{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O4JVCA4A3OSGTCJM6QWHGFPC3U","short_pith_number":"pith:O4JVCA4A","canonical_record":{"source":{"id":"1811.04423","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-11T14:30:10Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d679ecf3591ec4b9650f705b954c6d997cfa6b7703b0afdba9e70c0f3f99bdc2","abstract_canon_sha256":"3b20c1340ab9f5da5aed5fa880e82ba87536700153fd2b2cc23926275c7e3a22"},"schema_version":"1.0"},"canonical_sha256":"7713510380dba469892cf42c7315e2dd0042a0f04a86602c71816e87b650e43b","source":{"kind":"arxiv","id":"1811.04423","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04423","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04423v3","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04423","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_12","alias_value":"O4JVCA4A3OSG","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_16","alias_value":"O4JVCA4A3OSGTCJM","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_8","alias_value":"O4JVCA4A","created_at":"2026-07-05T08:37:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O4JVCA4A3OSGTCJM6QWHGFPC3U","target":"record","payload":{"canonical_record":{"source":{"id":"1811.04423","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-11T14:30:10Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d679ecf3591ec4b9650f705b954c6d997cfa6b7703b0afdba9e70c0f3f99bdc2","abstract_canon_sha256":"3b20c1340ab9f5da5aed5fa880e82ba87536700153fd2b2cc23926275c7e3a22"},"schema_version":"1.0"},"canonical_sha256":"7713510380dba469892cf42c7315e2dd0042a0f04a86602c71816e87b650e43b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:37:03.047876Z","signature_b64":"Bz3F/F7skiF6l53AjI+zt4eyAMKrXBzzbf2RHlcV4tKef2Cvs58zgpJzi8rOFIv64vbfktftA0IYr5zkkSF2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7713510380dba469892cf42c7315e2dd0042a0f04a86602c71816e87b650e43b","last_reissued_at":"2026-07-05T08:37:03.047385Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:37:03.047385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.04423","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":"2026-07-05T08:37:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0y71ojZPAels52coHAgNzMQMkjJI0FJ5YehTn/lU8cGMG8pH6/w/JrcsOz7H2MbkkvpfrU4xOZ8T1hXQ7FjgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:20:40.584759Z"},"content_sha256":"2efd36c8b029b9a7d2a543e071343ddf414085748abf94bd016cd057f5911ce3","schema_version":"1.0","event_id":"sha256:2efd36c8b029b9a7d2a543e071343ddf414085748abf94bd016cd057f5911ce3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O4JVCA4A3OSGTCJM6QWHGFPC3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When Locally Linear Embedding Hits Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Hau-Tieng Wu, Nan Wu","submitted_at":"2018-11-11T14:30:10Z","abstract_excerpt":"Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04423","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/1811.04423/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":"2026-07-05T08:37:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsJAzvIRkIM3xomCaNFTC9Ax8ey3MmU+l5mfKu4ktSUZSJYeIdy/XCmAAfOfTG5cs5e3reM3ybw7UWjP8HxYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:20:40.585295Z"},"content_sha256":"85a5df863030077c7e97528e41a8cc2ed02937b5149e72190244e9e7de9538f9","schema_version":"1.0","event_id":"sha256:85a5df863030077c7e97528e41a8cc2ed02937b5149e72190244e9e7de9538f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/bundle.json","state_url":"https://pith.science/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/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":"2026-08-04T19:20:40Z","links":{"resolver":"https://pith.science/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U","bundle":"https://pith.science/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/bundle.json","state":"https://pith.science/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4JVCA4A3OSGTCJM6QWHGFPC3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O4JVCA4A3OSGTCJM6QWHGFPC3U","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":"3b20c1340ab9f5da5aed5fa880e82ba87536700153fd2b2cc23926275c7e3a22","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-11T14:30:10Z","title_canon_sha256":"d679ecf3591ec4b9650f705b954c6d997cfa6b7703b0afdba9e70c0f3f99bdc2"},"schema_version":"1.0","source":{"id":"1811.04423","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04423","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04423v3","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04423","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_12","alias_value":"O4JVCA4A3OSG","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_16","alias_value":"O4JVCA4A3OSGTCJM","created_at":"2026-07-05T08:37:03Z"},{"alias_kind":"pith_short_8","alias_value":"O4JVCA4A","created_at":"2026-07-05T08:37:03Z"}],"graph_snapshots":[{"event_id":"sha256:85a5df863030077c7e97528e41a8cc2ed02937b5149e72190244e9e7de9538f9","target":"graph","created_at":"2026-07-05T08:37:03Z","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/1811.04423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algori","authors_text":"Hau-Tieng Wu, Nan Wu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-11T14:30:10Z","title":"When Locally Linear Embedding Hits Boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04423","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":"sha256:2efd36c8b029b9a7d2a543e071343ddf414085748abf94bd016cd057f5911ce3","target":"record","created_at":"2026-07-05T08:37:03Z","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":"3b20c1340ab9f5da5aed5fa880e82ba87536700153fd2b2cc23926275c7e3a22","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-11T14:30:10Z","title_canon_sha256":"d679ecf3591ec4b9650f705b954c6d997cfa6b7703b0afdba9e70c0f3f99bdc2"},"schema_version":"1.0","source":{"id":"1811.04423","kind":"arxiv","version":3}},"canonical_sha256":"7713510380dba469892cf42c7315e2dd0042a0f04a86602c71816e87b650e43b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7713510380dba469892cf42c7315e2dd0042a0f04a86602c71816e87b650e43b","first_computed_at":"2026-07-05T08:37:03.047385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:37:03.047385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bz3F/F7skiF6l53AjI+zt4eyAMKrXBzzbf2RHlcV4tKef2Cvs58zgpJzi8rOFIv64vbfktftA0IYr5zkkSF2AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:37:03.047876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04423","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2efd36c8b029b9a7d2a543e071343ddf414085748abf94bd016cd057f5911ce3","sha256:85a5df863030077c7e97528e41a8cc2ed02937b5149e72190244e9e7de9538f9"],"state_sha256":"9f4a917e7a9e8986e491034cffbeea730fb9bbd0efbe9c4f6d8abc04f24179e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cLZ2ftYyfZ2j4W+4E+hPcQ51HN8KzAVArUIbZxVFkKseGRTmZy+6uIBLaCmVys5LuGHPG54PBgFdXfXjz0qIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:20:40.591582Z","bundle_sha256":"1bcf193332a5e95be855d92aae38379c5e012f18df1979c3ab8225641c84a44e"}}