{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ORZDG5RDDPKHQWIDEMJQ2DD5DO","short_pith_number":"pith:ORZDG5RD","schema_version":"1.0","canonical_sha256":"74723376231bd478590323130d0c7d1b9c0f5cf609c05647fd6f5286d69bfc0c","source":{"kind":"arxiv","id":"2606.03975","version":1},"attestation_state":"computed","paper":{"title":"Planar Perfect Matching Counting is as Hard as Determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CC","authors_text":"Jiaheng Wang, Radu Curticapean","submitted_at":"2026-06-02T17:56:22Z","abstract_excerpt":"In the 1960s, Fisher, Kasteleyn and Temperley designed an ingenious algorithm for computing the partition function of the dimer model, or equivalently, for counting perfect matchings in edge-weighted planar graphs (Philos. Mag. 1961; J. Mathematical Phys. 1963). This FKT algorithm later became the foundation for Valiant's holographic algorithms (FOCS 2004; SIAM J. Comput. 2008), which motivated the study of counting problems under the Holant framework. Combined with an algorithm by Yuster (FOCS 2008), the FKT algorithm allows us to count edge-weighted perfect matchings in planar $n$-vertex gra"},"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":"2606.03975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-06-02T17:56:22Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"160d89811334449bbc33faad3ae812a2142f5877df1e08ecc4b5305f020a8ada","abstract_canon_sha256":"7551f441a287f33a217356ca6f62b2059782f88a8142339809f951f67e082f79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:08.402591Z","signature_b64":"QgVceVsxPm8dX9AQavtsZnoKqnZuuP0FkAtfVa+oF7e1lv9uo2rQoFEtktwZJfbjvWJ+4B933svjls2eK/UvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74723376231bd478590323130d0c7d1b9c0f5cf609c05647fd6f5286d69bfc0c","last_reissued_at":"2026-06-03T02:06:08.402170Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:08.402170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar Perfect Matching Counting is as Hard as Determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CC","authors_text":"Jiaheng Wang, Radu Curticapean","submitted_at":"2026-06-02T17:56:22Z","abstract_excerpt":"In the 1960s, Fisher, Kasteleyn and Temperley designed an ingenious algorithm for computing the partition function of the dimer model, or equivalently, for counting perfect matchings in edge-weighted planar graphs (Philos. Mag. 1961; J. Mathematical Phys. 1963). This FKT algorithm later became the foundation for Valiant's holographic algorithms (FOCS 2004; SIAM J. Comput. 2008), which motivated the study of counting problems under the Holant framework. Combined with an algorithm by Yuster (FOCS 2008), the FKT algorithm allows us to count edge-weighted perfect matchings in planar $n$-vertex gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03975","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/2606.03975/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":"2606.03975","created_at":"2026-06-03T02:06:08.402226+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.03975v1","created_at":"2026-06-03T02:06:08.402226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03975","created_at":"2026-06-03T02:06:08.402226+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORZDG5RDDPKH","created_at":"2026-06-03T02:06:08.402226+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORZDG5RDDPKHQWID","created_at":"2026-06-03T02:06:08.402226+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORZDG5RD","created_at":"2026-06-03T02:06:08.402226+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/ORZDG5RDDPKHQWIDEMJQ2DD5DO","json":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO.json","graph_json":"https://pith.science/api/pith-number/ORZDG5RDDPKHQWIDEMJQ2DD5DO/graph.json","events_json":"https://pith.science/api/pith-number/ORZDG5RDDPKHQWIDEMJQ2DD5DO/events.json","paper":"https://pith.science/paper/ORZDG5RD"},"agent_actions":{"view_html":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO","download_json":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO.json","view_paper":"https://pith.science/paper/ORZDG5RD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.03975&json=true","fetch_graph":"https://pith.science/api/pith-number/ORZDG5RDDPKHQWIDEMJQ2DD5DO/graph.json","fetch_events":"https://pith.science/api/pith-number/ORZDG5RDDPKHQWIDEMJQ2DD5DO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO/action/storage_attestation","attest_author":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO/action/author_attestation","sign_citation":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO/action/citation_signature","submit_replication":"https://pith.science/pith/ORZDG5RDDPKHQWIDEMJQ2DD5DO/action/replication_record"}},"created_at":"2026-06-03T02:06:08.402226+00:00","updated_at":"2026-06-03T02:06:08.402226+00:00"}