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The counting problem is formulated as computing a partition function that gives the sum of the weights of all matchings in a hypergraph. This problem unifies two extensively studied statistical physics models in approximate counting: the hardcore model (graph independent sets) and the monomer-dimer model (graph matchings).\n  For this model, the critical activity $\\lambda_c="},"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":"1503.05812","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-19T15:55:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4f8d865273231b5931a4e71217320ab7330cf69e8325f389ce5ce045c1b9d4b7","abstract_canon_sha256":"a7e3d059bd8d05b6da4380fd77fc04789432749a22c9f804360cc02d4bb3564a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:17.834755Z","signature_b64":"WpLwc3Qw3OZAWR6vZOJmh3hWG9LVj54ca2UMjj6wdvD5cCooReYLclqEqw92SiR2XnS6MvnurhZxq7nePK2mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"894a6125abc5ef43497b784975916b02e6771cb32a5122187bfe96a11addcd13","last_reissued_at":"2026-05-18T00:53:17.834222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:17.834222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting hypergraph matchings up to uniqueness threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Jinman Zhao, Renjie Song, Yitong Yin","submitted_at":"2015-03-19T15:55:36Z","abstract_excerpt":"We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. 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