{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KZC2DJ4LYWROSXMZ5AJRXVUNXZ","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":"6123dd3f6ed0a4265059980db41a3791dbdbd99228a73bc9a2741b8c98f7145b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-26T08:20:19Z","title_canon_sha256":"263a4014be61d12538f747e6fdd85eaabd11a041ca8e0c6fd92ae4bf56678ff6"},"schema_version":"1.0","source":{"id":"0908.3760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3760","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3760v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3760","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"KZC2DJ4LYWRO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KZC2DJ4LYWROSXMZ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KZC2DJ4L","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:715e9ab6f0b10db1f16698db4d1afd76dcdf9d237e213334a5b017958c6a022b","target":"graph","created_at":"2026-05-18T02:52:48Z","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":"A preliminary group classification of the class 2D nonlinear heat equations $u_t=f(x,y,u,u_x,u_y)(u_{xx}+u_{yy})$, where $f$ is arbitrary smooth function of the variables $x,y,u,u_x$ and $u_y$ using Lie method, is given. The paper is one of the few applications of an algebraic approach to the problem of group classification: the method of preliminary group classification.","authors_text":"Mehdi Nadjafikhah, Rouholah Bakhshandeh Chamazkoti","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-26T08:20:19Z","title":"Preliminarily group classification of a class of 2D nonlinear heat equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3760","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":"sha256:56cd07f80d3fe02e7138332eef5dc65f1023f2c8429e60c72d2cc6fefa83fcc6","target":"record","created_at":"2026-05-18T02:52:48Z","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":"6123dd3f6ed0a4265059980db41a3791dbdbd99228a73bc9a2741b8c98f7145b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-26T08:20:19Z","title_canon_sha256":"263a4014be61d12538f747e6fdd85eaabd11a041ca8e0c6fd92ae4bf56678ff6"},"schema_version":"1.0","source":{"id":"0908.3760","kind":"arxiv","version":1}},"canonical_sha256":"5645a1a78bc5a2e95d99e8131bd68dbe66949b3ff04627bca7fdf571eebdb2f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5645a1a78bc5a2e95d99e8131bd68dbe66949b3ff04627bca7fdf571eebdb2f4","first_computed_at":"2026-05-18T02:52:48.039160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:48.039160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/LHl35BsxwzhLOA1jf1sqSr5bSuspniIwBUOIZ4vtEvO4dKsTXFpphNCj3+YwxyG14omVOMrHVMNmZECiE4aDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:48.039559Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56cd07f80d3fe02e7138332eef5dc65f1023f2c8429e60c72d2cc6fefa83fcc6","sha256:715e9ab6f0b10db1f16698db4d1afd76dcdf9d237e213334a5b017958c6a022b"],"state_sha256":"d12b271f21e64f4fbd77562e788db52df8a2b2d62e8bbf04087317b9dfaf46cb"}