{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TYUJH2NREOI3CCI4L6MKCPN6UJ","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":"1f6ed967a33f681e2e288d21584e9f9bda9483aecaeb3d4523d7e008f030fa71","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-18T09:44:51Z","title_canon_sha256":"c442a38c6b923017e1694729a8ae6b2e7c5bd99a93c64a425ddae705a09b6de3"},"schema_version":"1.0","source":{"id":"1412.5780","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5780","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5780v3","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5780","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"TYUJH2NREOI3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TYUJH2NREOI3CCI4","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TYUJH2NR","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:eee2978a65edea59ac5822cb067bf59b08efee4a1c7b1ff5662b1048aac45f67","target":"graph","created_at":"2026-05-18T01:36:07Z","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":"It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fiel","authors_text":"Shin-itiro Goto","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-18T09:44:51Z","title":"Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5780","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":"sha256:570a62af4342c603b50728be591cf909858f59f68a40c241c8ba483f0f4181ae","target":"record","created_at":"2026-05-18T01:36:07Z","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":"1f6ed967a33f681e2e288d21584e9f9bda9483aecaeb3d4523d7e008f030fa71","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-18T09:44:51Z","title_canon_sha256":"c442a38c6b923017e1694729a8ae6b2e7c5bd99a93c64a425ddae705a09b6de3"},"schema_version":"1.0","source":{"id":"1412.5780","kind":"arxiv","version":3}},"canonical_sha256":"9e2893e9b12391b1091c5f98a13dbea2436e16ad4f316589a307e128fdf2247f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e2893e9b12391b1091c5f98a13dbea2436e16ad4f316589a307e128fdf2247f","first_computed_at":"2026-05-18T01:36:07.090142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:07.090142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HX4cbQhekChWiaH4txkzXr+48uXH+aEn06imRCgxlMm3xrP+zN/bT5JDB9sTe7zMZpeSr4QVyvTFfmf/4murCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:07.090676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5780","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:570a62af4342c603b50728be591cf909858f59f68a40c241c8ba483f0f4181ae","sha256:eee2978a65edea59ac5822cb067bf59b08efee4a1c7b1ff5662b1048aac45f67"],"state_sha256":"c6fdda6927d8a45ccb4ff808210bf414303055138b0bc1164d15411c33ee7fbf"}