{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:JYRMPS3MW7YKWS7U2ZUMKDLQNV","short_pith_number":"pith:JYRMPS3M","schema_version":"1.0","canonical_sha256":"4e22c7cb6cb7f0ab4bf4d668c50d706d603c76af5e33ac904e6e81e44748241c","source":{"kind":"arxiv","id":"math/0509393","version":2},"attestation_state":"computed","paper":{"title":"Reduction of Generalized Complex Structures","license":"","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.DG","authors_text":"Mathieu Stienon, Ping Xu","submitted_at":"2005-09-18T01:35:00Z","abstract_excerpt":"We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. Under what condition does $J$ descend to a generalized complex structure on $M_G$? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the r"},"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":"math/0509393","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-09-18T01:35:00Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"39fcdf47c719b5a2740d324b9dd360f8f79b2748dd47098665581413f666f9cc","abstract_canon_sha256":"b166ebe405b4919afd494595ee0fe29bc1296e2363920f1d07b333e9b679e58b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:25.203131Z","signature_b64":"shLbk3nwh5g337IEUeZ2JtoNHN0rqIGjSDNnVczp4HoSSMRA+4SomRUxvlWcY5EaDRfggjmhEKnqyo2iy3+lBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e22c7cb6cb7f0ab4bf4d668c50d706d603c76af5e33ac904e6e81e44748241c","last_reissued_at":"2026-05-18T03:58:25.202398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:25.202398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduction of Generalized Complex Structures","license":"","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.DG","authors_text":"Mathieu Stienon, Ping Xu","submitted_at":"2005-09-18T01:35:00Z","abstract_excerpt":"We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. Under what condition does $J$ descend to a generalized complex structure on $M_G$? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509393","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":"math/0509393","created_at":"2026-05-18T03:58:25.202519+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0509393v2","created_at":"2026-05-18T03:58:25.202519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509393","created_at":"2026-05-18T03:58:25.202519+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYRMPS3MW7YK","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYRMPS3MW7YKWS7U","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYRMPS3M","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.10819","citing_title":"Generalised Complex and Spinor Relations","ref_index":46,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV","json":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV.json","graph_json":"https://pith.science/api/pith-number/JYRMPS3MW7YKWS7U2ZUMKDLQNV/graph.json","events_json":"https://pith.science/api/pith-number/JYRMPS3MW7YKWS7U2ZUMKDLQNV/events.json","paper":"https://pith.science/paper/JYRMPS3M"},"agent_actions":{"view_html":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV","download_json":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV.json","view_paper":"https://pith.science/paper/JYRMPS3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0509393&json=true","fetch_graph":"https://pith.science/api/pith-number/JYRMPS3MW7YKWS7U2ZUMKDLQNV/graph.json","fetch_events":"https://pith.science/api/pith-number/JYRMPS3MW7YKWS7U2ZUMKDLQNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV/action/storage_attestation","attest_author":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV/action/author_attestation","sign_citation":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV/action/citation_signature","submit_replication":"https://pith.science/pith/JYRMPS3MW7YKWS7U2ZUMKDLQNV/action/replication_record"}},"created_at":"2026-05-18T03:58:25.202519+00:00","updated_at":"2026-05-18T03:58:25.202519+00:00"}