{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:USZNKBIFIKRWL7XFQWKIVKEMAC","short_pith_number":"pith:USZNKBIF","canonical_record":{"source":{"id":"1909.10228","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-23T08:55:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f94f883f59c146244dbc00c92302f23fda9a7240c33beefac63845b21e8e5172","abstract_canon_sha256":"57921800e88f69782ed8c17366bb5f9e195dfdaaa980b6a08f13c5ca8441aae3"},"schema_version":"1.0"},"canonical_sha256":"a4b2d5050542a365fee585948aa88c00b152c908720e956bbd19e11f20ac4718","source":{"kind":"arxiv","id":"1909.10228","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.10228","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1909.10228v3","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.10228","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"USZNKBIFIKRW","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_16","alias_value":"USZNKBIFIKRWL7XF","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_8","alias_value":"USZNKBIF","created_at":"2026-07-05T08:29:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:USZNKBIFIKRWL7XFQWKIVKEMAC","target":"record","payload":{"canonical_record":{"source":{"id":"1909.10228","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-23T08:55:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f94f883f59c146244dbc00c92302f23fda9a7240c33beefac63845b21e8e5172","abstract_canon_sha256":"57921800e88f69782ed8c17366bb5f9e195dfdaaa980b6a08f13c5ca8441aae3"},"schema_version":"1.0"},"canonical_sha256":"a4b2d5050542a365fee585948aa88c00b152c908720e956bbd19e11f20ac4718","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:29:11.211604Z","signature_b64":"X1yEuzHdVavgtOV1oWDD6nSIBNrxkJ/x9bjpwM6nXl5P5rNZZN4Qw5mhJliSob1qI2w1+7m6QYfUGB2npro8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4b2d5050542a365fee585948aa88c00b152c908720e956bbd19e11f20ac4718","last_reissued_at":"2026-07-05T08:29:11.211152Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:29:11.211152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.10228","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":"2026-07-05T08:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dvPIIG2WR9fUzIDtBVXILYYSGJn0yeas3Nsm4zYnvRYudEmRPZzZOK4kC2Co2CudUKuWVZ5rZ7DtCy7Ik6lNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:34:30.282331Z"},"content_sha256":"1ca9bb73e4219441dcecdd0e3773eb42a6fad2e68f03d62649973b24cf90e348","schema_version":"1.0","event_id":"sha256:1ca9bb73e4219441dcecdd0e3773eb42a6fad2e68f03d62649973b24cf90e348"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:USZNKBIFIKRWL7XFQWKIVKEMAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Manifold Fitting under Unbounded Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Yuqing Xia, Zhigang Yao","submitted_at":"2019-09-23T08:55:41Z","abstract_excerpt":"There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain concentration. Existing methods address this problem by constructing an approximated manifold based on the tangent space estimation at each sample point. Although theoretical convergence for these methods is guaranteed, either the samples are noiseless or the noise is bounded. However, if the noise is unbounded, which is a common scenario, the tangent space es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.10228","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.10228/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qmqyxq3HE/59R9UigKng1kDPF3aHJo/kiXNXCjxo9PLzzDiyCcvLG8AG6oCIWn9ObAavUK5l0b4zYXZFREe8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:34:30.283259Z"},"content_sha256":"a3c201b63708f9e8b6f55a11a4a142336c08cc5740d7f5e7f1cbe70fe9545815","schema_version":"1.0","event_id":"sha256:a3c201b63708f9e8b6f55a11a4a142336c08cc5740d7f5e7f1cbe70fe9545815"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/bundle.json","state_url":"https://pith.science/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/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":"2026-08-12T15:34:30Z","links":{"resolver":"https://pith.science/pith/USZNKBIFIKRWL7XFQWKIVKEMAC","bundle":"https://pith.science/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/bundle.json","state":"https://pith.science/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USZNKBIFIKRWL7XFQWKIVKEMAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:USZNKBIFIKRWL7XFQWKIVKEMAC","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":"57921800e88f69782ed8c17366bb5f9e195dfdaaa980b6a08f13c5ca8441aae3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-23T08:55:41Z","title_canon_sha256":"f94f883f59c146244dbc00c92302f23fda9a7240c33beefac63845b21e8e5172"},"schema_version":"1.0","source":{"id":"1909.10228","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.10228","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1909.10228v3","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.10228","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"USZNKBIFIKRW","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_16","alias_value":"USZNKBIFIKRWL7XF","created_at":"2026-07-05T08:29:11Z"},{"alias_kind":"pith_short_8","alias_value":"USZNKBIF","created_at":"2026-07-05T08:29:11Z"}],"graph_snapshots":[{"event_id":"sha256:a3c201b63708f9e8b6f55a11a4a142336c08cc5740d7f5e7f1cbe70fe9545815","target":"graph","created_at":"2026-07-05T08:29:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.10228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain concentration. Existing methods address this problem by constructing an approximated manifold based on the tangent space estimation at each sample point. Although theoretical convergence for these methods is guaranteed, either the samples are noiseless or the noise is bounded. However, if the noise is unbounded, which is a common scenario, the tangent space es","authors_text":"Yuqing Xia, Zhigang Yao","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-23T08:55:41Z","title":"Manifold Fitting under Unbounded Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.10228","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":"sha256:1ca9bb73e4219441dcecdd0e3773eb42a6fad2e68f03d62649973b24cf90e348","target":"record","created_at":"2026-07-05T08:29:11Z","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":"57921800e88f69782ed8c17366bb5f9e195dfdaaa980b6a08f13c5ca8441aae3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-23T08:55:41Z","title_canon_sha256":"f94f883f59c146244dbc00c92302f23fda9a7240c33beefac63845b21e8e5172"},"schema_version":"1.0","source":{"id":"1909.10228","kind":"arxiv","version":3}},"canonical_sha256":"a4b2d5050542a365fee585948aa88c00b152c908720e956bbd19e11f20ac4718","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4b2d5050542a365fee585948aa88c00b152c908720e956bbd19e11f20ac4718","first_computed_at":"2026-07-05T08:29:11.211152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:29:11.211152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X1yEuzHdVavgtOV1oWDD6nSIBNrxkJ/x9bjpwM6nXl5P5rNZZN4Qw5mhJliSob1qI2w1+7m6QYfUGB2npro8BA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:29:11.211604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.10228","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ca9bb73e4219441dcecdd0e3773eb42a6fad2e68f03d62649973b24cf90e348","sha256:a3c201b63708f9e8b6f55a11a4a142336c08cc5740d7f5e7f1cbe70fe9545815"],"state_sha256":"2c75ce9af208026b4893e88ca41054288661c7508ebbb852916d97222c2ea146"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZSP4jwbew663whDCi30a4FB1qiNTx/DJg9KjVKCcZnTLAbsv7zJeIt6JHUyrC0KPC/YrtBJOLyWSi+LAtm8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:34:30.288859Z","bundle_sha256":"05f145957d94df127ce6f735f71d1b0b75d2f369f028aa7ef8033664c8bee423"}}