{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NBDIXXIMIAIV2DWUCKHIVNTSLZ","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":"818076ec3db6c3b284d1d7cce4a16c42474394149665f6be4dba8168475ca6bb","cross_cats_sorted":["math.AG","math.AT","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-29T09:47:33Z","title_canon_sha256":"e9394b46661d079fef88570e82702b8c32ca05820553b72dfc302e4824543f46"},"schema_version":"1.0","source":{"id":"1811.12038","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12038","created_at":"2026-07-05T05:40:40Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12038v3","created_at":"2026-07-05T05:40:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12038","created_at":"2026-07-05T05:40:40Z"},{"alias_kind":"pith_short_12","alias_value":"NBDIXXIMIAIV","created_at":"2026-07-05T05:40:40Z"},{"alias_kind":"pith_short_16","alias_value":"NBDIXXIMIAIV2DWU","created_at":"2026-07-05T05:40:40Z"},{"alias_kind":"pith_short_8","alias_value":"NBDIXXIM","created_at":"2026-07-05T05:40:40Z"}],"graph_snapshots":[{"event_id":"sha256:fa38f9b9b60df3fc221be0269ddf9768e18d13cb5ee2159eb96bf8a39b1a1968","target":"graph","created_at":"2026-07-05T05:40:40Z","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/1811.12038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe the basic cohomology ring of the canonical holomorphic foliation on a moment-angle manifold, LVMB-manifold or any complex manifold with a maximal holomorphic torus action. Namely, we show that the basic cohomology has a description similar to the cohomology ring of a complete simplicial toric variety due to Danilov and Jurkiewicz. This settles a question of Battaglia and Zaffran, who previously computed the basic Betti numbers for the canonical holomorphic foliation in the case of a shellable fan. Our proof uses an Eilenberg-Moore spectral sequence argument; the key ingredient is t","authors_text":"Hiroaki Ishida, Roman Krutowski, Taras Panov","cross_cats":["math.AG","math.AT","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-29T09:47:33Z","title":"Basic cohomology of canonical holomorphic foliations on complex moment-angle manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12038","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":"sha256:76b90a55b1a73c397d8999742c58899289438ae01cd50fffbe7ca2be1753baca","target":"record","created_at":"2026-07-05T05:40:40Z","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":"818076ec3db6c3b284d1d7cce4a16c42474394149665f6be4dba8168475ca6bb","cross_cats_sorted":["math.AG","math.AT","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-29T09:47:33Z","title_canon_sha256":"e9394b46661d079fef88570e82702b8c32ca05820553b72dfc302e4824543f46"},"schema_version":"1.0","source":{"id":"1811.12038","kind":"arxiv","version":3}},"canonical_sha256":"68468bdd0c40115d0ed4128e8ab6725e546bcde478b7ba4adcee62db62e19c4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68468bdd0c40115d0ed4128e8ab6725e546bcde478b7ba4adcee62db62e19c4d","first_computed_at":"2026-07-05T05:40:40.522425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:40:40.522425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tANREMkveI6lfv7yxLQf+DOOiVfi1LC3q8ktIp7PNxTSQsB7ZO4dP0dQY/rVkC55hYnXwfMtBPnGIjhzryaoCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:40:40.522776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12038","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76b90a55b1a73c397d8999742c58899289438ae01cd50fffbe7ca2be1753baca","sha256:fa38f9b9b60df3fc221be0269ddf9768e18d13cb5ee2159eb96bf8a39b1a1968"],"state_sha256":"933339d408c04747473212cc6bc77127568e4e958765b56ebe14332b0fa13792"}