{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HYMV32HOY7MUDUK44LGSHTVGEE","short_pith_number":"pith:HYMV32HO","canonical_record":{"source":{"id":"1401.5814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2014-01-22T22:01:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e6c65c7248dea1cda720d695dc826fab94b25b5f3fc02126a6a6d843a388b463","abstract_canon_sha256":"25dd23d965b90e98b2d85b85d21efbd8f5dbd39887902d8c6a7d41a81fdfef1a"},"schema_version":"1.0"},"canonical_sha256":"3e195de8eec7d941d15ce2cd23cea6213e683e384dbd563c2af12948767092ef","source":{"kind":"arxiv","id":"1401.5814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5814","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5814v1","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5814","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"HYMV32HOY7MU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYMV32HOY7MUDUK4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYMV32HO","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HYMV32HOY7MUDUK44LGSHTVGEE","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2014-01-22T22:01:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e6c65c7248dea1cda720d695dc826fab94b25b5f3fc02126a6a6d843a388b463","abstract_canon_sha256":"25dd23d965b90e98b2d85b85d21efbd8f5dbd39887902d8c6a7d41a81fdfef1a"},"schema_version":"1.0"},"canonical_sha256":"3e195de8eec7d941d15ce2cd23cea6213e683e384dbd563c2af12948767092ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:23.768391Z","signature_b64":"jbOFbh4Gp7P7WEQesRfL8BCtbTf8kfXKoOnxAX1T41tXutinxIxLmDaZzH2wPqknA+RGR0s9/n9Ya1sLfTZ6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e195de8eec7d941d15ce2cd23cea6213e683e384dbd563c2af12948767092ef","last_reissued_at":"2026-05-18T03:01:23.767434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:23.767434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5814","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":"2026-05-18T03:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CeyfRHX55S0+QRfdE4+Y6z0yGJoqMKY8FKe4wHfMJLJSRATSSMTfd+4OpylAPjJkzkBIcMJgzhVBM8AjquVPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:15:45.387180Z"},"content_sha256":"a7f70ba91097ac21668bfaf25d36573be8e4887a64572a9101bb632f744bde54","schema_version":"1.0","event_id":"sha256:a7f70ba91097ac21668bfaf25d36573be8e4887a64572a9101bb632f744bde54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HYMV32HOY7MUDUK44LGSHTVGEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Randomly Projected Hierarchical Clustering with Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.IR","authors_text":"Johannes Schneider, Michail Vlachos","submitted_at":"2014-01-22T22:01:05Z","abstract_excerpt":"Hierarchical clustering (HC) algorithms are generally limited to small data instances due to their runtime costs. Here we mitigate this shortcoming and explore fast HC algorithms based on random projections for single (SLC) and average (ALC) linkage clustering as well as for the minimum spanning tree problem (MST). We present a thorough adaptive analysis of our algorithms that improve prior work from $O(N^2)$ by up to a factor of $N/(\\log N)^2$ for a dataset of $N$ points in Euclidean space. The algorithms maintain, with arbitrary high probability, the outcome of hierarchical clustering as wel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5814","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":"2026-05-18T03:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cjEOBd+J9ZaZnCZVD70ePAfEH0FBuo1V5NFWeU6KZ6QFDke2PXnUINzhgjLq7tuJMgBXAXBW27jnRZqQlq1bAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:15:45.387544Z"},"content_sha256":"1274c2d6a39c7dd52881369a37da668a37386be340250e649491ab9a0c6fce0f","schema_version":"1.0","event_id":"sha256:1274c2d6a39c7dd52881369a37da668a37386be340250e649491ab9a0c6fce0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYMV32HOY7MUDUK44LGSHTVGEE/bundle.json","state_url":"https://pith.science/pith/HYMV32HOY7MUDUK44LGSHTVGEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYMV32HOY7MUDUK44LGSHTVGEE/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":"2026-06-04T02:15:45Z","links":{"resolver":"https://pith.science/pith/HYMV32HOY7MUDUK44LGSHTVGEE","bundle":"https://pith.science/pith/HYMV32HOY7MUDUK44LGSHTVGEE/bundle.json","state":"https://pith.science/pith/HYMV32HOY7MUDUK44LGSHTVGEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYMV32HOY7MUDUK44LGSHTVGEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYMV32HOY7MUDUK44LGSHTVGEE","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":"25dd23d965b90e98b2d85b85d21efbd8f5dbd39887902d8c6a7d41a81fdfef1a","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2014-01-22T22:01:05Z","title_canon_sha256":"e6c65c7248dea1cda720d695dc826fab94b25b5f3fc02126a6a6d843a388b463"},"schema_version":"1.0","source":{"id":"1401.5814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5814","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5814v1","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5814","created_at":"2026-05-18T03:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"HYMV32HOY7MU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYMV32HOY7MUDUK4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYMV32HO","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:1274c2d6a39c7dd52881369a37da668a37386be340250e649491ab9a0c6fce0f","target":"graph","created_at":"2026-05-18T03:01:23Z","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 (HC) algorithms are generally limited to small data instances due to their runtime costs. Here we mitigate this shortcoming and explore fast HC algorithms based on random projections for single (SLC) and average (ALC) linkage clustering as well as for the minimum spanning tree problem (MST). We present a thorough adaptive analysis of our algorithms that improve prior work from $O(N^2)$ by up to a factor of $N/(\\log N)^2$ for a dataset of $N$ points in Euclidean space. The algorithms maintain, with arbitrary high probability, the outcome of hierarchical clustering as wel","authors_text":"Johannes Schneider, Michail Vlachos","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2014-01-22T22:01:05Z","title":"On Randomly Projected Hierarchical Clustering with Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5814","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:a7f70ba91097ac21668bfaf25d36573be8e4887a64572a9101bb632f744bde54","target":"record","created_at":"2026-05-18T03:01:23Z","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":"25dd23d965b90e98b2d85b85d21efbd8f5dbd39887902d8c6a7d41a81fdfef1a","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2014-01-22T22:01:05Z","title_canon_sha256":"e6c65c7248dea1cda720d695dc826fab94b25b5f3fc02126a6a6d843a388b463"},"schema_version":"1.0","source":{"id":"1401.5814","kind":"arxiv","version":1}},"canonical_sha256":"3e195de8eec7d941d15ce2cd23cea6213e683e384dbd563c2af12948767092ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e195de8eec7d941d15ce2cd23cea6213e683e384dbd563c2af12948767092ef","first_computed_at":"2026-05-18T03:01:23.767434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:23.767434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbOFbh4Gp7P7WEQesRfL8BCtbTf8kfXKoOnxAX1T41tXutinxIxLmDaZzH2wPqknA+RGR0s9/n9Ya1sLfTZ6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:23.768391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7f70ba91097ac21668bfaf25d36573be8e4887a64572a9101bb632f744bde54","sha256:1274c2d6a39c7dd52881369a37da668a37386be340250e649491ab9a0c6fce0f"],"state_sha256":"2e73af06dca3ec79962e22ce519df33527f8989b2a9be0a76da001613f84c302"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7CH2MVZZp6wgVKXfQp+obNVF7F04u/p+CMOYE3NKnPyIsf3JtQhgbvZp5vEilhuJROb4l7JtGCoRDU6rg5qDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:15:45.389840Z","bundle_sha256":"22b83e7f1d6755633b0fa52bc7ae4a3a129389d506f1968a948016e9a59d2bfd"}}