{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YPYEZAHTTINNR3XE4IOE6NUS64","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":"45db571603245115ff1e2bcba14a583b6b1f257f1332d4c9c03fb67b196fde94","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-12T13:37:49Z","title_canon_sha256":"60aa6d39e584212b4b0789205b7251f7b6d1fc44b317d455d8cb3994c1a64992"},"schema_version":"1.0","source":{"id":"1010.2388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2388","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2388v1","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2388","created_at":"2026-05-18T04:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"YPYEZAHTTINN","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YPYEZAHTTINNR3XE","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YPYEZAHT","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:e87bbe2fc40f84b5bf03663eabf8c06b9f46d736ad80539d8d9c4c7ca0e7457f","target":"graph","created_at":"2026-05-18T04:39:28Z","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":"Nonclassical symmetries of a class of generalized Huxley equations of form $u_t=u_{xx}+k(x)u^2(1-u)$ are found. More precisely, for the class under consideration we completely classify reduction operators with $\\tau=1$ and give a wide number of examples of equations admitting reduction operators with $\\tau=0$.","authors_text":"C. Sophocleous, Nataliya M. Ivanova","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-12T13:37:49Z","title":"On nonclassical symmetries of generalized Huxley equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2388","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:d30727f05784f9cdab68594c5cfe6a2eddaa5f32908ed065beacb205ff500cf6","target":"record","created_at":"2026-05-18T04:39:28Z","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":"45db571603245115ff1e2bcba14a583b6b1f257f1332d4c9c03fb67b196fde94","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-12T13:37:49Z","title_canon_sha256":"60aa6d39e584212b4b0789205b7251f7b6d1fc44b317d455d8cb3994c1a64992"},"schema_version":"1.0","source":{"id":"1010.2388","kind":"arxiv","version":1}},"canonical_sha256":"c3f04c80f39a1ad8eee4e21c4f3692f715246241ab6b5524bceaace6cb84236f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3f04c80f39a1ad8eee4e21c4f3692f715246241ab6b5524bceaace6cb84236f","first_computed_at":"2026-05-18T04:39:28.099399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:28.099399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVuViHAgzRlnYM5z/Sx5RSdV8Nh5uw4YccECxoGQjf2r1/l90DMzzctmfDPsXpbfC/qzJ/elkQbOEoFwS7AbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:28.099993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d30727f05784f9cdab68594c5cfe6a2eddaa5f32908ed065beacb205ff500cf6","sha256:e87bbe2fc40f84b5bf03663eabf8c06b9f46d736ad80539d8d9c4c7ca0e7457f"],"state_sha256":"657ed94579611a6d905e1abf8aadd34d36be92b431610732a42e8ee7dc5255ec"}