{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MTPWZ23T2YADQHGNADBCCGE5VK","short_pith_number":"pith:MTPWZ23T","canonical_record":{"source":{"id":"1208.1642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T11:09:39Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"e3e29fb6c7d2a55e76a75607eeadde94b5a3298788e29ebb0516be9107e78c94","abstract_canon_sha256":"46e865e205b7a96f440f9133289481b12f0046f2250cea2329a8b3c7c16f9a65"},"schema_version":"1.0"},"canonical_sha256":"64df6ceb73d600381ccd00c221189daa8a368cec79fd19585f95275ffc652993","source":{"kind":"arxiv","id":"1208.1642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1642","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1642v1","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1642","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"MTPWZ23T2YAD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MTPWZ23T2YADQHGN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MTPWZ23T","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MTPWZ23T2YADQHGNADBCCGE5VK","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T11:09:39Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"e3e29fb6c7d2a55e76a75607eeadde94b5a3298788e29ebb0516be9107e78c94","abstract_canon_sha256":"46e865e205b7a96f440f9133289481b12f0046f2250cea2329a8b3c7c16f9a65"},"schema_version":"1.0"},"canonical_sha256":"64df6ceb73d600381ccd00c221189daa8a368cec79fd19585f95275ffc652993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:11.010694Z","signature_b64":"r1yETdetobAyNFUn3q2a8ncyCsx3EZsrdE4VUbv24bXpQSmszjU7DZUo63BgaH1fIHKRoPjkQuSCtQdeV+QACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64df6ceb73d600381ccd00c221189daa8a368cec79fd19585f95275ffc652993","last_reissued_at":"2026-05-18T03:49:11.009818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:11.009818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1642","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":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/HnDAohnlSIM/FmsOwfrOW6rPPYc9n/sTX4tVwgpfSkGXtArj9r59QFw82AWjnwnS1KDIo3x8NGEusR7ETdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:52:16.092147Z"},"content_sha256":"f238d55edf563346b151ff4b5bc790e6393d837913a0f8438bc83742047f82d1","schema_version":"1.0","event_id":"sha256:f238d55edf563346b151ff4b5bc790e6393d837913a0f8438bc83742047f82d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MTPWZ23T2YADQHGNADBCCGE5VK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie--Poisson pencils related to semisimple Lie algebras: towards classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.DG","authors_text":"Andriy Panasyuk","submitted_at":"2012-08-08T11:09:39Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a vector space and $[,],[,]'$ be a pair of Lie brackets on $\\mathfrak{g}$. By definition they are compatible if $[,]+[,]'$ is again a Lie bracket. Such pairs play important role in bihamiltonian and $r$-matrix formalisms in the theory of integrable systems.\n  We propose an approach to a long standing problem of classification of such pairs in the case when one of them, say $[,]$, is semisimple. It is known that any such pair is determined by a linear operator on $(\\mathfrak{g},[,])$, which is defined up to adding a derivation. We propose a special fixing of this operator "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1642","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":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Boblh4mjrMn2qFNiWM/Ht3lRQuoNlTUYeBT5997tQ7sfWB4+qYSPB/G9Wfo4jQOJStwgZA/KEiqgVnKX7lDsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:52:16.092508Z"},"content_sha256":"ff94815ef3bc4ce92e396eca5d987452ef9cd48a4b46c7d1b9903e7dc3e53309","schema_version":"1.0","event_id":"sha256:ff94815ef3bc4ce92e396eca5d987452ef9cd48a4b46c7d1b9903e7dc3e53309"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTPWZ23T2YADQHGNADBCCGE5VK/bundle.json","state_url":"https://pith.science/pith/MTPWZ23T2YADQHGNADBCCGE5VK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTPWZ23T2YADQHGNADBCCGE5VK/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":"2026-06-24T17:52:16Z","links":{"resolver":"https://pith.science/pith/MTPWZ23T2YADQHGNADBCCGE5VK","bundle":"https://pith.science/pith/MTPWZ23T2YADQHGNADBCCGE5VK/bundle.json","state":"https://pith.science/pith/MTPWZ23T2YADQHGNADBCCGE5VK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTPWZ23T2YADQHGNADBCCGE5VK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MTPWZ23T2YADQHGNADBCCGE5VK","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":"46e865e205b7a96f440f9133289481b12f0046f2250cea2329a8b3c7c16f9a65","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T11:09:39Z","title_canon_sha256":"e3e29fb6c7d2a55e76a75607eeadde94b5a3298788e29ebb0516be9107e78c94"},"schema_version":"1.0","source":{"id":"1208.1642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1642","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1642v1","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1642","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"MTPWZ23T2YAD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MTPWZ23T2YADQHGN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MTPWZ23T","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:ff94815ef3bc4ce92e396eca5d987452ef9cd48a4b46c7d1b9903e7dc3e53309","target":"graph","created_at":"2026-05-18T03:49:11Z","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":"Let $\\mathfrak{g}$ be a vector space and $[,],[,]'$ be a pair of Lie brackets on $\\mathfrak{g}$. By definition they are compatible if $[,]+[,]'$ is again a Lie bracket. Such pairs play important role in bihamiltonian and $r$-matrix formalisms in the theory of integrable systems.\n  We propose an approach to a long standing problem of classification of such pairs in the case when one of them, say $[,]$, is semisimple. It is known that any such pair is determined by a linear operator on $(\\mathfrak{g},[,])$, which is defined up to adding a derivation. We propose a special fixing of this operator ","authors_text":"Andriy Panasyuk","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T11:09:39Z","title":"Lie--Poisson pencils related to semisimple Lie algebras: towards classification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1642","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:f238d55edf563346b151ff4b5bc790e6393d837913a0f8438bc83742047f82d1","target":"record","created_at":"2026-05-18T03:49:11Z","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":"46e865e205b7a96f440f9133289481b12f0046f2250cea2329a8b3c7c16f9a65","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T11:09:39Z","title_canon_sha256":"e3e29fb6c7d2a55e76a75607eeadde94b5a3298788e29ebb0516be9107e78c94"},"schema_version":"1.0","source":{"id":"1208.1642","kind":"arxiv","version":1}},"canonical_sha256":"64df6ceb73d600381ccd00c221189daa8a368cec79fd19585f95275ffc652993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64df6ceb73d600381ccd00c221189daa8a368cec79fd19585f95275ffc652993","first_computed_at":"2026-05-18T03:49:11.009818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:11.009818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r1yETdetobAyNFUn3q2a8ncyCsx3EZsrdE4VUbv24bXpQSmszjU7DZUo63BgaH1fIHKRoPjkQuSCtQdeV+QACg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:11.010694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f238d55edf563346b151ff4b5bc790e6393d837913a0f8438bc83742047f82d1","sha256:ff94815ef3bc4ce92e396eca5d987452ef9cd48a4b46c7d1b9903e7dc3e53309"],"state_sha256":"8c60487a14793e44e2e41bc013b6a018c88d36b57bd7aff872c311a5dc2d9514"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/WpTDa79PSlyGRCZvFq9UM4kiTjPMRXLEVgh5Y4b9doGWCNRB3Is+mTYJgZ2Vdv3tDpOR55NxxS0n9K7775DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:52:16.094552Z","bundle_sha256":"57a0e88cc0f7a3b50dbfed10c2e61778d10db56c5da642cabfcbafd8afe76a41"}}