{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:47O2WQZKE7YYMBUF2QT7ATA7FC","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":"1a6c6f2ba89988bf9474376aa6f28519164accee35a37096202a84c8fb01c574","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-20T15:26:47Z","title_canon_sha256":"1cc96ebc30979c951aa3d15c436cd949bc05ab1ce1289f87b57f9ff9563ab435"},"schema_version":"1.0","source":{"id":"1005.3736","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3736","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3736v2","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3736","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"47O2WQZKE7YY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"47O2WQZKE7YYMBUF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"47O2WQZK","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:eb14b4df10bb4ec7861842bc9ca1bf4d41b4c6b156c7ac36067195e4fffa798f","target":"graph","created_at":"2026-05-18T03:09:34Z","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":"New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear RD systems is examined to demonstrate applicability of the definitions proposed and it is shown when different definitions of $Q$-conditional symmetry lead to the same operators.","authors_text":"Roman Cherniha","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-20T15:26:47Z","title":"Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3736","kind":"arxiv","version":2},"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":"sha256:5219311eca377da699cd1f5fddceb1d3c7f21afeb4f825b3d013097d999de643","target":"record","created_at":"2026-05-18T03:09:34Z","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":"1a6c6f2ba89988bf9474376aa6f28519164accee35a37096202a84c8fb01c574","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-20T15:26:47Z","title_canon_sha256":"1cc96ebc30979c951aa3d15c436cd949bc05ab1ce1289f87b57f9ff9563ab435"},"schema_version":"1.0","source":{"id":"1005.3736","kind":"arxiv","version":2}},"canonical_sha256":"e7ddab432a27f1860685d427f04c1f288c1446e3d740bc690000d6bd4df70cd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ddab432a27f1860685d427f04c1f288c1446e3d740bc690000d6bd4df70cd2","first_computed_at":"2026-05-18T03:09:34.395196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:34.395196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DP47XyQqSfjVlOCVmsb6rfl/NStIgwDJtaBKHOe1cSyWt8gG4sJkBwJws99rKTe2yb+tG8g5cDw0PtLF8hJjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:34.395822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3736","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5219311eca377da699cd1f5fddceb1d3c7f21afeb4f825b3d013097d999de643","sha256:eb14b4df10bb4ec7861842bc9ca1bf4d41b4c6b156c7ac36067195e4fffa798f"],"state_sha256":"3de1ed2fef5144106e52b69a3f21d5e7b03f0e465ccec10d2b255842dc430718"}