{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:ULUAG7FQSTMHBAI24YJ5J3WDDV","short_pith_number":"pith:ULUAG7FQ","canonical_record":{"source":{"id":"0808.2604","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7321f84b9ec4d1a263888bd8494884d3dba7cc4c0cda8bdeee5299db089a38d7","abstract_canon_sha256":"9114297b4aea734da9389c6c88c191c06c5720938bfbe1a1472cd48a97ac3ecb"},"schema_version":"1.0"},"canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","source":{"kind":"arxiv","id":"0808.2604","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2604","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2604v4","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2604","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"ULUAG7FQSTMH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ULUAG7FQSTMHBAI2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ULUAG7FQ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:ULUAG7FQSTMHBAI24YJ5J3WDDV","target":"record","payload":{"canonical_record":{"source":{"id":"0808.2604","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7321f84b9ec4d1a263888bd8494884d3dba7cc4c0cda8bdeee5299db089a38d7","abstract_canon_sha256":"9114297b4aea734da9389c6c88c191c06c5720938bfbe1a1472cd48a97ac3ecb"},"schema_version":"1.0"},"canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.936129Z","signature_b64":"Jls5AT88wNycjku4dOPH/k/gBXcaXsiZYHAmd13XhaOx8EPlPIAYQyCDp8AERnEPus30hCBEsqFSSaZspv8PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","last_reissued_at":"2026-05-18T04:07:06.935447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.935447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.2604","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ES0s0yk9pbZ8MObSXGq45ByYZZ4LJjka/kjEIolcYlm2ZJ2vAp6zTE+nEmqxSuzSmK4MnrTkBf6/v3Se4GIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:40:03.826913Z"},"content_sha256":"cb307ff6831cd67d517c286871a66bd92bb2226445e9052f32a9d4a10f62f2b9","schema_version":"1.0","event_id":"sha256:cb307ff6831cd67d517c286871a66bd92bb2226445e9052f32a9d4a10f62f2b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:ULUAG7FQSTMHBAI24YJ5J3WDDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum groups and quantization of Weyl group symmetries of Painlev\\'e systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Gen Kuroki","submitted_at":"2008-08-19T14:53:54Z","abstract_excerpt":"We shall construct the quantized q-analogues of the birational Weyl group actions arising from nilpotent Poisson algebras, which are conceptual generalizations, proposed by Noumi and Yamada, of the B\\\"acklund transformations for Painlev\\'e equations. Consider a quotient Ore domain of the lower nilpotent part of a quantized universal enveloping algebra of arbitrary symmetrizable Kac-Moody type. Then non-integral powers of the image of the Chevalley generators generate the quantized q-analogue of the birational Weyl group action. Using the same method, we shall reconstruct the quantized B\\\"acklu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2604","kind":"arxiv","version":4},"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":"2026-05-18T04:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g36gi+VglYpAmP0rBPE6ENgCYLnGHOLS20yoxntgdsrTZIRgpUx0AlTHV3jIy2mbf1riFSgZo61be+VTZTIdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:40:03.827665Z"},"content_sha256":"4226fa2e7afc2138b77aa12e3a025deeb74eb0e11d68a54c0e0bfb062a84913a","schema_version":"1.0","event_id":"sha256:4226fa2e7afc2138b77aa12e3a025deeb74eb0e11d68a54c0e0bfb062a84913a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/bundle.json","state_url":"https://pith.science/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/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":"2026-06-12T00:40:03Z","links":{"resolver":"https://pith.science/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV","bundle":"https://pith.science/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/bundle.json","state":"https://pith.science/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULUAG7FQSTMHBAI24YJ5J3WDDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ULUAG7FQSTMHBAI24YJ5J3WDDV","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":"9114297b4aea734da9389c6c88c191c06c5720938bfbe1a1472cd48a97ac3ecb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","title_canon_sha256":"7321f84b9ec4d1a263888bd8494884d3dba7cc4c0cda8bdeee5299db089a38d7"},"schema_version":"1.0","source":{"id":"0808.2604","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2604","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2604v4","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2604","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"ULUAG7FQSTMH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ULUAG7FQSTMHBAI2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ULUAG7FQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:4226fa2e7afc2138b77aa12e3a025deeb74eb0e11d68a54c0e0bfb062a84913a","target":"graph","created_at":"2026-05-18T04:07:06Z","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 shall construct the quantized q-analogues of the birational Weyl group actions arising from nilpotent Poisson algebras, which are conceptual generalizations, proposed by Noumi and Yamada, of the B\\\"acklund transformations for Painlev\\'e equations. Consider a quotient Ore domain of the lower nilpotent part of a quantized universal enveloping algebra of arbitrary symmetrizable Kac-Moody type. Then non-integral powers of the image of the Chevalley generators generate the quantized q-analogue of the birational Weyl group action. Using the same method, we shall reconstruct the quantized B\\\"acklu","authors_text":"Gen Kuroki","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","title":"Quantum groups and quantization of Weyl group symmetries of Painlev\\'e systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2604","kind":"arxiv","version":4},"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:cb307ff6831cd67d517c286871a66bd92bb2226445e9052f32a9d4a10f62f2b9","target":"record","created_at":"2026-05-18T04:07:06Z","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":"9114297b4aea734da9389c6c88c191c06c5720938bfbe1a1472cd48a97ac3ecb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","title_canon_sha256":"7321f84b9ec4d1a263888bd8494884d3dba7cc4c0cda8bdeee5299db089a38d7"},"schema_version":"1.0","source":{"id":"0808.2604","kind":"arxiv","version":4}},"canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","first_computed_at":"2026-05-18T04:07:06.935447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:06.935447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jls5AT88wNycjku4dOPH/k/gBXcaXsiZYHAmd13XhaOx8EPlPIAYQyCDp8AERnEPus30hCBEsqFSSaZspv8PCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:06.936129Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2604","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb307ff6831cd67d517c286871a66bd92bb2226445e9052f32a9d4a10f62f2b9","sha256:4226fa2e7afc2138b77aa12e3a025deeb74eb0e11d68a54c0e0bfb062a84913a"],"state_sha256":"3329aced023a99acad46731a0ad5ccf5597bb30dfb3337e820f677bb7eab362f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvUr0GhtzNnS4gv/mKA7FoAsDycgKrKQ9BROmuB2uw4zYUq1oxOlZX0w5p6mvdDeKUAoRcwLfW9zqhUfQcYWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:40:03.831689Z","bundle_sha256":"6e2614e12daacb5e30238f2097f55054113621d82631f17468004426ffdbaff7"}}