{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:P5U25WLMRH2BIEMQ2E5FTUCHRH","short_pith_number":"pith:P5U25WLM","schema_version":"1.0","canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","source":{"kind":"arxiv","id":"0907.3785","version":1},"attestation_state":"computed","paper":{"title":"Complete list of Darboux Integrable Chains of the form $t_{1x}=t_x+d(t,t_1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asli Pekcan, Ismagil Habibullin, Natalya Zheltukhina","submitted_at":"2009-07-22T07:00:34Z","abstract_excerpt":"We study differential-difference equation of the form $$ \\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\\frac{d}{dx}t(n,x)) $$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$. Equation of such kind is called Darboux integrable, if there exist two functions $F$ and $I$ of a finite number of arguments $x$, $\\{t(n\\pm k,x)\\}_{k=-\\infty}^\\infty$, ${\\frac{d^k}{dx^k}t(n,x)}_{k=1}^\\infty$, such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. Reformulation of Darboux integrability"},"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":"0907.3785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-07-22T07:00:34Z","cross_cats_sorted":[],"title_canon_sha256":"ce905cd10b905361903a731bd59c8d73bc14c84a4a749bcd58f7b7eebe3000a0","abstract_canon_sha256":"f39b7934606d9d632ba132e6c069f51795795934fc1a47ae37f340c9cec03aea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:54.796710Z","signature_b64":"MmhNSh8+7i566TYt40tJtw/YCxn7KnZkmGdT9wOUtosmAYeG/QtOh/uMRjpSj6CXnJyeFVamX42tZEO9jB2OBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","last_reissued_at":"2026-05-18T02:12:54.796184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:54.796184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete list of Darboux Integrable Chains of the form $t_{1x}=t_x+d(t,t_1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asli Pekcan, Ismagil Habibullin, Natalya Zheltukhina","submitted_at":"2009-07-22T07:00:34Z","abstract_excerpt":"We study differential-difference equation of the form $$ \\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\\frac{d}{dx}t(n,x)) $$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$. Equation of such kind is called Darboux integrable, if there exist two functions $F$ and $I$ of a finite number of arguments $x$, $\\{t(n\\pm k,x)\\}_{k=-\\infty}^\\infty$, ${\\frac{d^k}{dx^k}t(n,x)}_{k=1}^\\infty$, such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. Reformulation of Darboux integrability"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3785","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":"0907.3785","created_at":"2026-05-18T02:12:54.796272+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.3785v1","created_at":"2026-05-18T02:12:54.796272+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3785","created_at":"2026-05-18T02:12:54.796272+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5U25WLMRH2B","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5U25WLMRH2BIEMQ","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5U25WLM","created_at":"2026-05-18T12:26:01.383474+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/P5U25WLMRH2BIEMQ2E5FTUCHRH","json":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH.json","graph_json":"https://pith.science/api/pith-number/P5U25WLMRH2BIEMQ2E5FTUCHRH/graph.json","events_json":"https://pith.science/api/pith-number/P5U25WLMRH2BIEMQ2E5FTUCHRH/events.json","paper":"https://pith.science/paper/P5U25WLM"},"agent_actions":{"view_html":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH","download_json":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH.json","view_paper":"https://pith.science/paper/P5U25WLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.3785&json=true","fetch_graph":"https://pith.science/api/pith-number/P5U25WLMRH2BIEMQ2E5FTUCHRH/graph.json","fetch_events":"https://pith.science/api/pith-number/P5U25WLMRH2BIEMQ2E5FTUCHRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/action/storage_attestation","attest_author":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/action/author_attestation","sign_citation":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/action/citation_signature","submit_replication":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/action/replication_record"}},"created_at":"2026-05-18T02:12:54.796272+00:00","updated_at":"2026-05-18T02:12:54.796272+00:00"}