{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZARDKWXVE2VALZDFRLXRMBO4OK","short_pith_number":"pith:ZARDKWXV","schema_version":"1.0","canonical_sha256":"c822355af526aa05e4658aef1605dc72b99e5c3ab5c85276efe7c0363ab97cae","source":{"kind":"arxiv","id":"1903.07531","version":1},"attestation_state":"computed","paper":{"title":"Counting independent sets and colorings on random regular bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao","submitted_at":"2019-03-18T16:17:36Z","abstract_excerpt":"We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every $\\Delta$-regular bipartite graph if $\\Delta\\ge 53$. In the weighted case, for all sufficiently large integers $\\Delta$ and weight parameters $\\lambda=\\tilde\\Omega\\left(\\frac{1}{\\Delta}\\right)$, we also obtain an FPTAS on almost every $\\Delta$-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all $q\\ge 3$ and sufficiently large integers $\\Delta=\\Delta(q"},"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":"1903.07531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-18T16:17:36Z","cross_cats_sorted":[],"title_canon_sha256":"e173d5403408f50e508d6c860677902a3e161204850c006bc06b3101de9b6ebb","abstract_canon_sha256":"643d3799c5a2e5da55c77c644507b8c0f3a3ea4c94d9df06592b81f0704bdedf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:01.131106Z","signature_b64":"EX4QCL+32YJCNEA0Y5moTIR2lZAonRDOEbY9Z7jIuN+vm1pagttK2qCostCDfcLUx7XotG9AnENdy63nM6/AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c822355af526aa05e4658aef1605dc72b99e5c3ab5c85276efe7c0363ab97cae","last_reissued_at":"2026-05-17T23:51:01.130434Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:01.130434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting independent sets and colorings on random regular bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao","submitted_at":"2019-03-18T16:17:36Z","abstract_excerpt":"We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every $\\Delta$-regular bipartite graph if $\\Delta\\ge 53$. In the weighted case, for all sufficiently large integers $\\Delta$ and weight parameters $\\lambda=\\tilde\\Omega\\left(\\frac{1}{\\Delta}\\right)$, we also obtain an FPTAS on almost every $\\Delta$-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all $q\\ge 3$ and sufficiently large integers $\\Delta=\\Delta(q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07531","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":"1903.07531","created_at":"2026-05-17T23:51:01.130551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07531v1","created_at":"2026-05-17T23:51:01.130551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07531","created_at":"2026-05-17T23:51:01.130551+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZARDKWXVE2VA","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZARDKWXVE2VALZDF","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZARDKWXV","created_at":"2026-05-18T12:33:33.725879+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/ZARDKWXVE2VALZDFRLXRMBO4OK","json":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK.json","graph_json":"https://pith.science/api/pith-number/ZARDKWXVE2VALZDFRLXRMBO4OK/graph.json","events_json":"https://pith.science/api/pith-number/ZARDKWXVE2VALZDFRLXRMBO4OK/events.json","paper":"https://pith.science/paper/ZARDKWXV"},"agent_actions":{"view_html":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK","download_json":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK.json","view_paper":"https://pith.science/paper/ZARDKWXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07531&json=true","fetch_graph":"https://pith.science/api/pith-number/ZARDKWXVE2VALZDFRLXRMBO4OK/graph.json","fetch_events":"https://pith.science/api/pith-number/ZARDKWXVE2VALZDFRLXRMBO4OK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK/action/storage_attestation","attest_author":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK/action/author_attestation","sign_citation":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK/action/citation_signature","submit_replication":"https://pith.science/pith/ZARDKWXVE2VALZDFRLXRMBO4OK/action/replication_record"}},"created_at":"2026-05-17T23:51:01.130551+00:00","updated_at":"2026-05-17T23:51:01.130551+00:00"}