{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4NZ6NFDPG7U624EQBLMZ4TYBT2","short_pith_number":"pith:4NZ6NFDP","canonical_record":{"source":{"id":"1008.3572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-20T20:46:39Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f18da9d636f702c953d11428256bd29fc447561680cdac781bd3f2752ecd5981","abstract_canon_sha256":"7c690b7dfd97919c8e2d56180f87dd59bb0e20481e004d8d2267ba6b4d795441"},"schema_version":"1.0"},"canonical_sha256":"e373e6946f37e9ed70900ad99e4f019e97f5aaaa20c81a37fe9cfa7eadb835a9","source":{"kind":"arxiv","id":"1008.3572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3572","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3572v1","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3572","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"4NZ6NFDPG7U6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4NZ6NFDPG7U624EQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4NZ6NFDP","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4NZ6NFDPG7U624EQBLMZ4TYBT2","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-20T20:46:39Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f18da9d636f702c953d11428256bd29fc447561680cdac781bd3f2752ecd5981","abstract_canon_sha256":"7c690b7dfd97919c8e2d56180f87dd59bb0e20481e004d8d2267ba6b4d795441"},"schema_version":"1.0"},"canonical_sha256":"e373e6946f37e9ed70900ad99e4f019e97f5aaaa20c81a37fe9cfa7eadb835a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:55.608056Z","signature_b64":"YzlV1wtxu1k4HQLhVRiqt5F5069WmT9iCFWgTYXMLVxX3+4dNV6tFeTlmfh47flMQriQSvGkXjBCtjmC29u9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e373e6946f37e9ed70900ad99e4f019e97f5aaaa20c81a37fe9cfa7eadb835a9","last_reissued_at":"2026-05-18T04:41:55.607671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:55.607671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3572","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":"2026-05-18T04:41:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+21h4oi8uo+nb0aV2Pug5NhWiWpyFOEUjYnv3GhTysk/sWcZfmtdyNY90DYJlDdANeE/YJi9AZJbim9j5T/GDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:38.626238Z"},"content_sha256":"7f367c620f51622870643aa538f8dc2c6aa75d36e8ece7e6a96738e3975887db","schema_version":"1.0","event_id":"sha256:7f367c620f51622870643aa538f8dc2c6aa75d36e8ece7e6a96738e3975887db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4NZ6NFDPG7U624EQBLMZ4TYBT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Stratification Learning through Homology Inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.GT","authors_text":"Bei Wang, Paul Bendich, Sayan Mukherjee","submitted_at":"2010-08-20T20:46:39Z","abstract_excerpt":"A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use methods derived from kernel and cokernel persistent homology to cluster the data points into different strata, and we prove a result which guarantees the correctness of our clustering, given certain topological conditions; some geometric intuition for these topological conditions is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3572","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":"2026-05-18T04:41:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DuIGKHF4Dm9Pv4huG78koKZxf0cHPZi6MosskRZWjl26uBYL87FMjOSu0yeIvY9KswZ/zFixdwm4Vq7Cfz9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:38.626859Z"},"content_sha256":"d409318cb3c9c1537f4a851fd9d02857a59b9358fe082e2f225dc55cf758f469","schema_version":"1.0","event_id":"sha256:d409318cb3c9c1537f4a851fd9d02857a59b9358fe082e2f225dc55cf758f469"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/bundle.json","state_url":"https://pith.science/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/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":"2026-05-28T13:34:38Z","links":{"resolver":"https://pith.science/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2","bundle":"https://pith.science/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/bundle.json","state":"https://pith.science/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NZ6NFDPG7U624EQBLMZ4TYBT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4NZ6NFDPG7U624EQBLMZ4TYBT2","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":"7c690b7dfd97919c8e2d56180f87dd59bb0e20481e004d8d2267ba6b4d795441","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-20T20:46:39Z","title_canon_sha256":"f18da9d636f702c953d11428256bd29fc447561680cdac781bd3f2752ecd5981"},"schema_version":"1.0","source":{"id":"1008.3572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3572","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3572v1","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3572","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"4NZ6NFDPG7U6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4NZ6NFDPG7U624EQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4NZ6NFDP","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:d409318cb3c9c1537f4a851fd9d02857a59b9358fe082e2f225dc55cf758f469","target":"graph","created_at":"2026-05-18T04:41:55Z","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":"A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use methods derived from kernel and cokernel persistent homology to cluster the data points into different strata, and we prove a result which guarantees the correctness of our clustering, given certain topological conditions; some geometric intuition for these topological conditions is","authors_text":"Bei Wang, Paul Bendich, Sayan Mukherjee","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-20T20:46:39Z","title":"Towards Stratification Learning through Homology Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3572","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":"sha256:7f367c620f51622870643aa538f8dc2c6aa75d36e8ece7e6a96738e3975887db","target":"record","created_at":"2026-05-18T04:41:55Z","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":"7c690b7dfd97919c8e2d56180f87dd59bb0e20481e004d8d2267ba6b4d795441","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-20T20:46:39Z","title_canon_sha256":"f18da9d636f702c953d11428256bd29fc447561680cdac781bd3f2752ecd5981"},"schema_version":"1.0","source":{"id":"1008.3572","kind":"arxiv","version":1}},"canonical_sha256":"e373e6946f37e9ed70900ad99e4f019e97f5aaaa20c81a37fe9cfa7eadb835a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e373e6946f37e9ed70900ad99e4f019e97f5aaaa20c81a37fe9cfa7eadb835a9","first_computed_at":"2026-05-18T04:41:55.607671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:55.607671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YzlV1wtxu1k4HQLhVRiqt5F5069WmT9iCFWgTYXMLVxX3+4dNV6tFeTlmfh47flMQriQSvGkXjBCtjmC29u9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:55.608056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f367c620f51622870643aa538f8dc2c6aa75d36e8ece7e6a96738e3975887db","sha256:d409318cb3c9c1537f4a851fd9d02857a59b9358fe082e2f225dc55cf758f469"],"state_sha256":"911f292110cb8ad9aee25964615bed461da84322c76cfe0a7169b45c6a115314"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wnbDYFpgYD5Bpf5kaSFD+RMLhY2vYRXHELslmN8t4rbBoGqvoof+WK3rs06wIxtGsIVLntB2+bHB/6uUtOOvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:34:38.630001Z","bundle_sha256":"bb394ed8accaa549dfe1df2a8669dd0517a187b9bb0e97ad676b05ac4302be5a"}}