{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WZJ43Z2R4UTJFJZQMGZNZK7TK7","short_pith_number":"pith:WZJ43Z2R","canonical_record":{"source":{"id":"1407.0358","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-01T18:54:20Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"ba3d3189f6946da1893934647f538cebcaae46a2cf69142b5816e04684134cea","abstract_canon_sha256":"04a407da5a17f1eeebc2b05bccfecbe43ceeaabf2c2163de72977f45760cc235"},"schema_version":"1.0"},"canonical_sha256":"b653cde751e52692a73061b2dcabf357f93a49b978da5735fe43abb77acbe1f9","source":{"kind":"arxiv","id":"1407.0358","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0358","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0358v3","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0358","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"WZJ43Z2R4UTJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WZJ43Z2R4UTJFJZQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WZJ43Z2R","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WZJ43Z2R4UTJFJZQMGZNZK7TK7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0358","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-01T18:54:20Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"ba3d3189f6946da1893934647f538cebcaae46a2cf69142b5816e04684134cea","abstract_canon_sha256":"04a407da5a17f1eeebc2b05bccfecbe43ceeaabf2c2163de72977f45760cc235"},"schema_version":"1.0"},"canonical_sha256":"b653cde751e52692a73061b2dcabf357f93a49b978da5735fe43abb77acbe1f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:49.449082Z","signature_b64":"iP3tag9xHZq8QqNd/yr5ZkmQA+n2FXpSY2liqT1dl/x17J07fOnfgHJ0Oj8yk+XG87hdbZ7UN0FY3on9TF7zBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b653cde751e52692a73061b2dcabf357f93a49b978da5735fe43abb77acbe1f9","last_reissued_at":"2026-05-18T01:37:49.448414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:49.448414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0358","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4G0mke4J04J9rwsHIATet8GITB418afaeISj+f/OPGRnxQoE1lb0eqBTQ/smgBDnG4Ufc3X/snfuNsooUgDbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T01:40:04.837972Z"},"content_sha256":"6c7a4173f77e708ad949f7e98e38b7fbe83c6307f1e2d1e52860715d781c8198","schema_version":"1.0","event_id":"sha256:6c7a4173f77e708ad949f7e98e38b7fbe83c6307f1e2d1e52860715d781c8198"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WZJ43Z2R4UTJFJZQMGZNZK7TK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Asma Hassannezhad, Gerasim Kokarev","submitted_at":"2014-07-01T18:54:20Z","abstract_excerpt":"We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues $\\lambda_k$ of conformal sub-Riemannian metrics that are asymptotically sharp as $k\\to +\\infty$. For Sasakian manifolds with a lower Ricci curvature bound, and more generally, for contact metric manifolds conformal to such Sasakian manifolds, we obtain eigenvalue inequalities that can be viewed as versions of the classical results by Korevaar and Buser in Riemannian geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0358","kind":"arxiv","version":3},"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":"2026-05-18T01:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/eK042cwGeeMFupkdxkm0qagogjbSYftb+qHLOaHP8hJhtUvvSkmjoUZSdpgNQuAeARQ7Li4eERve6WXsj6qCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T01:40:04.838308Z"},"content_sha256":"9672157ffdf54cb98b7302901a9c2cd0e36294115535efa219a5385f0ed5f016","schema_version":"1.0","event_id":"sha256:9672157ffdf54cb98b7302901a9c2cd0e36294115535efa219a5385f0ed5f016"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/bundle.json","state_url":"https://pith.science/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/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":"2026-06-28T01:40:04Z","links":{"resolver":"https://pith.science/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7","bundle":"https://pith.science/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/bundle.json","state":"https://pith.science/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZJ43Z2R4UTJFJZQMGZNZK7TK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WZJ43Z2R4UTJFJZQMGZNZK7TK7","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":"04a407da5a17f1eeebc2b05bccfecbe43ceeaabf2c2163de72977f45760cc235","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-01T18:54:20Z","title_canon_sha256":"ba3d3189f6946da1893934647f538cebcaae46a2cf69142b5816e04684134cea"},"schema_version":"1.0","source":{"id":"1407.0358","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0358","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0358v3","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0358","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"WZJ43Z2R4UTJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WZJ43Z2R4UTJFJZQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WZJ43Z2R","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:9672157ffdf54cb98b7302901a9c2cd0e36294115535efa219a5385f0ed5f016","target":"graph","created_at":"2026-05-18T01:37:49Z","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":"We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues $\\lambda_k$ of conformal sub-Riemannian metrics that are asymptotically sharp as $k\\to +\\infty$. For Sasakian manifolds with a lower Ricci curvature bound, and more generally, for contact metric manifolds conformal to such Sasakian manifolds, we obtain eigenvalue inequalities that can be viewed as versions of the classical results by Korevaar and Buser in Riemannian geometry.","authors_text":"Asma Hassannezhad, Gerasim Kokarev","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-01T18:54:20Z","title":"Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0358","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":"sha256:6c7a4173f77e708ad949f7e98e38b7fbe83c6307f1e2d1e52860715d781c8198","target":"record","created_at":"2026-05-18T01:37:49Z","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":"04a407da5a17f1eeebc2b05bccfecbe43ceeaabf2c2163de72977f45760cc235","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-01T18:54:20Z","title_canon_sha256":"ba3d3189f6946da1893934647f538cebcaae46a2cf69142b5816e04684134cea"},"schema_version":"1.0","source":{"id":"1407.0358","kind":"arxiv","version":3}},"canonical_sha256":"b653cde751e52692a73061b2dcabf357f93a49b978da5735fe43abb77acbe1f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b653cde751e52692a73061b2dcabf357f93a49b978da5735fe43abb77acbe1f9","first_computed_at":"2026-05-18T01:37:49.448414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:49.448414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iP3tag9xHZq8QqNd/yr5ZkmQA+n2FXpSY2liqT1dl/x17J07fOnfgHJ0Oj8yk+XG87hdbZ7UN0FY3on9TF7zBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:49.449082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0358","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c7a4173f77e708ad949f7e98e38b7fbe83c6307f1e2d1e52860715d781c8198","sha256:9672157ffdf54cb98b7302901a9c2cd0e36294115535efa219a5385f0ed5f016"],"state_sha256":"725fbd4d37722a55d2ec16e36f38cb06d65395e264749644615d27f9471b891d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKKwyAKT1LAAovsRAzV+/obqn3dA3r50V43oz4Q8J9FchkKxbfd3rbb9pCbK6pkXdhHw8/WVRKySsZQx3atqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T01:40:04.840132Z","bundle_sha256":"de077cf2c315ad7eb00548d7c359fbf5e813e6a294dfc0e9e136c8d2c004181a"}}