{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EMSMFZ5JS42FEOG622DKNA5WAY","short_pith_number":"pith:EMSMFZ5J","schema_version":"1.0","canonical_sha256":"2324c2e7a997345238ded686a683b60606cf9ffa5f25640c1a312aecb1cdc30f","source":{"kind":"arxiv","id":"2606.13583","version":1},"attestation_state":"computed","paper":{"title":"Testing Bipartiteness in Logarithmic Rounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ronitt Rubinfeld, Yumou Fei","submitted_at":"2026-06-11T17:07:00Z","abstract_excerpt":"The seminal work of Goldreich and Ron (\\textit{Combinatorica, 1999}) showed that bipartiteness of bounded-degree graphs can be tested using $O(\\sqrt{n\\log n})$ random walks of length $O(\\log^{6} n)$. In this work, we improve their result by showing that $O(\\sqrt{n})$ random walks of length $O(\\log n)$ suffice. As a corollary, we obtain an $O(\\log n)$-pass, $O(\\sqrt{n}\\log n)$-space streaming algorithm for testing bipartiteness, whose pass complexity is optimal in light of a recent lower bound of Fei, Minzer, and Wang (\\textit{arXiv, 2026}).\n  Our proof takes a different approach from that of G"},"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":"2606.13583","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-11T17:07:00Z","cross_cats_sorted":[],"title_canon_sha256":"cc570e2c49ca4088b1830bfa3718671cbb808225f3646861852dc49b97e57d6c","abstract_canon_sha256":"444fc559a6798426e66d603b2cf72fe4e200a77aec9798ff8b3b8a3ef09458e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:10:11.518804Z","signature_b64":"TB2cHX0xOxi5PjQit/ds6oJJp0NwoevcsRS4zonUa65ypCNrj4v4dmjbUcr3BmRdSsYkkBl20Eg0DFE+aHoeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2324c2e7a997345238ded686a683b60606cf9ffa5f25640c1a312aecb1cdc30f","last_reissued_at":"2026-06-12T01:10:11.517978Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:10:11.517978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing Bipartiteness in Logarithmic Rounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ronitt Rubinfeld, Yumou Fei","submitted_at":"2026-06-11T17:07:00Z","abstract_excerpt":"The seminal work of Goldreich and Ron (\\textit{Combinatorica, 1999}) showed that bipartiteness of bounded-degree graphs can be tested using $O(\\sqrt{n\\log n})$ random walks of length $O(\\log^{6} n)$. In this work, we improve their result by showing that $O(\\sqrt{n})$ random walks of length $O(\\log n)$ suffice. As a corollary, we obtain an $O(\\log n)$-pass, $O(\\sqrt{n}\\log n)$-space streaming algorithm for testing bipartiteness, whose pass complexity is optimal in light of a recent lower bound of Fei, Minzer, and Wang (\\textit{arXiv, 2026}).\n  Our proof takes a different approach from that of G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13583","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13583/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.13583","created_at":"2026-06-12T01:10:11.518115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.13583v1","created_at":"2026-06-12T01:10:11.518115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13583","created_at":"2026-06-12T01:10:11.518115+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMSMFZ5JS42F","created_at":"2026-06-12T01:10:11.518115+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMSMFZ5JS42FEOG6","created_at":"2026-06-12T01:10:11.518115+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMSMFZ5J","created_at":"2026-06-12T01:10:11.518115+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/EMSMFZ5JS42FEOG622DKNA5WAY","json":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY.json","graph_json":"https://pith.science/api/pith-number/EMSMFZ5JS42FEOG622DKNA5WAY/graph.json","events_json":"https://pith.science/api/pith-number/EMSMFZ5JS42FEOG622DKNA5WAY/events.json","paper":"https://pith.science/paper/EMSMFZ5J"},"agent_actions":{"view_html":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY","download_json":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY.json","view_paper":"https://pith.science/paper/EMSMFZ5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.13583&json=true","fetch_graph":"https://pith.science/api/pith-number/EMSMFZ5JS42FEOG622DKNA5WAY/graph.json","fetch_events":"https://pith.science/api/pith-number/EMSMFZ5JS42FEOG622DKNA5WAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY/action/storage_attestation","attest_author":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY/action/author_attestation","sign_citation":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY/action/citation_signature","submit_replication":"https://pith.science/pith/EMSMFZ5JS42FEOG622DKNA5WAY/action/replication_record"}},"created_at":"2026-06-12T01:10:11.518115+00:00","updated_at":"2026-06-12T01:10:11.518115+00:00"}