{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R4IQKAGOSAB4QWHG5XJWRYDNMZ","short_pith_number":"pith:R4IQKAGO","schema_version":"1.0","canonical_sha256":"8f110500ce9003c858e6edd368e06d665febc6ad5a8a99ce0f3042f74a7098c9","source":{"kind":"arxiv","id":"1812.11564","version":1},"attestation_state":"computed","paper":{"title":"Spectral methods for testing cluster structure of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jonathan Tidor, Sandeep Silwal","submitted_at":"2018-12-30T16:08:13Z","abstract_excerpt":"In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \\phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has conductance at least $\\phi$. We present an algorithm that accepts all graphs that are $(2, \\phi)$-clusterable with probability at least $\\frac{2}3$ and rejects all graphs that are $\\epsilon$-far from $(2, \\phi^*)$-clusterable for $\\phi^* \\le \\mu \\phi^2 \\epsilon^2$ with probability at least $\\frac{2}3$ where $\\mu > 0$ is a parameter that affects the query compl"},"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":"1812.11564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-12-30T16:08:13Z","cross_cats_sorted":[],"title_canon_sha256":"8a3c8b378dd734613b238f67fd24bd10bb1dc66667f5003c730c58df0e900de9","abstract_canon_sha256":"5bcf2cfb28cec1bb04f093232633b199740b465cd75375ec69b6a4cfe2dad882"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:11.640548Z","signature_b64":"U5YLkze9VwwUBZvLAHrtyLheUxo3nnVosdCeIVp5xLoBo3XCbAjb3V1FoZN0zfeiOj85AP5F+AUBHi/v33SzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f110500ce9003c858e6edd368e06d665febc6ad5a8a99ce0f3042f74a7098c9","last_reissued_at":"2026-05-17T23:57:11.639987Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:11.639987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral methods for testing cluster structure of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jonathan Tidor, Sandeep Silwal","submitted_at":"2018-12-30T16:08:13Z","abstract_excerpt":"In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \\phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has conductance at least $\\phi$. We present an algorithm that accepts all graphs that are $(2, \\phi)$-clusterable with probability at least $\\frac{2}3$ and rejects all graphs that are $\\epsilon$-far from $(2, \\phi^*)$-clusterable for $\\phi^* \\le \\mu \\phi^2 \\epsilon^2$ with probability at least $\\frac{2}3$ where $\\mu > 0$ is a parameter that affects the query compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11564","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.11564","created_at":"2026-05-17T23:57:11.640059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.11564v1","created_at":"2026-05-17T23:57:11.640059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11564","created_at":"2026-05-17T23:57:11.640059+00:00"},{"alias_kind":"pith_short_12","alias_value":"R4IQKAGOSAB4","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R4IQKAGOSAB4QWHG","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R4IQKAGO","created_at":"2026-05-18T12:32:50.500415+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/R4IQKAGOSAB4QWHG5XJWRYDNMZ","json":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ.json","graph_json":"https://pith.science/api/pith-number/R4IQKAGOSAB4QWHG5XJWRYDNMZ/graph.json","events_json":"https://pith.science/api/pith-number/R4IQKAGOSAB4QWHG5XJWRYDNMZ/events.json","paper":"https://pith.science/paper/R4IQKAGO"},"agent_actions":{"view_html":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ","download_json":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ.json","view_paper":"https://pith.science/paper/R4IQKAGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.11564&json=true","fetch_graph":"https://pith.science/api/pith-number/R4IQKAGOSAB4QWHG5XJWRYDNMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/R4IQKAGOSAB4QWHG5XJWRYDNMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ/action/storage_attestation","attest_author":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ/action/author_attestation","sign_citation":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ/action/citation_signature","submit_replication":"https://pith.science/pith/R4IQKAGOSAB4QWHG5XJWRYDNMZ/action/replication_record"}},"created_at":"2026-05-17T23:57:11.640059+00:00","updated_at":"2026-05-17T23:57:11.640059+00:00"}