{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2IZJ7NBCJAH4TKD3VJ2JJDR25V","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":"52be4c466798cbdaf6270a0a3cd5e9224c94557664cb909177166402d92249cc","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-02-17T02:07:53Z","title_canon_sha256":"de6a8e362baaeb2bf5911257e7f37efca8bc7c9ae88a0c817a3263cef6aa393c"},"schema_version":"1.0","source":{"id":"1902.06187","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06187","created_at":"2026-07-05T04:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06187v3","created_at":"2026-07-05T04:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06187","created_at":"2026-07-05T04:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"2IZJ7NBCJAH4","created_at":"2026-07-05T04:43:55Z"},{"alias_kind":"pith_short_16","alias_value":"2IZJ7NBCJAH4TKD3","created_at":"2026-07-05T04:43:55Z"},{"alias_kind":"pith_short_8","alias_value":"2IZJ7NBC","created_at":"2026-07-05T04:43:55Z"}],"graph_snapshots":[{"event_id":"sha256:f1176f6e0e0b14be8472fee0eb4b5030512025b7bf578bc89347a567cf4adafa","target":"graph","created_at":"2026-07-05T04:43:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.06187/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider the Hamiltonian action of a torus on a transversely symplectic foliation that is also Riemannian. When the transverse hard Lefschetz property is satisfied, we establish a foliated version of the Kirwan injectivity theorem, and use it to study Hamiltonian torus actions on transversely K\\\"ahler foliations. Among other things, we prove a foliated analogue of the Carrell--Liberman theorem. As an application, this confirms a conjecture raised by Battaglia--Zaffran on the basic Hodge numbers of symplectic toric quasifolds. Our methods also allow us to present a symplectic approach to the ca","authors_text":"Xiangdong Yang, Yi Lin","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-02-17T02:07:53Z","title":"Basic Kirwan injectivity and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06187","kind":"arxiv","version":3},"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:c39922b4d6fe1bb377dc654730485ab6a7df86048265741f0badbd273b21530d","target":"record","created_at":"2026-07-05T04:43:55Z","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":"52be4c466798cbdaf6270a0a3cd5e9224c94557664cb909177166402d92249cc","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-02-17T02:07:53Z","title_canon_sha256":"de6a8e362baaeb2bf5911257e7f37efca8bc7c9ae88a0c817a3263cef6aa393c"},"schema_version":"1.0","source":{"id":"1902.06187","kind":"arxiv","version":3}},"canonical_sha256":"d2329fb422480fc9a87baa74948e3aed58a3a4963a7fc45e0e2a029f46570b20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2329fb422480fc9a87baa74948e3aed58a3a4963a7fc45e0e2a029f46570b20","first_computed_at":"2026-07-05T04:43:55.532490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:55.532490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sWLMuagOoax2p0E/yDNKEuLHraEYhsZqCpkcKKKm25J2GPGfBTGxxSlDyAwtp5UuORv37CFIBrigtnGoWQEqBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:55.533007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06187","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c39922b4d6fe1bb377dc654730485ab6a7df86048265741f0badbd273b21530d","sha256:f1176f6e0e0b14be8472fee0eb4b5030512025b7bf578bc89347a567cf4adafa"],"state_sha256":"0ef635e5540df9db72384b2c29b48dff74e9d58b414e6d33521d60107112d548"}