{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KRMZYMG2JKFVAXPZ7NP75I4DXP","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":"ff94f866e0adc7a48dcc43e63f31e9f3313fd42c4c3d55d8d6dff1dd4df7e585","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-03-17T17:38:37Z","title_canon_sha256":"9f3eb23b3a6e83a48787658fb77bcde520efb06029fa0ceac3d6cc11a8fc2856"},"schema_version":"1.0","source":{"id":"2503.13409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.13409","created_at":"2026-07-05T10:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"2503.13409v1","created_at":"2026-07-05T10:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.13409","created_at":"2026-07-05T10:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"KRMZYMG2JKFV","created_at":"2026-07-05T10:33:00Z"},{"alias_kind":"pith_short_16","alias_value":"KRMZYMG2JKFVAXPZ","created_at":"2026-07-05T10:33:00Z"},{"alias_kind":"pith_short_8","alias_value":"KRMZYMG2","created_at":"2026-07-05T10:33:00Z"}],"graph_snapshots":[{"event_id":"sha256:1ea562092c46c4ef2814ba369d918d0df4ee3feefba580bd0d57d9a8e2bddecb","target":"graph","created_at":"2026-07-05T10:33:00Z","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/2503.13409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical relationships within the data. However, popular methods for computing them, such as linkage algorithms, suffer from quadratic time and space complexity, making them impractical for large datasets.\n  The \"best ultrametric embedding\" (a.k.a. \"best ultrametric fit\") problem, which aims to find the ultrametric that best preserves the distances between points in the origin","authors_text":"Gabriel Bathie, Guillaume Lagarde","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-03-17T17:38:37Z","title":"A $(1+\\epsilon)$-Approximation for Ultrametric Embedding in Subquadratic Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.13409","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":"sha256:98e3d7a5f273f94feb135ccae9956b7c130463b997f10a8b78f6b2591eb2eb4c","target":"record","created_at":"2026-07-05T10:33:00Z","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":"ff94f866e0adc7a48dcc43e63f31e9f3313fd42c4c3d55d8d6dff1dd4df7e585","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-03-17T17:38:37Z","title_canon_sha256":"9f3eb23b3a6e83a48787658fb77bcde520efb06029fa0ceac3d6cc11a8fc2856"},"schema_version":"1.0","source":{"id":"2503.13409","kind":"arxiv","version":1}},"canonical_sha256":"54599c30da4a8b505df9fb5ffea383bbd1da837751173e5b76b7fd0bdbf2a0b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54599c30da4a8b505df9fb5ffea383bbd1da837751173e5b76b7fd0bdbf2a0b6","first_computed_at":"2026-07-05T10:33:00.059087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:33:00.059087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aPh+5DBZl82Nvbj5UHIb3wwaXIrKKSoH2BRCvBPVwnYXmBHePEgjY0Ks7ewkNb7i7fRpIEdcDZMgTs7lHnZCDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:33:00.059559Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.13409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98e3d7a5f273f94feb135ccae9956b7c130463b997f10a8b78f6b2591eb2eb4c","sha256:1ea562092c46c4ef2814ba369d918d0df4ee3feefba580bd0d57d9a8e2bddecb"],"state_sha256":"354babd21bee9252b66d5a305e27d7951be879764470da2d6c969d4f12f864f3"}