{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:Y4RZHI3PD5MFJ4KBDAWAWW53XD","short_pith_number":"pith:Y4RZHI3P","schema_version":"1.0","canonical_sha256":"c72393a36f1f5854f141182c0b5bbbb8d3de3ff8e629c5fd59d2406f9fd27026","source":{"kind":"arxiv","id":"1002.0986","version":3},"attestation_state":"computed","paper":{"title":"Approximating the partition function of the ferromagnetic Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Leslie Ann Goldberg, Mark Jerrum","submitted_at":"2010-02-04T13:12:34Z","abstract_excerpt":"We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first order phase transition of the \"random cluster\" model, which is a probabi"},"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":"1002.0986","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-02-04T13:12:34Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"56d2109b9243373bba6215c38b5cb5e143396fe41762ca066e29aa6d969d7008","abstract_canon_sha256":"daf908a68b4fa714883f22006a3ba40373ff47f5fe040e38661bf32079444308"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:11.318309Z","signature_b64":"i1PB1hmdUZRtJSKgwY1ScwkOv/ZbU5F8r/fI8yN3IDj3MX4H0P4opRZFPJK0wH0FZC825xT1UfCNPjPrqc2+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c72393a36f1f5854f141182c0b5bbbb8d3de3ff8e629c5fd59d2406f9fd27026","last_reissued_at":"2026-05-18T03:41:11.317888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:11.317888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating the partition function of the ferromagnetic Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Leslie Ann Goldberg, Mark Jerrum","submitted_at":"2010-02-04T13:12:34Z","abstract_excerpt":"We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first order phase transition of the \"random cluster\" model, which is a probabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0986","kind":"arxiv","version":3},"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":"1002.0986","created_at":"2026-05-18T03:41:11.317952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0986v3","created_at":"2026-05-18T03:41:11.317952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0986","created_at":"2026-05-18T03:41:11.317952+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4RZHI3PD5MF","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4RZHI3PD5MFJ4KB","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4RZHI3P","created_at":"2026-05-18T12:26:17.028572+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/Y4RZHI3PD5MFJ4KBDAWAWW53XD","json":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD.json","graph_json":"https://pith.science/api/pith-number/Y4RZHI3PD5MFJ4KBDAWAWW53XD/graph.json","events_json":"https://pith.science/api/pith-number/Y4RZHI3PD5MFJ4KBDAWAWW53XD/events.json","paper":"https://pith.science/paper/Y4RZHI3P"},"agent_actions":{"view_html":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD","download_json":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD.json","view_paper":"https://pith.science/paper/Y4RZHI3P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0986&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4RZHI3PD5MFJ4KBDAWAWW53XD/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4RZHI3PD5MFJ4KBDAWAWW53XD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD/action/storage_attestation","attest_author":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD/action/author_attestation","sign_citation":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD/action/citation_signature","submit_replication":"https://pith.science/pith/Y4RZHI3PD5MFJ4KBDAWAWW53XD/action/replication_record"}},"created_at":"2026-05-18T03:41:11.317952+00:00","updated_at":"2026-05-18T03:41:11.317952+00:00"}