{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:J33NYQEUIEZWLHTHIGLP2DE26K","short_pith_number":"pith:J33NYQEU","schema_version":"1.0","canonical_sha256":"4ef6dc40944133659e674196fd0c9af282b9a0c932b719113aa4f7fcedcc4480","source":{"kind":"arxiv","id":"math-ph/0207023","version":1},"attestation_state":"computed","paper":{"title":"A precise definition of reduction of partial differential equations","license":"","headline":"","cross_cats":["math.AP","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Ivan M. Tsyfra, Renat Z. Zhdanov, Roman O. Popovych","submitted_at":"2002-07-18T17:13:05Z","abstract_excerpt":"We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math-ph/0207023","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-07-18T17:13:05Z","cross_cats_sorted":["math.AP","math.MP","nlin.SI"],"title_canon_sha256":"f7e58d0761b1662c771a3e27ae39a2ca042ce5afc5c8a19b1810726086224562","abstract_canon_sha256":"95c84ffb0b358a24dd4b16d1570fd92895b3fca3cf159ab51efb71c5127ef2f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:21.015461Z","signature_b64":"iT2T/jVcf1Oktt2uKY3+doXVu/CSQmVXgB3GOepIHMykf7NApBQeVWVxKysJaeawJU+hk7dRGT8kFsPheXbdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ef6dc40944133659e674196fd0c9af282b9a0c932b719113aa4f7fcedcc4480","last_reissued_at":"2026-05-18T04:37:21.015040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:21.015040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A precise definition of reduction of partial differential equations","license":"","headline":"","cross_cats":["math.AP","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Ivan M. Tsyfra, Renat Z. Zhdanov, Roman O. Popovych","submitted_at":"2002-07-18T17:13:05Z","abstract_excerpt":"We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0207023","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0207023","created_at":"2026-05-18T04:37:21.015100+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0207023v1","created_at":"2026-05-18T04:37:21.015100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0207023","created_at":"2026-05-18T04:37:21.015100+00:00"},{"alias_kind":"pith_short_12","alias_value":"J33NYQEUIEZW","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"J33NYQEUIEZWLHTH","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"J33NYQEU","created_at":"2026-05-18T12:25:50.845339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K","json":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K.json","graph_json":"https://pith.science/api/pith-number/J33NYQEUIEZWLHTHIGLP2DE26K/graph.json","events_json":"https://pith.science/api/pith-number/J33NYQEUIEZWLHTHIGLP2DE26K/events.json","paper":"https://pith.science/paper/J33NYQEU"},"agent_actions":{"view_html":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K","download_json":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K.json","view_paper":"https://pith.science/paper/J33NYQEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0207023&json=true","fetch_graph":"https://pith.science/api/pith-number/J33NYQEUIEZWLHTHIGLP2DE26K/graph.json","fetch_events":"https://pith.science/api/pith-number/J33NYQEUIEZWLHTHIGLP2DE26K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K/action/storage_attestation","attest_author":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K/action/author_attestation","sign_citation":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K/action/citation_signature","submit_replication":"https://pith.science/pith/J33NYQEUIEZWLHTHIGLP2DE26K/action/replication_record"}},"created_at":"2026-05-18T04:37:21.015100+00:00","updated_at":"2026-05-18T04:37:21.015100+00:00"}