{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZLRJJX4KND5ELZUPCMFVTSMSP2","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":"ebf7b08ad0b416ae3252471e7316a578dbfe74894fe91be076d090975ebc54d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-25T20:36:07Z","title_canon_sha256":"c5f4cfc083c2f6ef6f5c122f34bd65f8764f20b3993190a124d7f96a93f3793f"},"schema_version":"1.0","source":{"id":"1807.09843","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09843","created_at":"2026-07-05T00:21:46Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09843v2","created_at":"2026-07-05T00:21:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09843","created_at":"2026-07-05T00:21:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZLRJJX4KND5E","created_at":"2026-07-05T00:21:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZLRJJX4KND5ELZUP","created_at":"2026-07-05T00:21:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZLRJJX4K","created_at":"2026-07-05T00:21:46Z"}],"graph_snapshots":[{"event_id":"sha256:c5a6f7f272c318ef393e61e64dc6f6214941bd3e6c9f0089170b9d8dd48425bb","target":"graph","created_at":"2026-07-05T00:21:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.09843/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give the analogue for Hopf algebras of the polyuble Lie bialgebra construction by Fock and Rosli. By applying this construction to the Drinfeld-Jimbo quantum group, we obtain a deformation quantization $\\mathbb{C}_\\hslash[(N \\backslash G)^m]$ of a Poisson structure $\\pi^{(m)}$ on products $(N \\backslash G)^m$ of principal affine spaces of a connected and simply connected complex semisimple Lie group $G$. The Poisson structure $\\pi^{(m)}$ descends to a Poisson structure $\\pi_m$ on products $(B \\backslash G)^m$ of the flag variety of $G$ which was introduced and studied by the Lu and the auth","authors_text":"Victor Mouquin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-25T20:36:07Z","title":"Quantization of a Poisson structure on products of principal affine spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09843","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":"sha256:7e1d39a6f57125650013c05507007b8c679536cbd9306be22e70762e033e9182","target":"record","created_at":"2026-07-05T00:21:46Z","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":"ebf7b08ad0b416ae3252471e7316a578dbfe74894fe91be076d090975ebc54d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-25T20:36:07Z","title_canon_sha256":"c5f4cfc083c2f6ef6f5c122f34bd65f8764f20b3993190a124d7f96a93f3793f"},"schema_version":"1.0","source":{"id":"1807.09843","kind":"arxiv","version":2}},"canonical_sha256":"cae294df8a68fa45e68f130b59c9927e84782fd0349c545ff3137cc048bd5e76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cae294df8a68fa45e68f130b59c9927e84782fd0349c545ff3137cc048bd5e76","first_computed_at":"2026-07-05T00:21:46.957060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:21:46.957060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sv4r0WvKoTElK+KpOPDNrYEJlR+RgpJx4RYHOU+AYjIq9oR3FLMKiN1+g4iqiGM5QLPZbfHloMD6zbAybmxaBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:21:46.957502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09843","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e1d39a6f57125650013c05507007b8c679536cbd9306be22e70762e033e9182","sha256:c5a6f7f272c318ef393e61e64dc6f6214941bd3e6c9f0089170b9d8dd48425bb"],"state_sha256":"6cd6ce6bd5b708de9bb33f390919ae3296d65363ed2ef6fb4222229bec15b05b"}