{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:FBUP7LJFZC2OYAXCHO2WDWWPYW","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":"b2c6732085d6df5d9970cfebc7e7a989367e462fb8e4d2356971171a765f5ed6","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-04-01T04:13:13Z","title_canon_sha256":"7b49bb60571232d15b2824cadc5918aa7ef6731e099ee0693cae0f94fd55b8a1"},"schema_version":"1.0","source":{"id":"math-ph/0304003","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0304003","created_at":"2026-07-04T14:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0304003v3","created_at":"2026-07-04T14:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0304003","created_at":"2026-07-04T14:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"FBUP7LJFZC2O","created_at":"2026-07-04T14:33:47Z"},{"alias_kind":"pith_short_16","alias_value":"FBUP7LJFZC2OYAXC","created_at":"2026-07-04T14:33:47Z"},{"alias_kind":"pith_short_8","alias_value":"FBUP7LJF","created_at":"2026-07-04T14:33:47Z"}],"graph_snapshots":[{"event_id":"sha256:1da70cc74528f1e4492cf3655fb2603cedd7659bb66d0c22d221bacc7ef65011","target":"graph","created_at":"2026-07-04T14:33:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0304003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are also presented. The results are applied to systems of interacting classical and quantum particles, and to a lattice polymer model.","authors_text":"Daniel Ueltschi","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2003-04-01T04:13:13Z","title":"Cluster expansions and correlation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0304003","kind":"arxiv","version":3},"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":"sha256:90e6bc65032aa8aff6df64549124573a32801e0d7724858714832c1665db6800","target":"record","created_at":"2026-07-04T14:33:47Z","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":"b2c6732085d6df5d9970cfebc7e7a989367e462fb8e4d2356971171a765f5ed6","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-04-01T04:13:13Z","title_canon_sha256":"7b49bb60571232d15b2824cadc5918aa7ef6731e099ee0693cae0f94fd55b8a1"},"schema_version":"1.0","source":{"id":"math-ph/0304003","kind":"arxiv","version":3}},"canonical_sha256":"2868ffad25c8b4ec02e23bb561dacfc5b24959a3554e6176ad9ed9d93cc6a6e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2868ffad25c8b4ec02e23bb561dacfc5b24959a3554e6176ad9ed9d93cc6a6e0","first_computed_at":"2026-07-04T14:33:47.823037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:33:47.823037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hi4ATukbdgojlHXiNVW2KRyGccAMbk+Qr3ZrpjJY1ez9H22xFDZ3DLZBgEv46/myUz4aj/fIG1+srCAl7eiwAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:33:47.823381Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0304003","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e6bc65032aa8aff6df64549124573a32801e0d7724858714832c1665db6800","sha256:1da70cc74528f1e4492cf3655fb2603cedd7659bb66d0c22d221bacc7ef65011"],"state_sha256":"236e940035790551263bd1a60a167c9185f1cad5ba76db63b380260bb5d6b6fb"}