{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RE4IHFNSNW723QHIOJU3JTGXZ4","short_pith_number":"pith:RE4IHFNS","canonical_record":{"source":{"id":"1311.1431","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T16:12:45Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"bd7801df98bf9744fc3165f4694787f67a63daddb5d82bf76fae4809a70c0c2c","abstract_canon_sha256":"b371a06573ae00a73601b6137584da17b748b828b3db9dc39b54462244558d32"},"schema_version":"1.0"},"canonical_sha256":"89388395b26dbfadc0e87269b4ccd7cf2c8ba0a4361f898b850e76c01a983021","source":{"kind":"arxiv","id":"1311.1431","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1431","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1431v4","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1431","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"pith_short_12","alias_value":"RE4IHFNSNW72","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RE4IHFNSNW723QHI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RE4IHFNS","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RE4IHFNSNW723QHIOJU3JTGXZ4","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1431","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T16:12:45Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"bd7801df98bf9744fc3165f4694787f67a63daddb5d82bf76fae4809a70c0c2c","abstract_canon_sha256":"b371a06573ae00a73601b6137584da17b748b828b3db9dc39b54462244558d32"},"schema_version":"1.0"},"canonical_sha256":"89388395b26dbfadc0e87269b4ccd7cf2c8ba0a4361f898b850e76c01a983021","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.844337Z","signature_b64":"WYBOnUOQQZPuKV64eAHqj4MaqYASXgRmUfk7l1DjZXIdv8J9ks8xG+QONQOTquIEsSpp23iAfUSiYNOlSpy8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89388395b26dbfadc0e87269b4ccd7cf2c8ba0a4361f898b850e76c01a983021","last_reissued_at":"2026-05-18T01:06:24.843847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.843847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1431","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKMCNfRoFmzRtdduy34e69rhf+3y5DFnWW85sZaNGMCUNQ1drqzvppmPZwXlX+q4hu7hIIcyVclsxoBQ0HfkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:52:45.049678Z"},"content_sha256":"9ed5e8c90c18060d183c4843286ecc881eb1b82ca45495c5200914338977f9d3","schema_version":"1.0","event_id":"sha256:9ed5e8c90c18060d183c4843286ecc881eb1b82ca45495c5200914338977f9d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RE4IHFNSNW723QHIOJU3JTGXZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lefschetz contact manifolds and odd dimensional symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Yi Lin","submitted_at":"2013-11-06T16:12:45Z","abstract_excerpt":"In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for a compact $K$-contact manifold, which implies immediatel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1431","kind":"arxiv","version":4},"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":"2026-05-18T01:06:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOH126mOxNUyShvhRS3Wv0knPTZNQNxO+Rb5kOVtsPsu/rdT9C2M4gONTK5o0/YqSc3cC0LxnChto9iVWZC9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:52:45.050029Z"},"content_sha256":"75a78341a03576b60db7cd492a49d0e07f181e5db73216295a11a16899003e6f","schema_version":"1.0","event_id":"sha256:75a78341a03576b60db7cd492a49d0e07f181e5db73216295a11a16899003e6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/bundle.json","state_url":"https://pith.science/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/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":"2026-05-30T21:52:45Z","links":{"resolver":"https://pith.science/pith/RE4IHFNSNW723QHIOJU3JTGXZ4","bundle":"https://pith.science/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/bundle.json","state":"https://pith.science/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RE4IHFNSNW723QHIOJU3JTGXZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RE4IHFNSNW723QHIOJU3JTGXZ4","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":"b371a06573ae00a73601b6137584da17b748b828b3db9dc39b54462244558d32","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T16:12:45Z","title_canon_sha256":"bd7801df98bf9744fc3165f4694787f67a63daddb5d82bf76fae4809a70c0c2c"},"schema_version":"1.0","source":{"id":"1311.1431","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1431","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1431v4","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1431","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"pith_short_12","alias_value":"RE4IHFNSNW72","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RE4IHFNSNW723QHI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RE4IHFNS","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:75a78341a03576b60db7cd492a49d0e07f181e5db73216295a11a16899003e6f","target":"graph","created_at":"2026-05-18T01:06:24Z","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":"In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for a compact $K$-contact manifold, which implies immediatel","authors_text":"Yi Lin","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T16:12:45Z","title":"Lefschetz contact manifolds and odd dimensional symplectic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1431","kind":"arxiv","version":4},"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":"sha256:9ed5e8c90c18060d183c4843286ecc881eb1b82ca45495c5200914338977f9d3","target":"record","created_at":"2026-05-18T01:06:24Z","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":"b371a06573ae00a73601b6137584da17b748b828b3db9dc39b54462244558d32","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T16:12:45Z","title_canon_sha256":"bd7801df98bf9744fc3165f4694787f67a63daddb5d82bf76fae4809a70c0c2c"},"schema_version":"1.0","source":{"id":"1311.1431","kind":"arxiv","version":4}},"canonical_sha256":"89388395b26dbfadc0e87269b4ccd7cf2c8ba0a4361f898b850e76c01a983021","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89388395b26dbfadc0e87269b4ccd7cf2c8ba0a4361f898b850e76c01a983021","first_computed_at":"2026-05-18T01:06:24.843847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:24.843847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYBOnUOQQZPuKV64eAHqj4MaqYASXgRmUfk7l1DjZXIdv8J9ks8xG+QONQOTquIEsSpp23iAfUSiYNOlSpy8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:24.844337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1431","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed5e8c90c18060d183c4843286ecc881eb1b82ca45495c5200914338977f9d3","sha256:75a78341a03576b60db7cd492a49d0e07f181e5db73216295a11a16899003e6f"],"state_sha256":"394b3561d73bca836ae4eb1855036f16d547fff069629d30ecb31a60a304478f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ng0Tqv13jGeUWml5M5yx08I1ZIk7tL0PTzdVHeobFU5x40VBISrL1sunARaHThJHkwkZOgWwIr6Zi31Wt+ksCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:52:45.053714Z","bundle_sha256":"baf8d0e488ec3d3ddb6e721f847baf04f11796868d3725cbb80f0cce1fdbe1c0"}}