{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:3DJWOYHG4DXMX5LGFICMM4SJLU","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":"3ce510e0613d4a44936745a42784441fbc9fbab5f13b01ab907f30b29e2fc511","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.SI"],"license":"","primary_cat":"solv-int","submitted_at":"1999-01-31T15:12:17Z","title_canon_sha256":"d494558aceadf35608d1978536d9e19bc2253c8183e1a197a52814dd718d3f1a"},"schema_version":"1.0","source":{"id":"solv-int/9902002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"solv-int/9902002","created_at":"2026-05-18T00:34:05Z"},{"alias_kind":"arxiv_version","alias_value":"solv-int/9902002v1","created_at":"2026-05-18T00:34:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.solv-int/9902002","created_at":"2026-05-18T00:34:05Z"},{"alias_kind":"pith_short_12","alias_value":"3DJWOYHG4DXM","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"3DJWOYHG4DXMX5LG","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"3DJWOYHG","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:1edcb51d58465371a247139897ac2952644ba8d469d076f64111ea59a8ef48fb","target":"graph","created_at":"2026-05-18T00:34:05Z","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 present the explicit formulae, describing the structure of symmetries and formal symmetries of any scalar (1+1)-dimensional evolution equation. Using these results, the formulae for the leading terms of commutators of two symmetries and two formal symmetries are found. The generalization of these results to the case of system of evolution equations is also discussed.","authors_text":"Artur G. Sergyeyev (= Arthur G. Sergheyev) (Institute of Mathematics of NAS of Ukraine, Kyiv)","cross_cats":["math-ph","math.AP","math.MP","nlin.SI"],"headline":"","license":"","primary_cat":"solv-int","submitted_at":"1999-01-31T15:12:17Z","title":"On time-dependent symmetries and formal symmetries of evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9902002","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":"sha256:2030aad4512eaf954da8647fb824f8f1e9cc5d4b6ae781cd0ebeb25c2c120719","target":"record","created_at":"2026-05-18T00:34:05Z","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":"3ce510e0613d4a44936745a42784441fbc9fbab5f13b01ab907f30b29e2fc511","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.SI"],"license":"","primary_cat":"solv-int","submitted_at":"1999-01-31T15:12:17Z","title_canon_sha256":"d494558aceadf35608d1978536d9e19bc2253c8183e1a197a52814dd718d3f1a"},"schema_version":"1.0","source":{"id":"solv-int/9902002","kind":"arxiv","version":1}},"canonical_sha256":"d8d36760e6e0eecbf5662a04c672495d1550828e52094ddbaaba63a5f7d557fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8d36760e6e0eecbf5662a04c672495d1550828e52094ddbaaba63a5f7d557fe","first_computed_at":"2026-05-18T00:34:05.624186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:05.624186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"knMREYwX9m/uVYrxYTsSwj72+D1m16mrbfxxOeFXxvhO1YPI1TLK4MJ0eZPC5VsixoiaXBesJdsZPykue4TAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:05.624899Z","signed_message":"canonical_sha256_bytes"},"source_id":"solv-int/9902002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2030aad4512eaf954da8647fb824f8f1e9cc5d4b6ae781cd0ebeb25c2c120719","sha256:1edcb51d58465371a247139897ac2952644ba8d469d076f64111ea59a8ef48fb"],"state_sha256":"be7fa6ef726ef9e80dc556ce0b0ec38ce793dfd15d6061452c15ffba67a8db89"}