{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4HUYRNULJ2426NI6ED4EFMR5WZ","short_pith_number":"pith:4HUYRNUL","canonical_record":{"source":{"id":"1606.08934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T02:21:12Z","cross_cats_sorted":[],"title_canon_sha256":"5aa42d9bcfefa6526d45629f1fb8b26c2319b2d3c4e50f86a5e4345ded717cce","abstract_canon_sha256":"fe2918cecca03d6381d5c4962e9c1678b9280c6e76fccf599ad3699e86460d71"},"schema_version":"1.0"},"canonical_sha256":"e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9","source":{"kind":"arxiv","id":"1606.08934","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4HUYRNULJ2426NI6ED4EFMR5WZ","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T02:21:12Z","cross_cats_sorted":[],"title_canon_sha256":"5aa42d9bcfefa6526d45629f1fb8b26c2319b2d3c4e50f86a5e4345ded717cce","abstract_canon_sha256":"fe2918cecca03d6381d5c4962e9c1678b9280c6e76fccf599ad3699e86460d71"},"schema_version":"1.0"},"canonical_sha256":"e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:42.041743Z","signature_b64":"a754p8cdEMKEPkBLSMpBC60YMMn7qDOWBJco/261h0O2zqMn+JPEOrcCn/i/lWdUdrAtww8CAzhrNCMba0FdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9","last_reissued_at":"2026-05-18T01:11:42.041405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:42.041405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08934","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FkJha8k0dut4b0XjtKzHadxMC3KFkYBaQyfxoGPSxliumVNh0OvdzorfFDgdvdkWUUfiToKuGF+y2xWD2RzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:07:12.359709Z"},"content_sha256":"442d8b9b2c6a632b1453621758ffd255f2a288e70359f5d187ce4e8adcc04dcc","schema_version":"1.0","event_id":"sha256:442d8b9b2c6a632b1453621758ffd255f2a288e70359f5d187ce4e8adcc04dcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4HUYRNULJ2426NI6ED4EFMR5WZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Huili Liu, Seoung Dal Jung","submitted_at":"2016-06-29T02:21:12Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08934","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mX6YWN8tjSGII1Shv3BXjw7VyvkKBh52LlKTRNnDCkSlOb/JzP2t4+c/llx7deH3lQsMEKJtezbLdj0vtGi0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:07:12.360042Z"},"content_sha256":"696ca10effa69600fbdb4589d6f8979042893183cab41e1634d9123dc22bfc82","schema_version":"1.0","event_id":"sha256:696ca10effa69600fbdb4589d6f8979042893183cab41e1634d9123dc22bfc82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/bundle.json","state_url":"https://pith.science/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T00:07:12Z","links":{"resolver":"https://pith.science/pith/4HUYRNULJ2426NI6ED4EFMR5WZ","bundle":"https://pith.science/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/bundle.json","state":"https://pith.science/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HUYRNULJ2426NI6ED4EFMR5WZ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uHK1RdV15Dlctf66bz1qkP8ppJe6U9NHUncHwDQ+WkdMVWx6TNu8MVSH6awHkiT/0ND2yjj4uDsflfIQU9IQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:07:12.362190Z","bundle_sha256":"26b5efba49ab3db0343a9405f4041187f75ae657ffacb151ea039f4b715638d3"}}