XYBFKAPKFDR","json":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR.json","graph_json":"https://pith.science/api/pith-number/FAKI52YO4R6GEL2XYBFKAPKFDR/graph.json","events_json":"https://pith.science/api/pith-number/FAKI52YO4R6GEL2XYBFKAPKFDR/events.json","paper":"https://pith.science/paper/FAKI52YO"},"agent_actions":{"view_html":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR","download_json":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR.json","view_paper":"https://pith.science/paper/FAKI52YO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.3160&json=true","fetch_graph":"https://pith.science/api/pith-number/FAKI52YO4R6GEL2XYBFKAPKFDR/graph.json","fetch_events":"https://pith.science/api/pith-number/FAKI52YO4R6GEL2XYBFKAPKFDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR/action/storage_attestation","attest_author":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR/action/author_attestation","sign_citation":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR/action/citation_signature","submit_replication":"https://pith.science/pith/FAKI52YO4R6GEL2XYBFKAPKFDR/action/replication_record"}},"created_at":"2026-05-18T04:39:17.591569+00:00","updated_at":"2026-05-18T04:39:17.591569+00:00"}