{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4HUYRNULJ2426NI6ED4EFMR5WZ","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":"fe2918cecca03d6381d5c4962e9c1678b9280c6e76fccf599ad3699e86460d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T02:21:12Z","title_canon_sha256":"5aa42d9bcfefa6526d45629f1fb8b26c2319b2d3c4e50f86a5e4345ded717cce"},"schema_version":"1.0","source":{"id":"1606.08934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08934","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08934v1","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08934","created_at":"2026-05-18T01:11:42Z"},{"alias_kind":"pith_short_12","alias_value":"4HUYRNULJ242","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HUYRNULJ2426NI6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HUYRNUL","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:696ca10effa69600fbdb4589d6f8979042893183cab41e1634d9123dc22bfc82","target":"graph","created_at":"2026-05-18T01:11:42Z","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":"On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete foliated Riemannian manifold.","authors_text":"Huili Liu, Seoung Dal Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T02:21:12Z","title":"Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08934","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":"sha256:442d8b9b2c6a632b1453621758ffd255f2a288e70359f5d187ce4e8adcc04dcc","target":"record","created_at":"2026-05-18T01:11:42Z","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":"fe2918cecca03d6381d5c4962e9c1678b9280c6e76fccf599ad3699e86460d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T02:21:12Z","title_canon_sha256":"5aa42d9bcfefa6526d45629f1fb8b26c2319b2d3c4e50f86a5e4345ded717cce"},"schema_version":"1.0","source":{"id":"1606.08934","kind":"arxiv","version":1}},"canonical_sha256":"e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9","first_computed_at":"2026-05-18T01:11:42.041405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:42.041405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a754p8cdEMKEPkBLSMpBC60YMMn7qDOWBJco/261h0O2zqMn+JPEOrcCn/i/lWdUdrAtww8CAzhrNCMba0FdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:42.041743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:442d8b9b2c6a632b1453621758ffd255f2a288e70359f5d187ce4e8adcc04dcc","sha256:696ca10effa69600fbdb4589d6f8979042893183cab41e1634d9123dc22bfc82"],"state_sha256":"78d329ce7faeb93a0f429ae39a6662e52ee4ff52573367d0cba92d71d5e0b71a"}