{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:PDCNFE2IWSW45GODORYF5BWEGV","short_pith_number":"pith:PDCNFE2I","schema_version":"1.0","canonical_sha256":"78c4d29348b4adce99c374705e86c43572d67a0e51ab6181df662d0a54a3a2ef","source":{"kind":"arxiv","id":"0804.2020","version":3},"attestation_state":"computed","paper":{"title":"Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Artur Sergyeyev","submitted_at":"2008-04-12T18:08:57Z","abstract_excerpt":"We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\\alpha)z z_x, z_t &=& (1-2\\alpha)z_{xx} - 4\\alpha z w_x + (4-8\\alpha)w z_x - (4+8\\alpha)w^2 z + (-2+4\\alpha)z^3, (*) for which no recursion operator or master symmetry was known so far, and prove that the system (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal {\\em two-term} recursion relation rather than from a recursion operator."},"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":"0804.2020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-12T18:08:57Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9a987c2788b1b6b4476213816f3be9dd55448c513c6e2f9c03dca6fbd8b558f9","abstract_canon_sha256":"93e9460ac75ffe346b434c9e3ebe6bf6b362547eb0e103744d50a5f54cbffc99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:10.937765Z","signature_b64":"BcTEllV3D0WRycPPXPu9/A8QP5flywlPuGRCLQEGVglEt3e8kqYA9wKhJ4tlLEqBn0jhww7VmjmdKtdWZTWQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78c4d29348b4adce99c374705e86c43572d67a0e51ab6181df662d0a54a3a2ef","last_reissued_at":"2026-05-18T00:34:10.937006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:10.937006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Artur Sergyeyev","submitted_at":"2008-04-12T18:08:57Z","abstract_excerpt":"We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\\alpha)z z_x, z_t &=& (1-2\\alpha)z_{xx} - 4\\alpha z w_x + (4-8\\alpha)w z_x - (4+8\\alpha)w^2 z + (-2+4\\alpha)z^3, (*) for which no recursion operator or master symmetry was known so far, and prove that the system (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal {\\em two-term} recursion relation rather than from a recursion operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2020","kind":"arxiv","version":3},"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":"0804.2020","created_at":"2026-05-18T00:34:10.937125+00:00"},{"alias_kind":"arxiv_version","alias_value":"0804.2020v3","created_at":"2026-05-18T00:34:10.937125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.2020","created_at":"2026-05-18T00:34:10.937125+00:00"},{"alias_kind":"pith_short_12","alias_value":"PDCNFE2IWSW4","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"PDCNFE2IWSW45GOD","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"PDCNFE2I","created_at":"2026-05-18T12:25:57.157939+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/PDCNFE2IWSW45GODORYF5BWEGV","json":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV.json","graph_json":"https://pith.science/api/pith-number/PDCNFE2IWSW45GODORYF5BWEGV/graph.json","events_json":"https://pith.science/api/pith-number/PDCNFE2IWSW45GODORYF5BWEGV/events.json","paper":"https://pith.science/paper/PDCNFE2I"},"agent_actions":{"view_html":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV","download_json":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV.json","view_paper":"https://pith.science/paper/PDCNFE2I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0804.2020&json=true","fetch_graph":"https://pith.science/api/pith-number/PDCNFE2IWSW45GODORYF5BWEGV/graph.json","fetch_events":"https://pith.science/api/pith-number/PDCNFE2IWSW45GODORYF5BWEGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV/action/storage_attestation","attest_author":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV/action/author_attestation","sign_citation":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV/action/citation_signature","submit_replication":"https://pith.science/pith/PDCNFE2IWSW45GODORYF5BWEGV/action/replication_record"}},"created_at":"2026-05-18T00:34:10.937125+00:00","updated_at":"2026-05-18T00:34:10.937125+00:00"}