{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZIJYD63CMSFFHZL5ILGVIEEOVP","short_pith_number":"pith:ZIJYD63C","canonical_record":{"source":{"id":"1109.5239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-24T07:19:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"05cc7d88277dfed904b4fcb08c1004ec8524cd0061d32adc11dba3e7ebdf6d07","abstract_canon_sha256":"d1def02cd9c3656f115ff245e3fcd3c2bf6d01d2238ebc5a6ca2c47cebae66bc"},"schema_version":"1.0"},"canonical_sha256":"ca1381fb62648a53e57d42cd54108eabd307db9214cf8576a24315d7356e9cbd","source":{"kind":"arxiv","id":"1109.5239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5239","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5239v1","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5239","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZIJYD63CMSFF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZIJYD63CMSFFHZL5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZIJYD63C","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZIJYD63CMSFFHZL5ILGVIEEOVP","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-24T07:19:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"05cc7d88277dfed904b4fcb08c1004ec8524cd0061d32adc11dba3e7ebdf6d07","abstract_canon_sha256":"d1def02cd9c3656f115ff245e3fcd3c2bf6d01d2238ebc5a6ca2c47cebae66bc"},"schema_version":"1.0"},"canonical_sha256":"ca1381fb62648a53e57d42cd54108eabd307db9214cf8576a24315d7356e9cbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:20.292218Z","signature_b64":"dQ+2q4oxCQQ63At+dLUMBFmIDbZPYFiywjgZan4v9WTmhk2I5WDG2e6zhfLIn3nygWeQs4WIF3eBeV69LM4WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca1381fb62648a53e57d42cd54108eabd307db9214cf8576a24315d7356e9cbd","last_reissued_at":"2026-05-18T04:12:20.291488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:20.291488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5239","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySdHb0FnjiOQy0korbjuCOyFRK0cc+F2dqLWJ1yoifsoAN2kBjZaU6z/kFP428Tefwzs1Zq8ujK+U9a76iyICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:08:18.663435Z"},"content_sha256":"217a5a3ca72f31260aea1debcfe3211e04eed5b15f853b42b059f9d1a0019bac","schema_version":"1.0","event_id":"sha256:217a5a3ca72f31260aea1debcfe3211e04eed5b15f853b42b059f9d1a0019bac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZIJYD63CMSFFHZL5ILGVIEEOVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Dmitry A. Timashev, Vladimir S. Zhgoon","submitted_at":"2011-09-24T07:19:11Z","abstract_excerpt":"We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5239","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qO4RbfwiWdhFfVeHz/Ibeg8w8ZMH2bzDn+hKATM9+8eUGTyHLVc/jnHSq8uCqUg4/Q9g308pNFzMwjQfXKeJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:08:18.663787Z"},"content_sha256":"dded46fe01f9246738d4df8cf2dd77e35110054043a32416e1a57674f495f758","schema_version":"1.0","event_id":"sha256:dded46fe01f9246738d4df8cf2dd77e35110054043a32416e1a57674f495f758"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/bundle.json","state_url":"https://pith.science/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T20:08:18Z","links":{"resolver":"https://pith.science/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP","bundle":"https://pith.science/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/bundle.json","state":"https://pith.science/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIJYD63CMSFFHZL5ILGVIEEOVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZIJYD63CMSFFHZL5ILGVIEEOVP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d1def02cd9c3656f115ff245e3fcd3c2bf6d01d2238ebc5a6ca2c47cebae66bc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-24T07:19:11Z","title_canon_sha256":"05cc7d88277dfed904b4fcb08c1004ec8524cd0061d32adc11dba3e7ebdf6d07"},"schema_version":"1.0","source":{"id":"1109.5239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5239","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5239v1","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5239","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZIJYD63CMSFF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZIJYD63CMSFFHZL5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZIJYD63C","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:dded46fe01f9246738d4df8cf2dd77e35110054043a32416e1a57674f495f758","target":"graph","created_at":"2026-05-18T04:12:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the cotangent bundle over an invariant Lagrangian subvariety coincide. This implies that the complexity and rank of the Lagrangian subvariety are equal to the half of the corank and to the defect of the Hamiltonian variety, respectively. This result generalizes a theorem of Panyushev on the complexity and rank of a conormal bundle. A simple elementary proof of this theo","authors_text":"Dmitry A. Timashev, Vladimir S. Zhgoon","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-24T07:19:11Z","title":"Hamiltonian actions on symplectic varieties with invariant Lagrangian subvarieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5239","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:217a5a3ca72f31260aea1debcfe3211e04eed5b15f853b42b059f9d1a0019bac","target":"record","created_at":"2026-05-18T04:12:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d1def02cd9c3656f115ff245e3fcd3c2bf6d01d2238ebc5a6ca2c47cebae66bc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-24T07:19:11Z","title_canon_sha256":"05cc7d88277dfed904b4fcb08c1004ec8524cd0061d32adc11dba3e7ebdf6d07"},"schema_version":"1.0","source":{"id":"1109.5239","kind":"arxiv","version":1}},"canonical_sha256":"ca1381fb62648a53e57d42cd54108eabd307db9214cf8576a24315d7356e9cbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca1381fb62648a53e57d42cd54108eabd307db9214cf8576a24315d7356e9cbd","first_computed_at":"2026-05-18T04:12:20.291488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:20.291488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQ+2q4oxCQQ63At+dLUMBFmIDbZPYFiywjgZan4v9WTmhk2I5WDG2e6zhfLIn3nygWeQs4WIF3eBeV69LM4WAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:20.292218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217a5a3ca72f31260aea1debcfe3211e04eed5b15f853b42b059f9d1a0019bac","sha256:dded46fe01f9246738d4df8cf2dd77e35110054043a32416e1a57674f495f758"],"state_sha256":"1d661933daa8d89e35c031faeb3b84e23c2612b62429963a1419dc746216acbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfJCLjFROg/U5ovAcoCZJy0HVoLvCdIPsAo6dy3iDpmJ5RYx4lXOrEENnBOAMiXl9Jf7NleVfAyco5mzf2YkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:08:18.665723Z","bundle_sha256":"fc97066b380c9be5eb42cf90c12322cd6711afdcad46ddfcdf41267d8d8647d7"}}