{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7BKLMH3AGTPMM5P4QDVSTFRLGH","short_pith_number":"pith:7BKLMH3A","schema_version":"1.0","canonical_sha256":"f854b61f6034dec675fc80eb29962b31ff71d3171223b5efab20f48626edcc46","source":{"kind":"arxiv","id":"1404.1008","version":6},"attestation_state":"computed","paper":{"title":"Spectral concentration and greedy k-clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Alfred Rossi, Anastasios Sidiropoulos, Pan Peng, Tamal K. Dey","submitted_at":"2014-04-03T17:05:49Z","abstract_excerpt":"A popular graph clustering method is to consider the embedding of an input graph into R^k induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite the practical success of this methodology, there is limited understanding of several heuristics that follow this framework. We provide theoretical justification for one such natural and computationally efficient variant.\n  Our result can be summarized as follows. A partition of a graph is called strong if each cluster has small external conductance, and large "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1404.1008","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T17:05:49Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"efd641cfdfd877f5255cd27b161eb0134698ecb96d4cb3c701dd57596b28f4ae","abstract_canon_sha256":"7696ac7dd65d7980f7cb68869409b587a488163e50c32827ead4408583810d4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:56.983655Z","signature_b64":"xCTWAwEDAzaWP8CFaYEEElRcZT4q3nX2ppEW8AT9bESPXmHY5S94nkJFk3NRdTjwJvdhRW5YZhxfLGSAHYExBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f854b61f6034dec675fc80eb29962b31ff71d3171223b5efab20f48626edcc46","last_reissued_at":"2026-05-18T00:05:56.983188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:56.983188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral concentration and greedy k-clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Alfred Rossi, Anastasios Sidiropoulos, Pan Peng, Tamal K. Dey","submitted_at":"2014-04-03T17:05:49Z","abstract_excerpt":"A popular graph clustering method is to consider the embedding of an input graph into R^k induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite the practical success of this methodology, there is limited understanding of several heuristics that follow this framework. We provide theoretical justification for one such natural and computationally efficient variant.\n  Our result can be summarized as follows. A partition of a graph is called strong if each cluster has small external conductance, and large "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1008","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.1008","created_at":"2026-05-18T00:05:56.983279+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1008v6","created_at":"2026-05-18T00:05:56.983279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1008","created_at":"2026-05-18T00:05:56.983279+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BKLMH3AGTPM","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BKLMH3AGTPMM5P4","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BKLMH3A","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH","json":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH.json","graph_json":"https://pith.science/api/pith-number/7BKLMH3AGTPMM5P4QDVSTFRLGH/graph.json","events_json":"https://pith.science/api/pith-number/7BKLMH3AGTPMM5P4QDVSTFRLGH/events.json","paper":"https://pith.science/paper/7BKLMH3A"},"agent_actions":{"view_html":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH","download_json":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH.json","view_paper":"https://pith.science/paper/7BKLMH3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1008&json=true","fetch_graph":"https://pith.science/api/pith-number/7BKLMH3AGTPMM5P4QDVSTFRLGH/graph.json","fetch_events":"https://pith.science/api/pith-number/7BKLMH3AGTPMM5P4QDVSTFRLGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH/action/storage_attestation","attest_author":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH/action/author_attestation","sign_citation":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH/action/citation_signature","submit_replication":"https://pith.science/pith/7BKLMH3AGTPMM5P4QDVSTFRLGH/action/replication_record"}},"created_at":"2026-05-18T00:05:56.983279+00:00","updated_at":"2026-05-18T00:05:56.983279+00:00"}