{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2EFWZIJGLHM64IMNJWKQJUAMT5","short_pith_number":"pith:2EFWZIJG","schema_version":"1.0","canonical_sha256":"d10b6ca12659d9ee218d4d9504d00c9f497a237beb4ffd823b51d7ed5707a34f","source":{"kind":"arxiv","id":"1009.2403","version":1},"attestation_state":"computed","paper":{"title":"Cosymmetries and Nijenhuis recursion operators for difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis","submitted_at":"2010-09-13T14:20:23Z","abstract_excerpt":"In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion operator for the Viallet equation. Moreover, we show that this operator is Nijenhuis and thus generates infinitely many commuting local symmetries. This recursion operator and its factorisation into Hami"},"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":"1009.2403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-09-13T14:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"7c135f77ebd492197aa7867e7bb9d65240ef6ac3e4cf1b528afebc4ec4788931","abstract_canon_sha256":"f1ed85fab694ebcd628ad4d66a1f81185dc8ad7b9a631c6a3ff307fc4584d8dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:31.215005Z","signature_b64":"wdfZI22cvk3Mp+CoSAnI0XrB6Dcvn2dQbyVO7s+RJ3nTQooehk+HdL6S7ulz6FrxUU8kQfb/HYTFitgWAMM2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10b6ca12659d9ee218d4d9504d00c9f497a237beb4ffd823b51d7ed5707a34f","last_reissued_at":"2026-05-18T02:05:31.214347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:31.214347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cosymmetries and Nijenhuis recursion operators for difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis","submitted_at":"2010-09-13T14:20:23Z","abstract_excerpt":"In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion operator for the Viallet equation. Moreover, we show that this operator is Nijenhuis and thus generates infinitely many commuting local symmetries. This recursion operator and its factorisation into Hami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2403","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":"1009.2403","created_at":"2026-05-18T02:05:31.214420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2403v1","created_at":"2026-05-18T02:05:31.214420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2403","created_at":"2026-05-18T02:05:31.214420+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EFWZIJGLHM6","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EFWZIJGLHM64IMN","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EFWZIJG","created_at":"2026-05-18T12:26:03.138858+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/2EFWZIJGLHM64IMNJWKQJUAMT5","json":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5.json","graph_json":"https://pith.science/api/pith-number/2EFWZIJGLHM64IMNJWKQJUAMT5/graph.json","events_json":"https://pith.science/api/pith-number/2EFWZIJGLHM64IMNJWKQJUAMT5/events.json","paper":"https://pith.science/paper/2EFWZIJG"},"agent_actions":{"view_html":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5","download_json":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5.json","view_paper":"https://pith.science/paper/2EFWZIJG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2403&json=true","fetch_graph":"https://pith.science/api/pith-number/2EFWZIJGLHM64IMNJWKQJUAMT5/graph.json","fetch_events":"https://pith.science/api/pith-number/2EFWZIJGLHM64IMNJWKQJUAMT5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5/action/storage_attestation","attest_author":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5/action/author_attestation","sign_citation":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5/action/citation_signature","submit_replication":"https://pith.science/pith/2EFWZIJGLHM64IMNJWKQJUAMT5/action/replication_record"}},"created_at":"2026-05-18T02:05:31.214420+00:00","updated_at":"2026-05-18T02:05:31.214420+00:00"}