{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DRCCUNRNSF2MDKW26PKSO33S3B","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":"8a87c9d13dad8488c556f81eb06f9f19963cca421bf6c6382e8a94b57fd8a8a5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-05T17:14:14Z","title_canon_sha256":"b8a67ed960f1df6dc2f33edae67d6df2b82b7fe7421041075c9ec24582005ccd"},"schema_version":"1.0","source":{"id":"1604.01337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01337","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01337v2","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01337","created_at":"2026-05-18T00:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"DRCCUNRNSF2M","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DRCCUNRNSF2MDKW2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DRCCUNRN","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:f17c2a2ac3ae5c3c13ed37078b695a05573176ed7b5c80ca2f1d2c838f711738","target":"graph","created_at":"2026-05-18T00:49:18Z","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 study microcanonical lattice gas models with long range interactions, including power law interactions. We rigorously obtain a variational principle for the entropy. In a one dimensional example, we find a first order phase transition by proving the entropy is non-differentiable along a certain curve.","authors_text":"David Aristoff, Lingjiong Zhu","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-05T17:14:14Z","title":"Lattice Gas Models with Long Range Interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01337","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":"sha256:7dc5dcbb6e47a4dd76719f66a04ac8345dcd8a05fc3fc643d1e6436470abcde3","target":"record","created_at":"2026-05-18T00:49:18Z","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":"8a87c9d13dad8488c556f81eb06f9f19963cca421bf6c6382e8a94b57fd8a8a5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-05T17:14:14Z","title_canon_sha256":"b8a67ed960f1df6dc2f33edae67d6df2b82b7fe7421041075c9ec24582005ccd"},"schema_version":"1.0","source":{"id":"1604.01337","kind":"arxiv","version":2}},"canonical_sha256":"1c442a362d9174c1aadaf3d5276f72d850854aa6020ec3285c52fbefbd5aa7c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c442a362d9174c1aadaf3d5276f72d850854aa6020ec3285c52fbefbd5aa7c1","first_computed_at":"2026-05-18T00:49:18.915437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:18.915437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yg7mDGy5YQcd2sl3xmGBzkiGL+JkNeXX+oRqUh9FRdWrFcFvCteBYBuhZmQUy+CMRVrvuasjHHFk2e1SYG/5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:18.915927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dc5dcbb6e47a4dd76719f66a04ac8345dcd8a05fc3fc643d1e6436470abcde3","sha256:f17c2a2ac3ae5c3c13ed37078b695a05573176ed7b5c80ca2f1d2c838f711738"],"state_sha256":"d7365aae0e1f9c09636e5f980a8b9497c9d5a2d57f94917e222a48e65b245734"}