{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:P5U25WLMRH2BIEMQ2E5FTUCHRH","short_pith_number":"pith:P5U25WLM","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"},"canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","source":{"kind":"arxiv","id":"0907.3785","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3785","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3785v1","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3785","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"P5U25WLMRH2B","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P5U25WLMRH2BIEMQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P5U25WLM","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:P5U25WLMRH2BIEMQ2E5FTUCHRH","target":"record","payload":{"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"},"canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","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"},"source_kind":"arxiv","source_id":"0907.3785","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhEDINu2Kep0Snxel3aKEInauyiCkoNqkaME4hMtu2B2VumJyC5Xqh/H6qF2PO0keSQvPXeWAHnGY7qs8vCxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:22:50.475659Z"},"content_sha256":"8bf315d4171c6480816bd36176f17788ff4bd83f1c7cd145939c292cd83decc8","schema_version":"1.0","event_id":"sha256:8bf315d4171c6480816bd36176f17788ff4bd83f1c7cd145939c292cd83decc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:P5U25WLMRH2BIEMQ2E5FTUCHRH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLa0CoiPUTVxiQ2zwizQ1+wqdDGtJ/PKr5Rw+vQs77S76iytBnQMOTzNgtEyc9hOdHI6oev3OmPVpETtowkfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:22:50.475988Z"},"content_sha256":"55d16903f3467d104e4be75e8944dc2a2f696f32a527e3a4691c33c1d5f786c9","schema_version":"1.0","event_id":"sha256:55d16903f3467d104e4be75e8944dc2a2f696f32a527e3a4691c33c1d5f786c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/bundle.json","state_url":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T20:22:50Z","links":{"resolver":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH","bundle":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/bundle.json","state":"https://pith.science/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5U25WLMRH2BIEMQ2E5FTUCHRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:P5U25WLMRH2BIEMQ2E5FTUCHRH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f39b7934606d9d632ba132e6c069f51795795934fc1a47ae37f340c9cec03aea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-07-22T07:00:34Z","title_canon_sha256":"ce905cd10b905361903a731bd59c8d73bc14c84a4a749bcd58f7b7eebe3000a0"},"schema_version":"1.0","source":{"id":"0907.3785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3785","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3785v1","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3785","created_at":"2026-05-18T02:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"P5U25WLMRH2B","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P5U25WLMRH2BIEMQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P5U25WLM","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:55d16903f3467d104e4be75e8944dc2a2f696f32a527e3a4691c33c1d5f786c9","target":"graph","created_at":"2026-05-18T02:12:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Asli Pekcan, Ismagil Habibullin, Natalya Zheltukhina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-07-22T07:00:34Z","title":"Complete list of Darboux Integrable Chains of the form $t_{1x}=t_x+d(t,t_1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3785","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8bf315d4171c6480816bd36176f17788ff4bd83f1c7cd145939c292cd83decc8","target":"record","created_at":"2026-05-18T02:12:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f39b7934606d9d632ba132e6c069f51795795934fc1a47ae37f340c9cec03aea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-07-22T07:00:34Z","title_canon_sha256":"ce905cd10b905361903a731bd59c8d73bc14c84a4a749bcd58f7b7eebe3000a0"},"schema_version":"1.0","source":{"id":"0907.3785","kind":"arxiv","version":1}},"canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f69aed96c89f4141190d13a59d04789c7aa91a794f40d9c0dc6b5a3629d5abf","first_computed_at":"2026-05-18T02:12:54.796184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:54.796184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmhNSh8+7i566TYt40tJtw/YCxn7KnZkmGdT9wOUtosmAYeG/QtOh/uMRjpSj6CXnJyeFVamX42tZEO9jB2OBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:54.796710Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.3785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bf315d4171c6480816bd36176f17788ff4bd83f1c7cd145939c292cd83decc8","sha256:55d16903f3467d104e4be75e8944dc2a2f696f32a527e3a4691c33c1d5f786c9"],"state_sha256":"c636b953f18326b3cf758f2f4984b45c2b0387a76a3b4418e74c7cf86e2d867d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EBSTjDG3iNh2PmRhlbIh7nBugbeAwPntTqCxEicZj1Kq4Z7QFBhRTUnllUd/IeGqKpp91KuiLhjLRxqjcQY1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:22:50.477817Z","bundle_sha256":"e69887dba83e284ef92399350e0e004a36e0bc56390b679cc792ce41486ca810"}}