{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QNUNHIBOGUCI664HJOXXCRU66O","short_pith_number":"pith:QNUNHIBO","canonical_record":{"source":{"id":"1806.07798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-20T15:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"edeec786c7fb6e9afe22555a7aba3e7c473b60da3ed0b7f77b0e85c0b204fdaa","abstract_canon_sha256":"9c8c6a5b89e6ee458a5cd43a63d9875e288aa5c03ced6441758b47ecc28a3203"},"schema_version":"1.0"},"canonical_sha256":"8368d3a02e35048f7b874baf71469ef3a33b0311ec70c37a9ecc1e26b8435c74","source":{"kind":"arxiv","id":"1806.07798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07798","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07798v1","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07798","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"QNUNHIBOGUCI","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QNUNHIBOGUCI664H","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QNUNHIBO","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QNUNHIBOGUCI664HJOXXCRU66O","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-20T15:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"edeec786c7fb6e9afe22555a7aba3e7c473b60da3ed0b7f77b0e85c0b204fdaa","abstract_canon_sha256":"9c8c6a5b89e6ee458a5cd43a63d9875e288aa5c03ced6441758b47ecc28a3203"},"schema_version":"1.0"},"canonical_sha256":"8368d3a02e35048f7b874baf71469ef3a33b0311ec70c37a9ecc1e26b8435c74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:46.631483Z","signature_b64":"uQE6iGc7uhhx0dsZ7dptOYV8kh5AlN2LV3F35mSgRujAQUCt6bM4x4ov6xBfD+/uWitsyoL06ri9OZ4tmZU7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8368d3a02e35048f7b874baf71469ef3a33b0311ec70c37a9ecc1e26b8435c74","last_reissued_at":"2026-05-18T00:12:46.630825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:46.630825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07798","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":"2026-05-18T00:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3uWrVgW/7kUJPh5kqPs3Ot3w5uxy78fCudMgkjThMS7zgff9EJ+v93920QXZ/d7NYjMIWq3Hcvoj96wwOLkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:08:36.646640Z"},"content_sha256":"0872ff600b18c770415065b5c454e8f7124d9917c9010240de97ec5d739b79cf","schema_version":"1.0","event_id":"sha256:0872ff600b18c770415065b5c454e8f7124d9917c9010240de97ec5d739b79cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QNUNHIBOGUCI664HJOXXCRU66O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brown-York mass and positive scalar curvature I - First eigenvalue problem and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wei Yuan","submitted_at":"2018-06-20T15:38:10Z","abstract_excerpt":"In this article, we investigate the connection between scalar curvature and first eigenfunctions via positive mass theorem for Brown-York mass. For compact manifolds with nice boundary, we show that a sharp inequality holds for first eigenfunctions when posing appropriate assumptions on scalar curvature and first eigenvalue. This inequality implies that for a compact n-dimensional manifold with boundary, its first eigenvalue is no less that n, if its scalar curvature is at least n(n-1) with appropriate boundary conditions posed, where equality holds if and only the manifold is isometric to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07798","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":"2026-05-18T00:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Py6ah4LO/jdiPGPtuszXNwwC7YtuERdmxxmWfDzeWWe/TOFh3yTPTKr7fvM9cuJne8n6k49KC20o+IE7lgdcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:08:36.647003Z"},"content_sha256":"d58b7e483590a2d9e7e17cabfec23455c9b0db58c04ff538e088329f73f2a596","schema_version":"1.0","event_id":"sha256:d58b7e483590a2d9e7e17cabfec23455c9b0db58c04ff538e088329f73f2a596"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNUNHIBOGUCI664HJOXXCRU66O/bundle.json","state_url":"https://pith.science/pith/QNUNHIBOGUCI664HJOXXCRU66O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNUNHIBOGUCI664HJOXXCRU66O/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":"2026-06-01T02:08:36Z","links":{"resolver":"https://pith.science/pith/QNUNHIBOGUCI664HJOXXCRU66O","bundle":"https://pith.science/pith/QNUNHIBOGUCI664HJOXXCRU66O/bundle.json","state":"https://pith.science/pith/QNUNHIBOGUCI664HJOXXCRU66O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNUNHIBOGUCI664HJOXXCRU66O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QNUNHIBOGUCI664HJOXXCRU66O","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":"9c8c6a5b89e6ee458a5cd43a63d9875e288aa5c03ced6441758b47ecc28a3203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-20T15:38:10Z","title_canon_sha256":"edeec786c7fb6e9afe22555a7aba3e7c473b60da3ed0b7f77b0e85c0b204fdaa"},"schema_version":"1.0","source":{"id":"1806.07798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07798","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07798v1","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07798","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"QNUNHIBOGUCI","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QNUNHIBOGUCI664H","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QNUNHIBO","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:d58b7e483590a2d9e7e17cabfec23455c9b0db58c04ff538e088329f73f2a596","target":"graph","created_at":"2026-05-18T00:12:46Z","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 this article, we investigate the connection between scalar curvature and first eigenfunctions via positive mass theorem for Brown-York mass. For compact manifolds with nice boundary, we show that a sharp inequality holds for first eigenfunctions when posing appropriate assumptions on scalar curvature and first eigenvalue. This inequality implies that for a compact n-dimensional manifold with boundary, its first eigenvalue is no less that n, if its scalar curvature is at least n(n-1) with appropriate boundary conditions posed, where equality holds if and only the manifold is isometric to the","authors_text":"Wei Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-20T15:38:10Z","title":"Brown-York mass and positive scalar curvature I - First eigenvalue problem and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07798","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":"sha256:0872ff600b18c770415065b5c454e8f7124d9917c9010240de97ec5d739b79cf","target":"record","created_at":"2026-05-18T00:12:46Z","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":"9c8c6a5b89e6ee458a5cd43a63d9875e288aa5c03ced6441758b47ecc28a3203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-20T15:38:10Z","title_canon_sha256":"edeec786c7fb6e9afe22555a7aba3e7c473b60da3ed0b7f77b0e85c0b204fdaa"},"schema_version":"1.0","source":{"id":"1806.07798","kind":"arxiv","version":1}},"canonical_sha256":"8368d3a02e35048f7b874baf71469ef3a33b0311ec70c37a9ecc1e26b8435c74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8368d3a02e35048f7b874baf71469ef3a33b0311ec70c37a9ecc1e26b8435c74","first_computed_at":"2026-05-18T00:12:46.630825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:46.630825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQE6iGc7uhhx0dsZ7dptOYV8kh5AlN2LV3F35mSgRujAQUCt6bM4x4ov6xBfD+/uWitsyoL06ri9OZ4tmZU7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:46.631483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0872ff600b18c770415065b5c454e8f7124d9917c9010240de97ec5d739b79cf","sha256:d58b7e483590a2d9e7e17cabfec23455c9b0db58c04ff538e088329f73f2a596"],"state_sha256":"53690fabb419cbd302a16f129773bfef3d75e32458a478e2921747d461140ad7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8dxUBTXRtQZFKzSoeM85+FQtdkVgHfy5snyQaEkfxLEYtHzSrx9whz5HCo0040SVSjmAXT0yk/jrFLeUmAGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:08:36.649197Z","bundle_sha256":"9940b5ce9b4e78784c2c9944197a92d5194a7322a8178068304b50f256cbe8da"}}