{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EUE4IEOWVYW5A3Y4QO5E3DPGFL","short_pith_number":"pith:EUE4IEOW","schema_version":"1.0","canonical_sha256":"2509c411d6ae2dd06f1c83ba4d8de62adf87325ce330268f05a8d5f4c58a835a","source":{"kind":"arxiv","id":"1002.0988","version":2},"attestation_state":"computed","paper":{"title":"On Darboux Integrable Semi-Discrete Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Alfia Sakieva, Ismagil Habibullin, Natalya Zheltukhina","submitted_at":"2010-02-04T12:56:07Z","abstract_excerpt":"Differential-difference equation $\\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux integrable, if there exist two functions (called integrals) $F$ and $I$ of a finite number of dynamical variables 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: $Dp(n)=p(n+1)$. It is proved that the integrals can be brought to some canonical form. A method of construction of an ex"},"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":"1002.0988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-02-04T12:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"1d64604cb251ff4106bd7a03e0ae6bb64d4de1257a50995dce70409b64ff2193","abstract_canon_sha256":"ea497813863fcdb2365bd4d658485d4fbbd8caf87701dd1e2c7580514583a44c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:53.882838Z","signature_b64":"BSMtakxx0m5T1EvlSkUQ0wdFLMJSUlgenS5BYopjF8FmyK7WNzOOXoY30TUqTx/9FH5Bx4QwRTKh3GNQ4i+QBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2509c411d6ae2dd06f1c83ba4d8de62adf87325ce330268f05a8d5f4c58a835a","last_reissued_at":"2026-05-18T04:29:53.882121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:53.882121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Darboux Integrable Semi-Discrete Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Alfia Sakieva, Ismagil Habibullin, Natalya Zheltukhina","submitted_at":"2010-02-04T12:56:07Z","abstract_excerpt":"Differential-difference equation $\\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux integrable, if there exist two functions (called integrals) $F$ and $I$ of a finite number of dynamical variables 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: $Dp(n)=p(n+1)$. It is proved that the integrals can be brought to some canonical form. A method of construction of an ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0988","kind":"arxiv","version":2},"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":"1002.0988","created_at":"2026-05-18T04:29:53.882234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0988v2","created_at":"2026-05-18T04:29:53.882234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0988","created_at":"2026-05-18T04:29:53.882234+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUE4IEOWVYW5","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUE4IEOWVYW5A3Y4","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUE4IEOW","created_at":"2026-05-18T12:26:06.534383+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/EUE4IEOWVYW5A3Y4QO5E3DPGFL","json":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL.json","graph_json":"https://pith.science/api/pith-number/EUE4IEOWVYW5A3Y4QO5E3DPGFL/graph.json","events_json":"https://pith.science/api/pith-number/EUE4IEOWVYW5A3Y4QO5E3DPGFL/events.json","paper":"https://pith.science/paper/EUE4IEOW"},"agent_actions":{"view_html":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL","download_json":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL.json","view_paper":"https://pith.science/paper/EUE4IEOW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0988&json=true","fetch_graph":"https://pith.science/api/pith-number/EUE4IEOWVYW5A3Y4QO5E3DPGFL/graph.json","fetch_events":"https://pith.science/api/pith-number/EUE4IEOWVYW5A3Y4QO5E3DPGFL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL/action/storage_attestation","attest_author":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL/action/author_attestation","sign_citation":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL/action/citation_signature","submit_replication":"https://pith.science/pith/EUE4IEOWVYW5A3Y4QO5E3DPGFL/action/replication_record"}},"created_at":"2026-05-18T04:29:53.882234+00:00","updated_at":"2026-05-18T04:29:53.882234+00:00"}