{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IMTV45ATYSCWNXN7LB27WFATDG","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":"b8eceac7da0221f2f32bcecf5d3731a260f8be31a81419f40b24be6ebe1ef668","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-01-27T20:08:30Z","title_canon_sha256":"7ee8db604874488de7db65d0a90a0058736bb9353d07e1450f45ad9336464d0e"},"schema_version":"1.0","source":{"id":"1101.5375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5375","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5375v2","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5375","created_at":"2026-05-18T04:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"IMTV45ATYSCW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IMTV45ATYSCWNXN7","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IMTV45AT","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:43d9ef76bc9d60b58399a04d74156baa937a9efd49260d2980cbac0d013f2143","target":"graph","created_at":"2026-05-18T04:18:34Z","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":"In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian part and a complemental \"pure non-Lagrangian\" balance system. In the case when derivatives of the dynamical fields do not enter the constitutive relations of the balance system, the \"pure non-Lagrangian\" systems coincide with the systems introduced by S. Godunov [Soviet Math. Dokl.","authors_text":"Serge Preston","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-01-27T20:08:30Z","title":"Balance Systems and the Variational Bicomplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5375","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":"sha256:4f7d053c9a5787cbe3d6384d24932fd5adfc9c4c34e268e1ca24e9dfe23b1cde","target":"record","created_at":"2026-05-18T04:18:34Z","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":"b8eceac7da0221f2f32bcecf5d3731a260f8be31a81419f40b24be6ebe1ef668","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-01-27T20:08:30Z","title_canon_sha256":"7ee8db604874488de7db65d0a90a0058736bb9353d07e1450f45ad9336464d0e"},"schema_version":"1.0","source":{"id":"1101.5375","kind":"arxiv","version":2}},"canonical_sha256":"43275e7413c48566ddbf5875fb141319a96f107e00167671fc1ad2ae47ea58f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43275e7413c48566ddbf5875fb141319a96f107e00167671fc1ad2ae47ea58f2","first_computed_at":"2026-05-18T04:18:34.530244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:34.530244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCPerRTshHFxK3OJNdUKYY7c8PjCDBxRKVMoZE8uosM6QfuoeEDFSQevRurVFAYj9DiNLjZq/ZLlcY1abGC9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:34.530847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f7d053c9a5787cbe3d6384d24932fd5adfc9c4c34e268e1ca24e9dfe23b1cde","sha256:43d9ef76bc9d60b58399a04d74156baa937a9efd49260d2980cbac0d013f2143"],"state_sha256":"b751d5be54acf28a2269f89250e98053c893b27a8f9d9e8918f22d8d1a33d5d4"}