{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6NG7NA66GARCR46PDAWSXHEC2P","short_pith_number":"pith:6NG7NA66","canonical_record":{"source":{"id":"1209.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-09-18T07:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"dca06cb047bdd8d77f95ce456f28b203363029f1fe9f306da7926425e0856735","abstract_canon_sha256":"2a7cc45082f7b939757b694f34df13ccb1a6609c955fed2801a7d017f606c1d8"},"schema_version":"1.0"},"canonical_sha256":"f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40","source":{"kind":"arxiv","id":"1209.4231","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4231","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4231v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4231","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"6NG7NA66GARC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NG7NA66GARCR46P","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NG7NA66","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6NG7NA66GARCR46PDAWSXHEC2P","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-09-18T07:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"dca06cb047bdd8d77f95ce456f28b203363029f1fe9f306da7926425e0856735","abstract_canon_sha256":"2a7cc45082f7b939757b694f34df13ccb1a6609c955fed2801a7d017f606c1d8"},"schema_version":"1.0"},"canonical_sha256":"f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.245419Z","signature_b64":"SbhWdS28bv3hpHmBo0RJ4ZTeEVVurxV+Cii/JkEz7erx01la/6NT7OAqx8AIJCjycLNj2y/21k8+qpvtIaD8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40","last_reissued_at":"2026-05-18T02:54:47.244986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.244986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4231","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aw2gXBx961TBHumuXGKgSCqi1ikp7VxvqB5e/XPL+oNL1Ws1dYNOi3zaaOCUxd6Gn663NVvPxDoWGoaDdCEwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:15.219650Z"},"content_sha256":"f407ce78076f7ebae09c17e6c7bcd2c6dab7223d5b8ec37547ddcfd565f77d8e","schema_version":"1.0","event_id":"sha256:f407ce78076f7ebae09c17e6c7bcd2c6dab7223d5b8ec37547ddcfd565f77d8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6NG7NA66GARCR46PDAWSXHEC2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The microscopic meaning of grand potential: cluster properties of the one-dimensional lattice gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Agata Fronczak","submitted_at":"2012-09-18T07:13:51Z","abstract_excerpt":"We demonstrate, with a concrete example, how the combinatorial approach to a general system of particles, which was introduced in detail in the earlier paper arXiv:1205.4986, works and where it enters to provide a genuine extension of results obtainable by more traditional methods of statistical mechanics. To this end, an effort is made to study cluster properties of the one-dimensional lattice gas with nearest neighbor interactions. Three cases: the infinite temperature limit, the range of finite temperatures, and the zero temperature limit are discussed separately, yielding some new results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4231","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyX/Q1J6LryKu88nxLnjEo4qDO6AX9Fi07ZFQkICjo4EdP4EbNhAwxrhpLAWa+APNv308WBgd7/I7OPpUV2JCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:15.219997Z"},"content_sha256":"5af585c2b1073643e05ad9c2d4b76e4a162d649c54ea8b416270d0072e8807d4","schema_version":"1.0","event_id":"sha256:5af585c2b1073643e05ad9c2d4b76e4a162d649c54ea8b416270d0072e8807d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NG7NA66GARCR46PDAWSXHEC2P/bundle.json","state_url":"https://pith.science/pith/6NG7NA66GARCR46PDAWSXHEC2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NG7NA66GARCR46PDAWSXHEC2P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T10:30:15Z","links":{"resolver":"https://pith.science/pith/6NG7NA66GARCR46PDAWSXHEC2P","bundle":"https://pith.science/pith/6NG7NA66GARCR46PDAWSXHEC2P/bundle.json","state":"https://pith.science/pith/6NG7NA66GARCR46PDAWSXHEC2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NG7NA66GARCR46PDAWSXHEC2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6NG7NA66GARCR46PDAWSXHEC2P","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":"2a7cc45082f7b939757b694f34df13ccb1a6609c955fed2801a7d017f606c1d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-09-18T07:13:51Z","title_canon_sha256":"dca06cb047bdd8d77f95ce456f28b203363029f1fe9f306da7926425e0856735"},"schema_version":"1.0","source":{"id":"1209.4231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4231","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4231v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4231","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"6NG7NA66GARC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NG7NA66GARCR46P","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NG7NA66","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:5af585c2b1073643e05ad9c2d4b76e4a162d649c54ea8b416270d0072e8807d4","target":"graph","created_at":"2026-05-18T02:54:47Z","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"},"paper":{"abstract_excerpt":"We demonstrate, with a concrete example, how the combinatorial approach to a general system of particles, which was introduced in detail in the earlier paper arXiv:1205.4986, works and where it enters to provide a genuine extension of results obtainable by more traditional methods of statistical mechanics. To this end, an effort is made to study cluster properties of the one-dimensional lattice gas with nearest neighbor interactions. Three cases: the infinite temperature limit, the range of finite temperatures, and the zero temperature limit are discussed separately, yielding some new results ","authors_text":"Agata Fronczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-09-18T07:13:51Z","title":"The microscopic meaning of grand potential: cluster properties of the one-dimensional lattice gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4231","kind":"arxiv","version":1},"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:f407ce78076f7ebae09c17e6c7bcd2c6dab7223d5b8ec37547ddcfd565f77d8e","target":"record","created_at":"2026-05-18T02:54:47Z","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":"2a7cc45082f7b939757b694f34df13ccb1a6609c955fed2801a7d017f606c1d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-09-18T07:13:51Z","title_canon_sha256":"dca06cb047bdd8d77f95ce456f28b203363029f1fe9f306da7926425e0856735"},"schema_version":"1.0","source":{"id":"1209.4231","kind":"arxiv","version":1}},"canonical_sha256":"f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40","first_computed_at":"2026-05-18T02:54:47.244986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.244986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SbhWdS28bv3hpHmBo0RJ4ZTeEVVurxV+Cii/JkEz7erx01la/6NT7OAqx8AIJCjycLNj2y/21k8+qpvtIaD8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.245419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f407ce78076f7ebae09c17e6c7bcd2c6dab7223d5b8ec37547ddcfd565f77d8e","sha256:5af585c2b1073643e05ad9c2d4b76e4a162d649c54ea8b416270d0072e8807d4"],"state_sha256":"db39d4ae88f2afd8bc3fba1ebe249013ab263ad864d14a2f7b291104a71f8e52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zm2MWeDph8gele98IAxyoU+ydB2VcDcpQUaYVs0j/eHeXXhtsxZ3uAOy8wc/ajtLY0oWOyhw22K3I/iYWK0cDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:30:15.221909Z","bundle_sha256":"cbd8af874097b31b0c1c75ff4866ffe5892c6e6eeb0b6a5dcdb3227a32b56173"}}