{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XTWLWRX7WLIDJAYVCCYGIEZJSA","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":"454c6689e50f494cac9e4a6b029e879d91ae5f78f61906387e9d9e052ed8fd61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-07-05T05:54:12Z","title_canon_sha256":"b12bb9a166b0a6c56cf20562758723ba352c7a659ec9b69bce497970ebe85106"},"schema_version":"1.0","source":{"id":"1107.0784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0784","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0784v2","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0784","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"XTWLWRX7WLID","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XTWLWRX7WLIDJAYV","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XTWLWRX7","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:913ba8a6f972dbf08aa594ee379e91fb4a0b86ac4560a82a174866d91cefcf76","target":"graph","created_at":"2026-05-18T02:01:24Z","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 new approach to construction of recursion operators for multidimensional integrable systems which have a Lax-type representation in terms of a pair of commuting vector fields. It is illustrated by the examples of the Manakov--Santini system which is a hyperbolic system in N dependent and N + 4 independent variables, where N is an arbitrary natural number, the six-dimensional generalization of the first heavenly equation, the modified heavenly equation, and the dispersionless Hirota equation.","authors_text":"A. Sergyeyev, M. Marvan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-07-05T05:54:12Z","title":"Recursion operators for dispersionless integrable systems in any dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0784","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:fc9a6f85bd8ea595ddf263a905601e4e649dd2b9389fd1e4c7313bf0044176e8","target":"record","created_at":"2026-05-18T02:01:24Z","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":"454c6689e50f494cac9e4a6b029e879d91ae5f78f61906387e9d9e052ed8fd61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-07-05T05:54:12Z","title_canon_sha256":"b12bb9a166b0a6c56cf20562758723ba352c7a659ec9b69bce497970ebe85106"},"schema_version":"1.0","source":{"id":"1107.0784","kind":"arxiv","version":2}},"canonical_sha256":"bcecbb46ffb2d034831510b0641329901f65cfcbcc443700c1ae7690fdcb134c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcecbb46ffb2d034831510b0641329901f65cfcbcc443700c1ae7690fdcb134c","first_computed_at":"2026-05-18T02:01:24.831083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:24.831083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qudZOqLv4OdaCO4Zk6YOI4U0ZuHyYsnjzDrZpOX9nmjGV0gYIbsuaT1lPqGjHLbUmDbSvVEFBcokUqE/qsQ5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:24.831496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc9a6f85bd8ea595ddf263a905601e4e649dd2b9389fd1e4c7313bf0044176e8","sha256:913ba8a6f972dbf08aa594ee379e91fb4a0b86ac4560a82a174866d91cefcf76"],"state_sha256":"e77cd9d03a3b9afd40dbdbcddd70e30f0cbbb74026080a817d9e4107e038ff18"}