{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:K3C3GGAQ2ZJUXL3MQVEFPXI7XW","short_pith_number":"pith:K3C3GGAQ","schema_version":"1.0","canonical_sha256":"56c5b31810d6534baf6c854857dd1fbda178b1a17e87ea6ff3ef22931f2ec4f1","source":{"kind":"arxiv","id":"1310.8405","version":2},"attestation_state":"computed","paper":{"title":"Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Min Kyu Kim, Yunhyung Cho","submitted_at":"2013-10-31T06:57:46Z","abstract_excerpt":"In this paper, we study the hard Lefschetz property of a symplectic manifold which admits a Hamiltonian torus action. More precisely, let $(M,\\omega)$ be a 6-dimensional compact symplectic manifold with a Hamiltonian $T^2$-action. We will show that if the moment map image of $M$ is a GKM-graph and if the graph is index-increasing, then $(M,\\omega)$ satisfies the hard Lefschetz property."},"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":"1310.8405","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-10-31T06:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"d54328c6bec17af5caf610f6ef3c0583c87ead0b16110cd313002fd5cb571987","abstract_canon_sha256":"05566008db7e4e3c96f8f25434b1ccd4d622310f790d8b6e4b5d0a9227378737"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:35.400928Z","signature_b64":"W2Xgkxn5AefTr9XdoH3/Dpa5IQ6j0NHqti3DTAlsnDyngaOLNuWqX51xMBBPSFLqdt9G36sgH3yWEjbLHlLNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56c5b31810d6534baf6c854857dd1fbda178b1a17e87ea6ff3ef22931f2ec4f1","last_reissued_at":"2026-05-17T23:57:35.400422Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:35.400422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Min Kyu Kim, Yunhyung Cho","submitted_at":"2013-10-31T06:57:46Z","abstract_excerpt":"In this paper, we study the hard Lefschetz property of a symplectic manifold which admits a Hamiltonian torus action. More precisely, let $(M,\\omega)$ be a 6-dimensional compact symplectic manifold with a Hamiltonian $T^2$-action. We will show that if the moment map image of $M$ is a GKM-graph and if the graph is index-increasing, then $(M,\\omega)$ satisfies the hard Lefschetz property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8405","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":"1310.8405","created_at":"2026-05-17T23:57:35.400501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8405v2","created_at":"2026-05-17T23:57:35.400501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8405","created_at":"2026-05-17T23:57:35.400501+00:00"},{"alias_kind":"pith_short_12","alias_value":"K3C3GGAQ2ZJU","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"K3C3GGAQ2ZJUXL3M","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"K3C3GGAQ","created_at":"2026-05-18T12:27:49.015174+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/K3C3GGAQ2ZJUXL3MQVEFPXI7XW","json":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW.json","graph_json":"https://pith.science/api/pith-number/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/graph.json","events_json":"https://pith.science/api/pith-number/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/events.json","paper":"https://pith.science/paper/K3C3GGAQ"},"agent_actions":{"view_html":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW","download_json":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW.json","view_paper":"https://pith.science/paper/K3C3GGAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8405&json=true","fetch_graph":"https://pith.science/api/pith-number/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/graph.json","fetch_events":"https://pith.science/api/pith-number/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/action/storage_attestation","attest_author":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/action/author_attestation","sign_citation":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/action/citation_signature","submit_replication":"https://pith.science/pith/K3C3GGAQ2ZJUXL3MQVEFPXI7XW/action/replication_record"}},"created_at":"2026-05-17T23:57:35.400501+00:00","updated_at":"2026-05-17T23:57:35.400501+00:00"}