{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:32D6DL7RUTCYR57BS6FX6CDT33","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":"377fb5738dd76445e5167dea2d18dbaf1abf938d3d9ade63fdf066b48ed97cc7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-10-11T09:18:27Z","title_canon_sha256":"3033af01733a06444fae5ad61e05af23a353353177f82e7b431928f9dc0a64b1"},"schema_version":"1.0","source":{"id":"1010.2046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2046","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2046v1","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2046","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"32D6DL7RUTCY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"32D6DL7RUTCYR57B","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"32D6DL7R","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c33bc7aeff02146d46a725a668c647f4384e4ae07fc14b8ce9fef0a1b38e1aef","target":"graph","created_at":"2026-05-18T04:39:29Z","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":"Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm involving a mapping between classes of differential equations, which is generated by a family of point transformations. A special attention is paid for checking whether reduction operators are inequivalent to Lie symmetry operators. The derived reduction operators are applied to construction of exact solutions.","authors_text":"C. Sophocleous, O.O. Vaneeva, R.O. Popovych","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-10-11T09:18:27Z","title":"Reduction operators of variable coefficient semilinear diffusion equations with an exponential source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2046","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:aff1c97aff9a75c6cebd49844d7700839c9377cbf6c1056f7cef076836aa42d9","target":"record","created_at":"2026-05-18T04:39:29Z","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":"377fb5738dd76445e5167dea2d18dbaf1abf938d3d9ade63fdf066b48ed97cc7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-10-11T09:18:27Z","title_canon_sha256":"3033af01733a06444fae5ad61e05af23a353353177f82e7b431928f9dc0a64b1"},"schema_version":"1.0","source":{"id":"1010.2046","kind":"arxiv","version":1}},"canonical_sha256":"de87e1aff1a4c588f7e1978b7f0873dedc994529fa0907db64189856e137d16f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de87e1aff1a4c588f7e1978b7f0873dedc994529fa0907db64189856e137d16f","first_computed_at":"2026-05-18T04:39:29.822928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:29.822928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BonRJohg1sgj1TqbBnALxqiHb5TNvBeBgS5HxFxABCaaSK5ydOkIkmAWNDN6bZI5K4LTTgCUXyMPD30UuGkAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:29.823500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aff1c97aff9a75c6cebd49844d7700839c9377cbf6c1056f7cef076836aa42d9","sha256:c33bc7aeff02146d46a725a668c647f4384e4ae07fc14b8ce9fef0a1b38e1aef"],"state_sha256":"5bda256d632c866e8b8beab07cf4b6c3a21c5dac46b550697f2c5ba2cab5ecec"}