{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LKGAVBD3KWPOT2FVBWHEJRO7HC","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":"365689da2b6b255f17a7a8edb8448adf439c50a0ebd469f94d25c8511cb69042","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-09-21T06:59:45Z","title_canon_sha256":"bf546fa6023bfa762e3a7504764e98981128fee799ca41b70f516233d89adeea"},"schema_version":"1.0","source":{"id":"1209.4721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4721","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4721v2","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4721","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"LKGAVBD3KWPO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKGAVBD3KWPOT2FV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKGAVBD3","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:8d976196acbed076ff6a36a2ab55520c66cbec37d18f86902db348c1ebeded5b","target":"graph","created_at":"2026-05-18T03:15:32Z","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 present a method of determining a Lax representation for similarity reductions of autonomous and non-autonomous partial difference equations. This method may be used to obtain Lax representations that are general enough to provide the Lax integrability for entire hierarchies of reductions. A main result is, as an example of this framework, how we may obtain the q-Painlev\\'e equation whose group of B\\\"acklund transformations is an affine Weyl group of type E_6^{(1)} as a similarity reduction of the discrete Schwarzian Korteweg-de Vries equation.","authors_text":"C. M. Ormerod, G. R. W. Quispel, Peter H. van der Kamp","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-09-21T06:59:45Z","title":"Discrete Painlev\\'e equations and their Lax pairs as reductions of integrable lattice equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4721","kind":"arxiv","version":2},"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:b03a33ab21b6f9e95da7db80c7ac46c05e66aceec2d696c9b58e5346017c4561","target":"record","created_at":"2026-05-18T03:15:32Z","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":"365689da2b6b255f17a7a8edb8448adf439c50a0ebd469f94d25c8511cb69042","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-09-21T06:59:45Z","title_canon_sha256":"bf546fa6023bfa762e3a7504764e98981128fee799ca41b70f516233d89adeea"},"schema_version":"1.0","source":{"id":"1209.4721","kind":"arxiv","version":2}},"canonical_sha256":"5a8c0a847b559ee9e8b50d8e44c5df38a6bf1f27c5d69706c6030286033d4d34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a8c0a847b559ee9e8b50d8e44c5df38a6bf1f27c5d69706c6030286033d4d34","first_computed_at":"2026-05-18T03:15:32.568928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:32.568928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/oufRJdVnWU/2gQ7/3wGtX7AUVdwmbZtBXycPdG7n1TgEH4GV3/kORKB0ghnIdC/Fmf23TWPg+d92ylQNYqSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:32.569663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b03a33ab21b6f9e95da7db80c7ac46c05e66aceec2d696c9b58e5346017c4561","sha256:8d976196acbed076ff6a36a2ab55520c66cbec37d18f86902db348c1ebeded5b"],"state_sha256":"9a9598f5e37808215a7c3401c322f1f3b81860c16f90089fb6364c5807586279"}