{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:U23W3BEBVPFL3FHNIVIS5X2CYB","short_pith_number":"pith:U23W3BEB","schema_version":"1.0","canonical_sha256":"a6b76d8481abcabd94ed45512edf42c07a219283be853ef3fad2d936c139f61e","source":{"kind":"arxiv","id":"1405.6740","version":1},"attestation_state":"computed","paper":{"title":"Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Mikl\\'os Ab\\'ert, P\\'eter Csikv\\'ari, Tam\\'as Hubai","submitted_at":"2014-05-26T20:20:56Z","abstract_excerpt":"We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer-dimer partition function of a sequence of finite graphs converging to L.\n  This allows us to express the monomer-dimer free energy of L in terms of the measure. Exploiting an analytic advantage of the matching measure over the Mayer series then leads to new, rigorous bounds on the monomer-dimer free energies of various Euclidean lattices. While our estimates use only the computational data given in previous papers, they improve the known bounds"},"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":"1405.6740","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-26T20:20:56Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"f9e19154c9e0a71e854798da6f395ebca2a428d6dce1dd83e373100aaf0522f4","abstract_canon_sha256":"4101de2804bd152b37c322a3e2b54c09f6bdb8563868253a56a8e49ba4baf364"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:46.625794Z","signature_b64":"8YKPKC8fXi7sX3LlNv96QsAC0Gzpua4AjZR8SAErq2mL2DZiJMobiE2ag4YA+KCnYA3FrjBVzVon9L8Q/QGjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6b76d8481abcabd94ed45512edf42c07a219283be853ef3fad2d936c139f61e","last_reissued_at":"2026-05-18T01:31:46.625400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:46.625400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Mikl\\'os Ab\\'ert, P\\'eter Csikv\\'ari, Tam\\'as Hubai","submitted_at":"2014-05-26T20:20:56Z","abstract_excerpt":"We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer-dimer partition function of a sequence of finite graphs converging to L.\n  This allows us to express the monomer-dimer free energy of L in terms of the measure. Exploiting an analytic advantage of the matching measure over the Mayer series then leads to new, rigorous bounds on the monomer-dimer free energies of various Euclidean lattices. While our estimates use only the computational data given in previous papers, they improve the known bounds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6740","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":"1405.6740","created_at":"2026-05-18T01:31:46.625472+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6740v1","created_at":"2026-05-18T01:31:46.625472+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6740","created_at":"2026-05-18T01:31:46.625472+00:00"},{"alias_kind":"pith_short_12","alias_value":"U23W3BEBVPFL","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"U23W3BEBVPFL3FHN","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"U23W3BEB","created_at":"2026-05-18T12:28:52.271510+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/U23W3BEBVPFL3FHNIVIS5X2CYB","json":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB.json","graph_json":"https://pith.science/api/pith-number/U23W3BEBVPFL3FHNIVIS5X2CYB/graph.json","events_json":"https://pith.science/api/pith-number/U23W3BEBVPFL3FHNIVIS5X2CYB/events.json","paper":"https://pith.science/paper/U23W3BEB"},"agent_actions":{"view_html":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB","download_json":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB.json","view_paper":"https://pith.science/paper/U23W3BEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6740&json=true","fetch_graph":"https://pith.science/api/pith-number/U23W3BEBVPFL3FHNIVIS5X2CYB/graph.json","fetch_events":"https://pith.science/api/pith-number/U23W3BEBVPFL3FHNIVIS5X2CYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB/action/storage_attestation","attest_author":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB/action/author_attestation","sign_citation":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB/action/citation_signature","submit_replication":"https://pith.science/pith/U23W3BEBVPFL3FHNIVIS5X2CYB/action/replication_record"}},"created_at":"2026-05-18T01:31:46.625472+00:00","updated_at":"2026-05-18T01:31:46.625472+00:00"}