{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JTFPMPEH57YD3VKIPHD7RIKZ44","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":"60d7f4b36cd5f7b8b4cb2c054bf9e0d3ff23e80f8fa3022e110ce84dc6bc1dc1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-21T23:19:37Z","title_canon_sha256":"b4936a59d6459aa9d3b1384123921c95c3c60d599fc61326c5125237a5132c18"},"schema_version":"1.0","source":{"id":"1506.06422","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06422","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06422v2","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06422","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"JTFPMPEH57YD","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JTFPMPEH57YD3VKI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JTFPMPEH","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:0c37818596fd4426c45c050c3097d4d183e39bc22107e8561bcd97fa0dc11c3f","target":"graph","created_at":"2026-05-18T01:37:01Z","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":"Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given density can look very different than the correct limit tree. Specifically, Hartigan consistency permits two types of undesirable configurations which we term over-segmentation and improper nesting. Moreover, Hartigan consistency is a limit property and does not directly quantify diff","authors_text":"Justin Eldridge, Mikhail Belkin, Yusu Wang","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-21T23:19:37Z","title":"Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06422","kind":"arxiv","version":2},"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:af1dced44e6f60b884675f79b99da7e778e226bf41ff1d21890da26515c3bc57","target":"record","created_at":"2026-05-18T01:37:01Z","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":"60d7f4b36cd5f7b8b4cb2c054bf9e0d3ff23e80f8fa3022e110ce84dc6bc1dc1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-21T23:19:37Z","title_canon_sha256":"b4936a59d6459aa9d3b1384123921c95c3c60d599fc61326c5125237a5132c18"},"schema_version":"1.0","source":{"id":"1506.06422","kind":"arxiv","version":2}},"canonical_sha256":"4ccaf63c87eff03dd54879c7f8a159e7124d0aead274fa55188b5e6f66715a0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ccaf63c87eff03dd54879c7f8a159e7124d0aead274fa55188b5e6f66715a0d","first_computed_at":"2026-05-18T01:37:01.337928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:01.337928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jgNQpv5587R0x2HB2uUru7XF/oJ8rTw97dvGtUSoPpc9ZBz/J1wqfbdsvKsW9JbeTPerAn2+zzS1pZHY3hoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:01.338364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06422","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af1dced44e6f60b884675f79b99da7e778e226bf41ff1d21890da26515c3bc57","sha256:0c37818596fd4426c45c050c3097d4d183e39bc22107e8561bcd97fa0dc11c3f"],"state_sha256":"376cfd19202d4bbd433aab1c392d6d0563868a8f6600aa6d6d59c7d8cc90e884"}