{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X2KYOXBF2CK77VBXNIQZUNHZGD","short_pith_number":"pith:X2KYOXBF","canonical_record":{"source":{"id":"1709.00143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-01T03:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"898c0844d9009856f77f4616d7ab840cd261aab9f5a475dba0b31c0a4b35d609","abstract_canon_sha256":"5bac8bfe3046eab949aa007dc579d2fbb4faf96ffa41167a5d690b7ed33e83bc"},"schema_version":"1.0"},"canonical_sha256":"be95875c25d095ffd4376a219a34f930c6d7a8f8cf8e26b2dc8efcf5c9960bc0","source":{"kind":"arxiv","id":"1709.00143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00143","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00143v1","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00143","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"X2KYOXBF2CK7","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X2KYOXBF2CK77VBX","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X2KYOXBF","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X2KYOXBF2CK77VBXNIQZUNHZGD","target":"record","payload":{"canonical_record":{"source":{"id":"1709.00143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-01T03:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"898c0844d9009856f77f4616d7ab840cd261aab9f5a475dba0b31c0a4b35d609","abstract_canon_sha256":"5bac8bfe3046eab949aa007dc579d2fbb4faf96ffa41167a5d690b7ed33e83bc"},"schema_version":"1.0"},"canonical_sha256":"be95875c25d095ffd4376a219a34f930c6d7a8f8cf8e26b2dc8efcf5c9960bc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:13.279882Z","signature_b64":"JUVWjiLWgbm00nV+XeHi81fuzECx/3TV/oEUiQ1jpMMt8W+nAp0nvkTQUXOVCBXrTpU9p6hLARn0kORz0sPRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be95875c25d095ffd4376a219a34f930c6d7a8f8cf8e26b2dc8efcf5c9960bc0","last_reissued_at":"2026-05-18T00:36:13.279202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:13.279202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.00143","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":"2026-05-18T00:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"78Y7h0sQxgd0dgxMCeYmmcF6tii8t1R2h+bn8yXhODIocDmawb+qoSeHuqzd1FKNlT0/T3qC9VvRVpeV3LqoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:14:25.222884Z"},"content_sha256":"683b8cc5430b8bc0b89d42cfdee1224ab9b0e81fcf88ff766e1cfbcb5b61afda","schema_version":"1.0","event_id":"sha256:683b8cc5430b8bc0b89d42cfdee1224ab9b0e81fcf88ff766e1cfbcb5b61afda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X2KYOXBF2CK77VBXNIQZUNHZGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level set flow in 3D steady gradient Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chih-Wei Chen, Kuo-Wei Lee","submitted_at":"2017-09-01T03:36:20Z","abstract_excerpt":"Let $(M^3, g, f)$ be a nontrivial 3-dimensional steady gradient Ricci soliton. If the scalar curvature $R$ satisfies $c_1r^{-b}\\leq R\\leq c_2r^{-a}$ for some $a\\in(0,1], b\\geq a$, and $c_1,c_2>0$, then the umbilical ratio of the level sets of $f$ satisfies $\\frac{2|A|^2-H^2}{H^2}\\in O(r^{6a-\\frac{8a^2}{b}})\\cap O(r^{2b-4a})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00143","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":"2026-05-18T00:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuRYvfYv6uPzuKp+WKiQss/0jQ9ODBuJeHFQNCBrSXxEL5Du2q8kX/2iwRRmELjP/jX1CoUyZb39fxBHJvtqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:14:25.223233Z"},"content_sha256":"3c5402e3b80340a4ff1f8f5588e2c1ebfa5e40ff007d2f0d6c2142fdd9054981","schema_version":"1.0","event_id":"sha256:3c5402e3b80340a4ff1f8f5588e2c1ebfa5e40ff007d2f0d6c2142fdd9054981"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/bundle.json","state_url":"https://pith.science/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/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":"2026-06-22T11:14:25Z","links":{"resolver":"https://pith.science/pith/X2KYOXBF2CK77VBXNIQZUNHZGD","bundle":"https://pith.science/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/bundle.json","state":"https://pith.science/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2KYOXBF2CK77VBXNIQZUNHZGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X2KYOXBF2CK77VBXNIQZUNHZGD","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":"5bac8bfe3046eab949aa007dc579d2fbb4faf96ffa41167a5d690b7ed33e83bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-01T03:36:20Z","title_canon_sha256":"898c0844d9009856f77f4616d7ab840cd261aab9f5a475dba0b31c0a4b35d609"},"schema_version":"1.0","source":{"id":"1709.00143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00143","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00143v1","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00143","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"X2KYOXBF2CK7","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X2KYOXBF2CK77VBX","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X2KYOXBF","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:3c5402e3b80340a4ff1f8f5588e2c1ebfa5e40ff007d2f0d6c2142fdd9054981","target":"graph","created_at":"2026-05-18T00:36:13Z","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":"Let $(M^3, g, f)$ be a nontrivial 3-dimensional steady gradient Ricci soliton. If the scalar curvature $R$ satisfies $c_1r^{-b}\\leq R\\leq c_2r^{-a}$ for some $a\\in(0,1], b\\geq a$, and $c_1,c_2>0$, then the umbilical ratio of the level sets of $f$ satisfies $\\frac{2|A|^2-H^2}{H^2}\\in O(r^{6a-\\frac{8a^2}{b}})\\cap O(r^{2b-4a})$.","authors_text":"Chih-Wei Chen, Kuo-Wei Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-01T03:36:20Z","title":"Level set flow in 3D steady gradient Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00143","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":"sha256:683b8cc5430b8bc0b89d42cfdee1224ab9b0e81fcf88ff766e1cfbcb5b61afda","target":"record","created_at":"2026-05-18T00:36:13Z","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":"5bac8bfe3046eab949aa007dc579d2fbb4faf96ffa41167a5d690b7ed33e83bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-01T03:36:20Z","title_canon_sha256":"898c0844d9009856f77f4616d7ab840cd261aab9f5a475dba0b31c0a4b35d609"},"schema_version":"1.0","source":{"id":"1709.00143","kind":"arxiv","version":1}},"canonical_sha256":"be95875c25d095ffd4376a219a34f930c6d7a8f8cf8e26b2dc8efcf5c9960bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be95875c25d095ffd4376a219a34f930c6d7a8f8cf8e26b2dc8efcf5c9960bc0","first_computed_at":"2026-05-18T00:36:13.279202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:13.279202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JUVWjiLWgbm00nV+XeHi81fuzECx/3TV/oEUiQ1jpMMt8W+nAp0nvkTQUXOVCBXrTpU9p6hLARn0kORz0sPRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:13.279882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:683b8cc5430b8bc0b89d42cfdee1224ab9b0e81fcf88ff766e1cfbcb5b61afda","sha256:3c5402e3b80340a4ff1f8f5588e2c1ebfa5e40ff007d2f0d6c2142fdd9054981"],"state_sha256":"d82923803ffa84eb23060c394850edb2af4b796dc755ab488bfe1144e231b743"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weS8ed8RqWWI+bjnDo+EKJrQjkkNMxk8S9Tvm6OAAqtcC/DpJEAnqgZDBeTqnqr/yJjZyXvQSXxYtzXO2yb/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:14:25.225108Z","bundle_sha256":"4e7c704cc3099d57c0bb31448e473526becdb94e134faeca4ad6793870a095d9"}}