{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NBNTPJNOQC4MEVWFOAU2RZFCOZ","short_pith_number":"pith:NBNTPJNO","schema_version":"1.0","canonical_sha256":"685b37a5ae80b8c256c57029a8e4a2767636499407d1d3ada54d9c554aaeabd4","source":{"kind":"arxiv","id":"2607.09617","version":1},"attestation_state":"computed","paper":{"title":"Generalized skew-gradient embedding for thermodynamically consistent systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qi Wang, Xuelong Gu","submitted_at":"2026-07-10T17:17:14Z","abstract_excerpt":"The skew-gradient embedding (SGE) framework~\\cite{GuWangSGE2025} reformulates a thermodynamically consistent system as a generalized gradient flow by embedding its zero-energy contribution in a skew-symmetric operator. In a time-discrete scheme, the profiles defining this operator may be evaluated at previous time levels. The resulting operator remains skew-symmetric, so its contribution to the discrete energy balance vanishes; this explicit treatment often decouples multiphysics systems. We show that this operator is not unique: the admissible gauges form an affine space, and we call the resu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.09617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-10T17:17:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"893c3e42b13a9efa4838fff76e800e3028f08e8b9fb11b415c80a191661df07a","abstract_canon_sha256":"0472e04d1285d8f45ea5f410a7d8ccb6ff162416d6036ff4bf0bac88d7486c83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:20:24.488868Z","signature_b64":"O4pTYLobM4n8xqMjGaybzbV0SIDA/hdbcIyzgh2ZPZWRytOPgVRONJXE59RLuOMpL+hB0xWm5lJzZPXnuEKJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"685b37a5ae80b8c256c57029a8e4a2767636499407d1d3ada54d9c554aaeabd4","last_reissued_at":"2026-07-13T01:20:24.487738Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:20:24.487738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized skew-gradient embedding for thermodynamically consistent systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qi Wang, Xuelong Gu","submitted_at":"2026-07-10T17:17:14Z","abstract_excerpt":"The skew-gradient embedding (SGE) framework~\\cite{GuWangSGE2025} reformulates a thermodynamically consistent system as a generalized gradient flow by embedding its zero-energy contribution in a skew-symmetric operator. In a time-discrete scheme, the profiles defining this operator may be evaluated at previous time levels. The resulting operator remains skew-symmetric, so its contribution to the discrete energy balance vanishes; this explicit treatment often decouples multiphysics systems. We show that this operator is not unique: the admissible gauges form an affine space, and we call the resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09617","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09617/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.09617","created_at":"2026-07-13T01:20:24.488309+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.09617v1","created_at":"2026-07-13T01:20:24.488309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09617","created_at":"2026-07-13T01:20:24.488309+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBNTPJNOQC4M","created_at":"2026-07-13T01:20:24.488309+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBNTPJNOQC4MEVWF","created_at":"2026-07-13T01:20:24.488309+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBNTPJNO","created_at":"2026-07-13T01:20:24.488309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ","json":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ.json","graph_json":"https://pith.science/api/pith-number/NBNTPJNOQC4MEVWFOAU2RZFCOZ/graph.json","events_json":"https://pith.science/api/pith-number/NBNTPJNOQC4MEVWFOAU2RZFCOZ/events.json","paper":"https://pith.science/paper/NBNTPJNO"},"agent_actions":{"view_html":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ","download_json":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ.json","view_paper":"https://pith.science/paper/NBNTPJNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.09617&json=true","fetch_graph":"https://pith.science/api/pith-number/NBNTPJNOQC4MEVWFOAU2RZFCOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NBNTPJNOQC4MEVWFOAU2RZFCOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ/action/storage_attestation","attest_author":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ/action/author_attestation","sign_citation":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ/action/citation_signature","submit_replication":"https://pith.science/pith/NBNTPJNOQC4MEVWFOAU2RZFCOZ/action/replication_record"}},"created_at":"2026-07-13T01:20:24.488309+00:00","updated_at":"2026-07-13T01:20:24.488309+00:00"}