{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OCOQB2NH2RNI3BM3OQ56OCRJ7Z","short_pith_number":"pith:OCOQB2NH","canonical_record":{"source":{"id":"1809.08502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-22T23:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"7b668c07583bbbc2b071e7c4b5dfb21b2600d6a008abdb032384272882685d9d","abstract_canon_sha256":"597078b12ae1715a0f62ea8f870a7ba68502a83a2c924650990065ffb729e1e2"},"schema_version":"1.0"},"canonical_sha256":"709d00e9a7d45a8d859b743be70a29fe50f4bd944b666ea222d1c058d8468568","source":{"kind":"arxiv","id":"1809.08502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08502","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08502v1","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08502","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"OCOQB2NH2RNI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OCOQB2NH2RNI3BM3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OCOQB2NH","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OCOQB2NH2RNI3BM3OQ56OCRJ7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-22T23:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"7b668c07583bbbc2b071e7c4b5dfb21b2600d6a008abdb032384272882685d9d","abstract_canon_sha256":"597078b12ae1715a0f62ea8f870a7ba68502a83a2c924650990065ffb729e1e2"},"schema_version":"1.0"},"canonical_sha256":"709d00e9a7d45a8d859b743be70a29fe50f4bd944b666ea222d1c058d8468568","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:04.251453Z","signature_b64":"CJm8QxJ/VTzTVG6wBINpU0o1TvC750BepGTAGTzVVu/lZxESQ4E6ubj6OxX72SxEC86aUvLuwi5Xljbjh3ptCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"709d00e9a7d45a8d859b743be70a29fe50f4bd944b666ea222d1c058d8468568","last_reissued_at":"2026-05-18T00:05:04.250797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:04.250797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08502","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":"2026-05-18T00:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qi+LKUjtxToA3Gyzs3KSCYCRTI8J5j1nVDeSKKG1t1SUdKcfzT5etdraOBqTElDQVViXJGAXgOA8QgRMBRbnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:58:42.868800Z"},"content_sha256":"ad63588edb4ff878f47867ce4ed1785ea1e2c108d72686bad807c1fff484da25","schema_version":"1.0","event_id":"sha256:ad63588edb4ff878f47867ce4ed1785ea1e2c108d72686bad807c1fff484da25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OCOQB2NH2RNI3BM3OQ56OCRJ7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of gradient steady Ricci solitons with linear curvature decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaohua Zhu, Yuxing Deng","submitted_at":"2018-09-22T23:18:18Z","abstract_excerpt":"In this paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional $\\kappa$-noncollpased steady Ricci solitons with nonnegative sectional curvature under the linear curvature decay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08502","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":"2026-05-18T00:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIQksWLnhEjPLJjlwVQ8WQIEEOgjevoD0R1fU3ZI+ZXbEOqUzStGHuH09SmY6euDYnRtaMuAnBqppVOBX15TDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:58:42.869483Z"},"content_sha256":"e594ab54df76815f1a2ed9eb9be06a245cc74d9bd89b0a8d1f37ee6afe9dcd82","schema_version":"1.0","event_id":"sha256:e594ab54df76815f1a2ed9eb9be06a245cc74d9bd89b0a8d1f37ee6afe9dcd82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/bundle.json","state_url":"https://pith.science/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/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":"2026-05-30T03:58:42Z","links":{"resolver":"https://pith.science/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z","bundle":"https://pith.science/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/bundle.json","state":"https://pith.science/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OCOQB2NH2RNI3BM3OQ56OCRJ7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OCOQB2NH2RNI3BM3OQ56OCRJ7Z","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":"597078b12ae1715a0f62ea8f870a7ba68502a83a2c924650990065ffb729e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-22T23:18:18Z","title_canon_sha256":"7b668c07583bbbc2b071e7c4b5dfb21b2600d6a008abdb032384272882685d9d"},"schema_version":"1.0","source":{"id":"1809.08502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08502","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08502v1","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08502","created_at":"2026-05-18T00:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"OCOQB2NH2RNI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OCOQB2NH2RNI3BM3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OCOQB2NH","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:e594ab54df76815f1a2ed9eb9be06a245cc74d9bd89b0a8d1f37ee6afe9dcd82","target":"graph","created_at":"2026-05-18T00:05:04Z","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 paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional $\\kappa$-noncollpased steady Ricci solitons with nonnegative sectional curvature under the linear curvature decay.","authors_text":"Xiaohua Zhu, Yuxing Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-22T23:18:18Z","title":"Classification of gradient steady Ricci solitons with linear curvature decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08502","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:ad63588edb4ff878f47867ce4ed1785ea1e2c108d72686bad807c1fff484da25","target":"record","created_at":"2026-05-18T00:05:04Z","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":"597078b12ae1715a0f62ea8f870a7ba68502a83a2c924650990065ffb729e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-22T23:18:18Z","title_canon_sha256":"7b668c07583bbbc2b071e7c4b5dfb21b2600d6a008abdb032384272882685d9d"},"schema_version":"1.0","source":{"id":"1809.08502","kind":"arxiv","version":1}},"canonical_sha256":"709d00e9a7d45a8d859b743be70a29fe50f4bd944b666ea222d1c058d8468568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"709d00e9a7d45a8d859b743be70a29fe50f4bd944b666ea222d1c058d8468568","first_computed_at":"2026-05-18T00:05:04.250797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:04.250797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CJm8QxJ/VTzTVG6wBINpU0o1TvC750BepGTAGTzVVu/lZxESQ4E6ubj6OxX72SxEC86aUvLuwi5Xljbjh3ptCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:04.251453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad63588edb4ff878f47867ce4ed1785ea1e2c108d72686bad807c1fff484da25","sha256:e594ab54df76815f1a2ed9eb9be06a245cc74d9bd89b0a8d1f37ee6afe9dcd82"],"state_sha256":"dabecfbaf0189d6029a0bd7e520a6c0c12b4ed8d39720559964f97f5b741a9ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbLkqP5RRUQuy1Xnf98DTYt65xLm299mXWZHWlV/mvu4cykSRewiO4uh5jQ0j0wRzaxLx7LCuu40b8CVwFWCCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:58:42.873116Z","bundle_sha256":"f398da11643679bd2e9ac1a953b9f5005d3b44d292c00b9e000314104b996a54"}}