{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IGJXLDW6FQFL2E4JY46RP6BB5H","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":"f54e51925be4fe4c753725bc3b0ce2d15e2a39c82b55a70aa3dda0f3fff157e1","cross_cats_sorted":["cond-mat.mes-hall"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-30T19:48:26Z","title_canon_sha256":"bc246847840911dd79a857ccc00ad7a5896414d1391eaab3a2534d995018626a"},"schema_version":"1.0","source":{"id":"0710.5743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5743","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5743v2","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5743","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"pith_short_12","alias_value":"IGJXLDW6FQFL","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IGJXLDW6FQFL2E4J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IGJXLDW6","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:75e518454ce224dd668b612421561eaf2447607e4d71df9d3f7a9d1eacc6dfd3","target":"graph","created_at":"2026-05-18T02:16:10Z","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":"When making the connection between the thermodynamics of irreversible processes and the theory of stochastic processes through the fluctuation-dissipation theorem, it is necessary to invoke a postulate of the Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations must be included, the velocity is a dynamical variable and although the entropy cannot depend directly on the velocity, $\\delta^{2} S$ will depend on velocity variations. Some authors do not include velocity variations in $\\delta^{2} S$, and so have to introduce a non-thermodynamic function which replaces the entr","authors_text":"A. J. McKane, F. Vazquez, M. A. Olivares-Robles","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-30T19:48:26Z","title":"The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic Fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5743","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:d417222160f66ea0430cc55feda4fef705396572db51f41e8cab58d66e8145bb","target":"record","created_at":"2026-05-18T02:16:10Z","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":"f54e51925be4fe4c753725bc3b0ce2d15e2a39c82b55a70aa3dda0f3fff157e1","cross_cats_sorted":["cond-mat.mes-hall"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-30T19:48:26Z","title_canon_sha256":"bc246847840911dd79a857ccc00ad7a5896414d1391eaab3a2534d995018626a"},"schema_version":"1.0","source":{"id":"0710.5743","kind":"arxiv","version":2}},"canonical_sha256":"4193758ede2c0abd1389c73d17f821e9e744fad93de48f9a0bba7e1ef8662ec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4193758ede2c0abd1389c73d17f821e9e744fad93de48f9a0bba7e1ef8662ec2","first_computed_at":"2026-05-18T02:16:10.071349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:10.071349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UrnM1wly4vp90l7WxnxlhKpMdqNRjQdVKBR/OrM060GzPgtroCry1cHALgeZuBA8ZMvxrjvZNe4UangnT9qYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:10.071897Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.5743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d417222160f66ea0430cc55feda4fef705396572db51f41e8cab58d66e8145bb","sha256:75e518454ce224dd668b612421561eaf2447607e4d71df9d3f7a9d1eacc6dfd3"],"state_sha256":"5d1236d5ecb087ca2c2c3dfd6be0713fda40b8aefb094286c596193e01ff9836"}