{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RFCYY5ZPJP4SFK5XJFBUUI2RQL","short_pith_number":"pith:RFCYY5ZP","schema_version":"1.0","canonical_sha256":"89458c772f4bf922abb749434a235182d70c1daa11c2105c37e2155318fe149d","source":{"kind":"arxiv","id":"1806.11548","version":4},"attestation_state":"computed","paper":{"title":"Algorithmic Pirogov-Sinai theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Guus Regts, Tyler Helmuth, Will Perkins","submitted_at":"2018-06-29T17:32:10Z","abstract_excerpt":"We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\\mathbb Z^d$ and on the torus $(\\mathbb Z/n \\mathbb Z)^d$. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-core model at sufficiently high fugacity on subsets of $\\mathbb Z^d$ with "},"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":"1806.11548","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-29T17:32:10Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.PR"],"title_canon_sha256":"d62059fffd2691998ff63e82d9515e34a3230d7d9b7955674e97fc7d5f1cc5e6","abstract_canon_sha256":"0685f567d3096ace40e765e1f6831c1568c92cb681bcef91bc4be412bf87d884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:21:11.343172Z","signature_b64":"np+tl7VO9wqyTdMRk4dNHrWiHlS9XOpBSGLfHnIslF2NUI53mTVgwd4s8+wGXROr2rb5mcUF1x/C6bSQJBsHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89458c772f4bf922abb749434a235182d70c1daa11c2105c37e2155318fe149d","last_reissued_at":"2026-07-05T06:21:11.342781Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:21:11.342781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithmic Pirogov-Sinai theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Guus Regts, Tyler Helmuth, Will Perkins","submitted_at":"2018-06-29T17:32:10Z","abstract_excerpt":"We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\\mathbb Z^d$ and on the torus $(\\mathbb Z/n \\mathbb Z)^d$. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-core model at sufficiently high fugacity on subsets of $\\mathbb Z^d$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11548","kind":"arxiv","version":4},"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/1806.11548/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":"1806.11548","created_at":"2026-07-05T06:21:11.342834+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.11548v4","created_at":"2026-07-05T06:21:11.342834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11548","created_at":"2026-07-05T06:21:11.342834+00:00"},{"alias_kind":"pith_short_12","alias_value":"RFCYY5ZPJP4S","created_at":"2026-07-05T06:21:11.342834+00:00"},{"alias_kind":"pith_short_16","alias_value":"RFCYY5ZPJP4SFK5X","created_at":"2026-07-05T06:21:11.342834+00:00"},{"alias_kind":"pith_short_8","alias_value":"RFCYY5ZP","created_at":"2026-07-05T06:21:11.342834+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/RFCYY5ZPJP4SFK5XJFBUUI2RQL","json":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL.json","graph_json":"https://pith.science/api/pith-number/RFCYY5ZPJP4SFK5XJFBUUI2RQL/graph.json","events_json":"https://pith.science/api/pith-number/RFCYY5ZPJP4SFK5XJFBUUI2RQL/events.json","paper":"https://pith.science/paper/RFCYY5ZP"},"agent_actions":{"view_html":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL","download_json":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL.json","view_paper":"https://pith.science/paper/RFCYY5ZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.11548&json=true","fetch_graph":"https://pith.science/api/pith-number/RFCYY5ZPJP4SFK5XJFBUUI2RQL/graph.json","fetch_events":"https://pith.science/api/pith-number/RFCYY5ZPJP4SFK5XJFBUUI2RQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL/action/storage_attestation","attest_author":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL/action/author_attestation","sign_citation":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL/action/citation_signature","submit_replication":"https://pith.science/pith/RFCYY5ZPJP4SFK5XJFBUUI2RQL/action/replication_record"}},"created_at":"2026-07-05T06:21:11.342834+00:00","updated_at":"2026-07-05T06:21:11.342834+00:00"}