{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JJGNLAYT6IKFBZORCLAGPUIWXH","short_pith_number":"pith:JJGNLAYT","schema_version":"1.0","canonical_sha256":"4a4cd58313f21450e5d112c067d116b9c3a9452a9d5ac9804abbeff74111b99f","source":{"kind":"arxiv","id":"1105.5814","version":2},"attestation_state":"computed","paper":{"title":"The Action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.SG","authors_text":"Egor Shelukhin","submitted_at":"2011-05-29T19:18:32Z","abstract_excerpt":"We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound on the symplectic areas of geodesic triangles the resulting homomorphism extends to a quasimorphism on the universal cover of the group. We apply these principles to finite dimensional Hermitian Lie groups like Sp(2n,R), reinterpreting the Guichardet-Wigner quasimorphisms, and to the infinite dimensional groups of Hamiltonian diffeomorphisms Ham(M,\\om) of cl"},"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":"1105.5814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-05-29T19:18:32Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"8470c6f5249aee376dab02e3e15fd9325509888433c65b664affaef929334719","abstract_canon_sha256":"ed198bd6aa2a9a0636910f557e2dee818b62c99f06978d49a05d7024bc5a1216"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:51.083938Z","signature_b64":"O0N8MvWXfsFK5vDtjTUriW+8ac5Q9YVQXkSlw6lRHcKeKUC0vG3GfPn9d9ZPi59EV0wTWJz8YjYK9zFzBBmHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a4cd58313f21450e5d112c067d116b9c3a9452a9d5ac9804abbeff74111b99f","last_reissued_at":"2026-05-18T04:01:51.083285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:51.083285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.SG","authors_text":"Egor Shelukhin","submitted_at":"2011-05-29T19:18:32Z","abstract_excerpt":"We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound on the symplectic areas of geodesic triangles the resulting homomorphism extends to a quasimorphism on the universal cover of the group. We apply these principles to finite dimensional Hermitian Lie groups like Sp(2n,R), reinterpreting the Guichardet-Wigner quasimorphisms, and to the infinite dimensional groups of Hamiltonian diffeomorphisms Ham(M,\\om) of cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5814","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":"1105.5814","created_at":"2026-05-18T04:01:51.083363+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.5814v2","created_at":"2026-05-18T04:01:51.083363+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5814","created_at":"2026-05-18T04:01:51.083363+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJGNLAYT6IKF","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJGNLAYT6IKFBZOR","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJGNLAYT","created_at":"2026-05-18T12:26:32.869790+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/JJGNLAYT6IKFBZORCLAGPUIWXH","json":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH.json","graph_json":"https://pith.science/api/pith-number/JJGNLAYT6IKFBZORCLAGPUIWXH/graph.json","events_json":"https://pith.science/api/pith-number/JJGNLAYT6IKFBZORCLAGPUIWXH/events.json","paper":"https://pith.science/paper/JJGNLAYT"},"agent_actions":{"view_html":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH","download_json":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH.json","view_paper":"https://pith.science/paper/JJGNLAYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.5814&json=true","fetch_graph":"https://pith.science/api/pith-number/JJGNLAYT6IKFBZORCLAGPUIWXH/graph.json","fetch_events":"https://pith.science/api/pith-number/JJGNLAYT6IKFBZORCLAGPUIWXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH/action/storage_attestation","attest_author":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH/action/author_attestation","sign_citation":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH/action/citation_signature","submit_replication":"https://pith.science/pith/JJGNLAYT6IKFBZORCLAGPUIWXH/action/replication_record"}},"created_at":"2026-05-18T04:01:51.083363+00:00","updated_at":"2026-05-18T04:01:51.083363+00:00"}