{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:KJXILAQWMZGUBBBLILK5UVEOUH","short_pith_number":"pith:KJXILAQW","canonical_record":{"source":{"id":"nlin/0606036","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2006-06-13T15:10:36Z","cross_cats_sorted":[],"title_canon_sha256":"ca1605140dc1ab160edbe9c9e8fa108779a9919c158a94c2aa7827f199aa23a8","abstract_canon_sha256":"f72fbebd0ada4cb2e0585ffc47112485b35363fcba12b3c72f29e8221e9cd969"},"schema_version":"1.0"},"canonical_sha256":"526e858216664d40842b42d5da548ea1fa7b59f88e4a1e70601af79eaade321a","source":{"kind":"arxiv","id":"nlin/0606036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0606036","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0606036v1","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0606036","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"KJXILAQWMZGU","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KJXILAQWMZGUBBBL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KJXILAQW","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:KJXILAQWMZGUBBBLILK5UVEOUH","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0606036","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2006-06-13T15:10:36Z","cross_cats_sorted":[],"title_canon_sha256":"ca1605140dc1ab160edbe9c9e8fa108779a9919c158a94c2aa7827f199aa23a8","abstract_canon_sha256":"f72fbebd0ada4cb2e0585ffc47112485b35363fcba12b3c72f29e8221e9cd969"},"schema_version":"1.0"},"canonical_sha256":"526e858216664d40842b42d5da548ea1fa7b59f88e4a1e70601af79eaade321a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:18.043736Z","signature_b64":"wOAy7q2QqFtTybpcdYO1nZxPLA1LcD3ZEWQxKpkZ3pAclqldOO9aAcOmf11NrDLbvCGcwqEjm1wwKASt9oryBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"526e858216664d40842b42d5da548ea1fa7b59f88e4a1e70601af79eaade321a","last_reissued_at":"2026-05-18T01:38:18.043080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:18.043080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0606036","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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MILE+yXVMsbHDk1AXaK8h9Whgem89kIeK3rzcdkAlGEq6g0xa5FTetZEnMm9cvCD7qFzUGlHrPHkWE8tgaczDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:11:49.786137Z"},"content_sha256":"6979f3b74316d8d81bac6fd6281172dbfd5bf37b4af3d504a58737a2b9ef536d","schema_version":"1.0","event_id":"sha256:6979f3b74316d8d81bac6fd6281172dbfd5bf37b4af3d504a58737a2b9ef536d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:KJXILAQWMZGUBBBLILK5UVEOUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of $(2+1)$--dimensional commutative and noncommutative integrable equations","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Jing Ping Wang","submitted_at":"2006-06-13T15:10:36Z","abstract_excerpt":"We develop the symbolic representation method to derive the hierarchies of $(2+1)$-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in ${\\mathbb C}$ or a noncommutative associative algebra. We prove that these hierarchies are indeed quasi-local in the commutative case as conjectured by Mikhailov and Yamilov in 1998. We propose a ring extension based on the symbolic representation. As examples, we give noncommutative vers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0606036","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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppkhfM3BC6hjyhuY+iL4RX3Egpl7tRNPSfrno98RlplY1cZqJSTyabVIE/l+MgbZ6MyfKuaiTBs+6QW6m7cGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:11:49.786957Z"},"content_sha256":"dca39c5d1b915d9c9cbb19e41f93fc985282b7cbe079b6aa1e792dc971570737","schema_version":"1.0","event_id":"sha256:dca39c5d1b915d9c9cbb19e41f93fc985282b7cbe079b6aa1e792dc971570737"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJXILAQWMZGUBBBLILK5UVEOUH/bundle.json","state_url":"https://pith.science/pith/KJXILAQWMZGUBBBLILK5UVEOUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJXILAQWMZGUBBBLILK5UVEOUH/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":"2026-06-06T11:11:49Z","links":{"resolver":"https://pith.science/pith/KJXILAQWMZGUBBBLILK5UVEOUH","bundle":"https://pith.science/pith/KJXILAQWMZGUBBBLILK5UVEOUH/bundle.json","state":"https://pith.science/pith/KJXILAQWMZGUBBBLILK5UVEOUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJXILAQWMZGUBBBLILK5UVEOUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KJXILAQWMZGUBBBLILK5UVEOUH","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":"f72fbebd0ada4cb2e0585ffc47112485b35363fcba12b3c72f29e8221e9cd969","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2006-06-13T15:10:36Z","title_canon_sha256":"ca1605140dc1ab160edbe9c9e8fa108779a9919c158a94c2aa7827f199aa23a8"},"schema_version":"1.0","source":{"id":"nlin/0606036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0606036","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0606036v1","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0606036","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"KJXILAQWMZGU","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KJXILAQWMZGUBBBL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KJXILAQW","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:dca39c5d1b915d9c9cbb19e41f93fc985282b7cbe079b6aa1e792dc971570737","target":"graph","created_at":"2026-05-18T01:38:18Z","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 develop the symbolic representation method to derive the hierarchies of $(2+1)$-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in ${\\mathbb C}$ or a noncommutative associative algebra. We prove that these hierarchies are indeed quasi-local in the commutative case as conjectured by Mikhailov and Yamilov in 1998. We propose a ring extension based on the symbolic representation. As examples, we give noncommutative vers","authors_text":"Jing Ping Wang","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2006-06-13T15:10:36Z","title":"On the structure of $(2+1)$--dimensional commutative and noncommutative integrable equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0606036","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":"sha256:6979f3b74316d8d81bac6fd6281172dbfd5bf37b4af3d504a58737a2b9ef536d","target":"record","created_at":"2026-05-18T01:38:18Z","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":"f72fbebd0ada4cb2e0585ffc47112485b35363fcba12b3c72f29e8221e9cd969","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2006-06-13T15:10:36Z","title_canon_sha256":"ca1605140dc1ab160edbe9c9e8fa108779a9919c158a94c2aa7827f199aa23a8"},"schema_version":"1.0","source":{"id":"nlin/0606036","kind":"arxiv","version":1}},"canonical_sha256":"526e858216664d40842b42d5da548ea1fa7b59f88e4a1e70601af79eaade321a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"526e858216664d40842b42d5da548ea1fa7b59f88e4a1e70601af79eaade321a","first_computed_at":"2026-05-18T01:38:18.043080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:18.043080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOAy7q2QqFtTybpcdYO1nZxPLA1LcD3ZEWQxKpkZ3pAclqldOO9aAcOmf11NrDLbvCGcwqEjm1wwKASt9oryBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:18.043736Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0606036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6979f3b74316d8d81bac6fd6281172dbfd5bf37b4af3d504a58737a2b9ef536d","sha256:dca39c5d1b915d9c9cbb19e41f93fc985282b7cbe079b6aa1e792dc971570737"],"state_sha256":"15593d9aff72e96ab6da5a197f84799d8cea206da34c3ea78a34d07e9a4a9750"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGiH+eJnadjW3Gt61jRqODQ9yQnzA17/9VhBsvYiA9O4P/lgS4jiETNeS+ED3x9JSbVd5Xz9kH/EsVQgTolzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T11:11:49.792375Z","bundle_sha256":"74278dd4952f27d71c611a9f0fd867659fc21d248491fe07272a2cce6f3cc6d8"}}