{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:CB6SSLORZQLYNEPN2W2FYY4C4D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0d8aae26129783387162a8a8d7d865a6407c3fbd7501f7191433ff58c76d4117","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-09-15T17:34:44Z","title_canon_sha256":"27328e9a9926aa89842089f5e7c9f199d2168255375a33429a7dd8c3d78385b3"},"schema_version":"1.0","source":{"id":"cond-mat/0309352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0309352","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0309352v2","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0309352","created_at":"2026-05-18T01:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"CB6SSLORZQLY","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"CB6SSLORZQLYNEPN","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"CB6SSLOR","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:e237da997130d891ecdc66b3c2f1c2d9eb98babd27b23b6ccfc1ee14b7461fc7","target":"graph","created_at":"2026-05-18T01:39:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovasz local lemma -- which provides a sufficient condition for this to occur -- corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial i","authors_text":"Alan D. Sokal, Alexander D. Scott","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-09-15T17:34:44Z","title":"The repulsive lattice gas, the independent-set polynomial, and the Lov\\'asz local lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0309352","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cbe16bc2d1b63ce94f274f38efd32168a20342b58bb84dc83b2314da236eedd5","target":"record","created_at":"2026-05-18T01:39:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0d8aae26129783387162a8a8d7d865a6407c3fbd7501f7191433ff58c76d4117","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-09-15T17:34:44Z","title_canon_sha256":"27328e9a9926aa89842089f5e7c9f199d2168255375a33429a7dd8c3d78385b3"},"schema_version":"1.0","source":{"id":"cond-mat/0309352","kind":"arxiv","version":2}},"canonical_sha256":"107d292dd1cc178691edd5b45c6382e0e762ac0d05ac9c4595deae2bc18a012d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"107d292dd1cc178691edd5b45c6382e0e762ac0d05ac9c4595deae2bc18a012d","first_computed_at":"2026-05-18T01:39:59.205454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:59.205454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cecp0qQs/FbHMU8FYbfrVSspbJGgb+RG13aL4ZFVxrluZPiArVzF/YbZENp6cei02v/jlpQHR+fPQrQGYHASAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:59.206022Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0309352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbe16bc2d1b63ce94f274f38efd32168a20342b58bb84dc83b2314da236eedd5","sha256:e237da997130d891ecdc66b3c2f1c2d9eb98babd27b23b6ccfc1ee14b7461fc7"],"state_sha256":"4bf00d0548d3b37bd5932e5a91add78006430714f633c50bab37e04270f50481"}