{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:72UB5VIIWO2GJWOPKYI5AM6TR6","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":"cd4e7a80a6726d26fadb8da956e2b031612eca358fe0aa6c3912ce8e80fad49f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T04:14:15Z","title_canon_sha256":"2807c6a186a7274e17afbeb56e470d66f3ad6d72f30a8d3dc1ae6017ed5229cb"},"schema_version":"1.0","source":{"id":"1302.4513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4513","created_at":"2026-05-18T03:33:13Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4513v1","created_at":"2026-05-18T03:33:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4513","created_at":"2026-05-18T03:33:13Z"},{"alias_kind":"pith_short_12","alias_value":"72UB5VIIWO2G","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"72UB5VIIWO2GJWOP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"72UB5VII","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:326705a4bbefac2e45a84f97fb341c5f213857f6d4f48d07a8876c1739605a65","target":"graph","created_at":"2026-05-18T03:33:13Z","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":"We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved density as the continuous conservation law, while its flux is found by replacing all derivatives of the conserved density appearing in the continuous flux by discrete gradients.","authors_text":"G R W Quispel, Robert I McLachlan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T04:14:15Z","title":"Discrete gradient methods have an energy conservation law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4513","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":"sha256:6da5ddf127389d003b42708000eacc132d14a7cd5f41ffd2720e40ee21e95fc2","target":"record","created_at":"2026-05-18T03:33:13Z","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":"cd4e7a80a6726d26fadb8da956e2b031612eca358fe0aa6c3912ce8e80fad49f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T04:14:15Z","title_canon_sha256":"2807c6a186a7274e17afbeb56e470d66f3ad6d72f30a8d3dc1ae6017ed5229cb"},"schema_version":"1.0","source":{"id":"1302.4513","kind":"arxiv","version":1}},"canonical_sha256":"fea81ed508b3b464d9cf5611d033d38fa2501caf3b175ef52ca300e9887a540f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fea81ed508b3b464d9cf5611d033d38fa2501caf3b175ef52ca300e9887a540f","first_computed_at":"2026-05-18T03:33:13.068175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:13.068175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDc1eunegVk7LiIDQ3lO6SEOdLrJ16Ub8K7st8bxIjHq0WIThFXPlvWzY4D2+acAJDbE+lcv3TZq9BkSQXrgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:13.068996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6da5ddf127389d003b42708000eacc132d14a7cd5f41ffd2720e40ee21e95fc2","sha256:326705a4bbefac2e45a84f97fb341c5f213857f6d4f48d07a8876c1739605a65"],"state_sha256":"a1e3491577c86283215a49939fc7cbd09f5ba1290318ecbea0addfa8e50d4af3"}