{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A6QQDEVDKIQAPSRFM6RR6MMQCO","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":"71a73b6039504f9faf45c116f53a004244385878d0bfbdb17fdeacd92b2b310d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-02-05T14:21:50Z","title_canon_sha256":"7fc15d627381681fee913790d61575c1383cc87032d70e24d5c0de04222077c9"},"schema_version":"1.0","source":{"id":"1402.1048","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1048","created_at":"2026-05-18T01:24:33Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1048v5","created_at":"2026-05-18T01:24:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1048","created_at":"2026-05-18T01:24:33Z"},{"alias_kind":"pith_short_12","alias_value":"A6QQDEVDKIQA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A6QQDEVDKIQAPSRF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A6QQDEVD","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:7e03dd9ca75d200fcfb569fb2776b33ffc39d01a95080ba9b9af50f0426981ee","target":"graph","created_at":"2026-05-18T01:24:33Z","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 study the discrete quantum groups $\\Gamma$ whose group algebra has an inner faithful representation of type $\\pi:C^*(\\Gamma)\\to M_K(\\mathbb C)$. Such a representation can be thought of as coming from an embedding $\\Gamma\\subset U_K$. Our main result, concerning a certain class of examples of such quantum groups, is an asymptotic convergence theorem for the random walk on $\\Gamma$. The proof uses various algebraic and probabilistic techniques.","authors_text":"Julien Bichon, Teodor Banica","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-02-05T14:21:50Z","title":"Random walk questions for linear quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1048","kind":"arxiv","version":5},"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":"sha256:25ae1308246399179322a6fd2521a074b4ac55fab790114e6d7cc9eb8ffabe22","target":"record","created_at":"2026-05-18T01:24:33Z","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":"71a73b6039504f9faf45c116f53a004244385878d0bfbdb17fdeacd92b2b310d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-02-05T14:21:50Z","title_canon_sha256":"7fc15d627381681fee913790d61575c1383cc87032d70e24d5c0de04222077c9"},"schema_version":"1.0","source":{"id":"1402.1048","kind":"arxiv","version":5}},"canonical_sha256":"07a10192a3522007ca2567a31f319013a9baacb07ee090003e6ed2584bd8a094","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07a10192a3522007ca2567a31f319013a9baacb07ee090003e6ed2584bd8a094","first_computed_at":"2026-05-18T01:24:33.399242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:33.399242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ri8/FgpnCjghehE/C93xW2sqf/TmA2MaoHr5lV/UxAZFjnoH+kInmNX0qnzRC3HdXN2Te1PlJadwq1T7jeCiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:33.399882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1048","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25ae1308246399179322a6fd2521a074b4ac55fab790114e6d7cc9eb8ffabe22","sha256:7e03dd9ca75d200fcfb569fb2776b33ffc39d01a95080ba9b9af50f0426981ee"],"state_sha256":"2d049ef9c02d34111bde5c2602bd8ef848bf7545318bebc33e08f5db96560708"}