{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WUBO452RUNN4KWNAHOXDQTH2SR","short_pith_number":"pith:WUBO452R","schema_version":"1.0","canonical_sha256":"b502ee7751a35bc559a03bae384cfa947292b996173e3837a7ee7ea5e0559a72","source":{"kind":"arxiv","id":"1407.3526","version":2},"attestation_state":"computed","paper":{"title":"The Morse-Bott-Kirwan condition is local","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Tara Holm, Yael Karshon","submitted_at":"2014-07-14T01:56:04Z","abstract_excerpt":"Kirwan identified a condition on a smooth function under which the usual techniques of Morse-Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it also satisfies the condition globally. As an application, we use the local normal form theorem to recover Kirwan's result that the norm-square of a momentum map satisfies Kirwan's condition."},"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":"1407.3526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-07-14T01:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"fb1114f785e3511e4527dae7c2ed32691a9a31f23bb2e80593cf56d97ee79303","abstract_canon_sha256":"3d9b72c532eb44738026d971657927821dfae6db2f919a89f8a3398824470684"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:49.550806Z","signature_b64":"BFXPYcdYxLQ/PlcdkKkjkvtmGu7JhfrhLGXwZUo8Fco35zpSFAbz/G/dK/AxkvkzLyR7HyxMf1MNCtd5s0VkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b502ee7751a35bc559a03bae384cfa947292b996173e3837a7ee7ea5e0559a72","last_reissued_at":"2026-05-18T00:59:49.550111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:49.550111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Morse-Bott-Kirwan condition is local","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Tara Holm, Yael Karshon","submitted_at":"2014-07-14T01:56:04Z","abstract_excerpt":"Kirwan identified a condition on a smooth function under which the usual techniques of Morse-Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it also satisfies the condition globally. As an application, we use the local normal form theorem to recover Kirwan's result that the norm-square of a momentum map satisfies Kirwan's condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3526","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":"1407.3526","created_at":"2026-05-18T00:59:49.550235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3526v2","created_at":"2026-05-18T00:59:49.550235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3526","created_at":"2026-05-18T00:59:49.550235+00:00"},{"alias_kind":"pith_short_12","alias_value":"WUBO452RUNN4","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WUBO452RUNN4KWNA","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WUBO452R","created_at":"2026-05-18T12:28:54.890064+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/WUBO452RUNN4KWNAHOXDQTH2SR","json":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR.json","graph_json":"https://pith.science/api/pith-number/WUBO452RUNN4KWNAHOXDQTH2SR/graph.json","events_json":"https://pith.science/api/pith-number/WUBO452RUNN4KWNAHOXDQTH2SR/events.json","paper":"https://pith.science/paper/WUBO452R"},"agent_actions":{"view_html":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR","download_json":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR.json","view_paper":"https://pith.science/paper/WUBO452R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3526&json=true","fetch_graph":"https://pith.science/api/pith-number/WUBO452RUNN4KWNAHOXDQTH2SR/graph.json","fetch_events":"https://pith.science/api/pith-number/WUBO452RUNN4KWNAHOXDQTH2SR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR/action/storage_attestation","attest_author":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR/action/author_attestation","sign_citation":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR/action/citation_signature","submit_replication":"https://pith.science/pith/WUBO452RUNN4KWNAHOXDQTH2SR/action/replication_record"}},"created_at":"2026-05-18T00:59:49.550235+00:00","updated_at":"2026-05-18T00:59:49.550235+00:00"}