{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EX6LH6C6YF36SSJTIGFCQFLY6R","short_pith_number":"pith:EX6LH6C6","canonical_record":{"source":{"id":"1804.06234","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-13T23:09:12Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"11d81ecdda60b572d29241ae015afb5568c4473aff8a12b8ed17fe368476f3be","abstract_canon_sha256":"84bbeb390fa01cebb73a7d98b4fa633c1fd8dea8fd137f6ae2f57dbc068b8861"},"schema_version":"1.0"},"canonical_sha256":"25fcb3f85ec177e94933418a281578f478d4a0c8f48b914bbd53d2c51dbfd024","source":{"kind":"arxiv","id":"1804.06234","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06234","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06234v6","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06234","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"EX6LH6C6YF36","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"EX6LH6C6YF36SSJT","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"EX6LH6C6","created_at":"2026-07-05T00:33:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EX6LH6C6YF36SSJTIGFCQFLY6R","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06234","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-13T23:09:12Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"11d81ecdda60b572d29241ae015afb5568c4473aff8a12b8ed17fe368476f3be","abstract_canon_sha256":"84bbeb390fa01cebb73a7d98b4fa633c1fd8dea8fd137f6ae2f57dbc068b8861"},"schema_version":"1.0"},"canonical_sha256":"25fcb3f85ec177e94933418a281578f478d4a0c8f48b914bbd53d2c51dbfd024","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:33:08.729850Z","signature_b64":"BVO8xr4BevW+iVMmhCb00xt84kMM/DPSYBYJaO+RIFPTk4jJj3D2efSUXWiI5nsbG1w44TBo3vqyzsfaWRiyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25fcb3f85ec177e94933418a281578f478d4a0c8f48b914bbd53d2c51dbfd024","last_reissued_at":"2026-07-05T00:33:08.729441Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:33:08.729441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06234","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frxl08XzIOEg7IP0kJWzyfxtdgpiX4SZxPdC1O3SgK6Xdc2q2MZIp9dXTh54IurOTjY56psKqhWR8MnN3KckDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:20:06.174691Z"},"content_sha256":"2e3f92da15ce7fc0e16efb8fbf3d656f69a2398f0b1e01ecbdfbea4d0eeb435b","schema_version":"1.0","event_id":"sha256:2e3f92da15ce7fc0e16efb8fbf3d656f69a2398f0b1e01ecbdfbea4d0eeb435b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EX6LH6C6YF36SSJTIGFCQFLY6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Nan Rao, Qidi Peng, Ran Zhao","submitted_at":"2018-04-13T23:09:12Z","abstract_excerpt":"We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approximately asymptotically consistent clustering algorithms. In simulation studies, clustering data sampled from multifractional Brownian motions with distinct functional Hurst parameters illustrates the approximated asymptotic consistency of the proposed algorithms. Clustering global f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06234","kind":"arxiv","version":6},"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/1804.06234/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":"2026-07-05T00:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8g+uev6pSG77dTDGPTycbdy0/mlijm+8hnR+RubBlKqT+TFXYFIGll62mEltLpCH3fqt9EbbtHe8gbPKOAHLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:20:06.175663Z"},"content_sha256":"34bc16fd0fa23d8a104047507514af4c93b56c92304c2902e35eeec78caf960d","schema_version":"1.0","event_id":"sha256:34bc16fd0fa23d8a104047507514af4c93b56c92304c2902e35eeec78caf960d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/bundle.json","state_url":"https://pith.science/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/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":"2026-08-16T14:20:06Z","links":{"resolver":"https://pith.science/pith/EX6LH6C6YF36SSJTIGFCQFLY6R","bundle":"https://pith.science/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/bundle.json","state":"https://pith.science/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EX6LH6C6YF36SSJTIGFCQFLY6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EX6LH6C6YF36SSJTIGFCQFLY6R","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":"84bbeb390fa01cebb73a7d98b4fa633c1fd8dea8fd137f6ae2f57dbc068b8861","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-13T23:09:12Z","title_canon_sha256":"11d81ecdda60b572d29241ae015afb5568c4473aff8a12b8ed17fe368476f3be"},"schema_version":"1.0","source":{"id":"1804.06234","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06234","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06234v6","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06234","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"EX6LH6C6YF36","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"EX6LH6C6YF36SSJT","created_at":"2026-07-05T00:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"EX6LH6C6","created_at":"2026-07-05T00:33:08Z"}],"graph_snapshots":[{"event_id":"sha256:34bc16fd0fa23d8a104047507514af4c93b56c92304c2902e35eeec78caf960d","target":"graph","created_at":"2026-07-05T00:33:08Z","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/1804.06234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approximately asymptotically consistent clustering algorithms. In simulation studies, clustering data sampled from multifractional Brownian motions with distinct functional Hurst parameters illustrates the approximated asymptotic consistency of the proposed algorithms. Clustering global f","authors_text":"Nan Rao, Qidi Peng, Ran Zhao","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-13T23:09:12Z","title":"Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06234","kind":"arxiv","version":6},"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":"sha256:2e3f92da15ce7fc0e16efb8fbf3d656f69a2398f0b1e01ecbdfbea4d0eeb435b","target":"record","created_at":"2026-07-05T00:33:08Z","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":"84bbeb390fa01cebb73a7d98b4fa633c1fd8dea8fd137f6ae2f57dbc068b8861","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-13T23:09:12Z","title_canon_sha256":"11d81ecdda60b572d29241ae015afb5568c4473aff8a12b8ed17fe368476f3be"},"schema_version":"1.0","source":{"id":"1804.06234","kind":"arxiv","version":6}},"canonical_sha256":"25fcb3f85ec177e94933418a281578f478d4a0c8f48b914bbd53d2c51dbfd024","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25fcb3f85ec177e94933418a281578f478d4a0c8f48b914bbd53d2c51dbfd024","first_computed_at":"2026-07-05T00:33:08.729441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:33:08.729441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVO8xr4BevW+iVMmhCb00xt84kMM/DPSYBYJaO+RIFPTk4jJj3D2efSUXWiI5nsbG1w44TBo3vqyzsfaWRiyBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:33:08.729850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06234","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3f92da15ce7fc0e16efb8fbf3d656f69a2398f0b1e01ecbdfbea4d0eeb435b","sha256:34bc16fd0fa23d8a104047507514af4c93b56c92304c2902e35eeec78caf960d"],"state_sha256":"62cf345136b437b5523e9f1ffec373c55223b57cbe4663c499eddc165daabf25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAdffYvAMkEhetSSUvqrWiC8OjzJKyhrw5FwmEUtCuwwFcNA8O/ymUUPqyNW+zJNiPOG9GN9xQsqJdVGaflxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:20:06.181540Z","bundle_sha256":"215d0644df22a9ea0d63f0ef0a0e61115f66139588f7887ef8eb914111c19489"}}