{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OVJWOZAHYSRQPKWHXVKSOZTDDM","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":"b4a1e7575f653a56328fad193eb4eee8971aa65c4e205c18e32e6dac89caa544","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-08T17:39:58Z","title_canon_sha256":"93662774ab2ac199c35949d5aef8e96de5218e212ba6d55921f06a2a78d127a9"},"schema_version":"1.0","source":{"id":"1908.03211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03211","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03211v1","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03211","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"OVJWOZAHYSRQ","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_16","alias_value":"OVJWOZAHYSRQPKWH","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_8","alias_value":"OVJWOZAH","created_at":"2026-07-05T00:54:29Z"}],"graph_snapshots":[{"event_id":"sha256:eba896e8e57178bcf2ee4288a21196b867b803d03d27d54eb522b8c545af826c","target":"graph","created_at":"2026-07-05T00:54:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.03211/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we use quadratic forms diagonalization methods applied to the function thermodynamic energy to analyze the stability of physical systems. Taylor's expansion was useful to write a quadratic expression for the energy function. We consider the same methodology to expanding the thermodynamic entropy and investigate the signs of the second-order derivatives of the entropy as well as previously to the thermodynamic energy function. The signs of the second-order derivatives to the Helmholtz, enthalpy and Gibbs functions are also analysed. We show the immediate consequences on the stabi","authors_text":"F. N. Lima, J. M. de Sousa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-08T17:39:58Z","title":"Mathematical methods of diagonalization of quadratic forms applied to the study of stability of thermodynamic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03211","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":"sha256:77f78581df6e63e1c59e5be2b22edaf98f6b10d8c7924057150840d5f836e901","target":"record","created_at":"2026-07-05T00:54:29Z","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":"b4a1e7575f653a56328fad193eb4eee8971aa65c4e205c18e32e6dac89caa544","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-08T17:39:58Z","title_canon_sha256":"93662774ab2ac199c35949d5aef8e96de5218e212ba6d55921f06a2a78d127a9"},"schema_version":"1.0","source":{"id":"1908.03211","kind":"arxiv","version":1}},"canonical_sha256":"7553676407c4a307aac7bd552766631b2a8b9a7ca91e58bad283025a18ae3242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7553676407c4a307aac7bd552766631b2a8b9a7ca91e58bad283025a18ae3242","first_computed_at":"2026-07-05T00:54:29.937069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:29.937069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rd+vaRVAWgssgEd033bL7TP8R9ximyiymKKzYhdloafwfiVD8YZlVgc7iMJHIXT1xlWDxIBf4gyGrekkjxUNCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:29.937437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77f78581df6e63e1c59e5be2b22edaf98f6b10d8c7924057150840d5f836e901","sha256:eba896e8e57178bcf2ee4288a21196b867b803d03d27d54eb522b8c545af826c"],"state_sha256":"e143ed918c4e09db9e7308e66b1a1991279761ef977a02263efea04dbe5c82e1"}