{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BEQQRMGUIOSPVOVEC3L7AD7ILZ","short_pith_number":"pith:BEQQRMGU","schema_version":"1.0","canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","source":{"kind":"arxiv","id":"1712.06137","version":1},"attestation_state":"computed","paper":{"title":"Cyclotomic shuffles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.CO","authors_text":"O. Ogievetsky, V. Petrova","submitted_at":"2017-12-17T16:35:24Z","abstract_excerpt":"Analogues of 1-shuffle elements for complex reflection groups of type $G(m,1,n)$ are introduced. A geometric interpretation for $G(m,1,n)$ in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group $G(m,1,n)$. Considering shuffling as a random walk on the group $G(m,1,n)$, we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra $H(m,1,n)$ for $m=2$ and small $n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.06137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-17T16:35:24Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"364670faf3b76b132714c6ba10e2d61449048b331716948eff0c75d1a564159f","abstract_canon_sha256":"ac917b52cce14edfb69284d3cf6df9173eafbef92314a2e7a261a51204fbd971"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:59.591729Z","signature_b64":"yXpmr+zUPssau8UMOrbu5pmv3s9QuDM0+1u0vlw2HiocJK3eCAZjebapr7wnA7uxEuejtldrvl0FXQLWnBIpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","last_reissued_at":"2026-05-18T00:00:59.591188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:59.591188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cyclotomic shuffles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.CO","authors_text":"O. Ogievetsky, V. Petrova","submitted_at":"2017-12-17T16:35:24Z","abstract_excerpt":"Analogues of 1-shuffle elements for complex reflection groups of type $G(m,1,n)$ are introduced. A geometric interpretation for $G(m,1,n)$ in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group $G(m,1,n)$. Considering shuffling as a random walk on the group $G(m,1,n)$, we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra $H(m,1,n)$ for $m=2$ and small $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06137","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.06137","created_at":"2026-05-18T00:00:59.591264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06137v1","created_at":"2026-05-18T00:00:59.591264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06137","created_at":"2026-05-18T00:00:59.591264+00:00"},{"alias_kind":"pith_short_12","alias_value":"BEQQRMGUIOSP","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BEQQRMGUIOSPVOVE","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BEQQRMGU","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ","json":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ.json","graph_json":"https://pith.science/api/pith-number/BEQQRMGUIOSPVOVEC3L7AD7ILZ/graph.json","events_json":"https://pith.science/api/pith-number/BEQQRMGUIOSPVOVEC3L7AD7ILZ/events.json","paper":"https://pith.science/paper/BEQQRMGU"},"agent_actions":{"view_html":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ","download_json":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ.json","view_paper":"https://pith.science/paper/BEQQRMGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06137&json=true","fetch_graph":"https://pith.science/api/pith-number/BEQQRMGUIOSPVOVEC3L7AD7ILZ/graph.json","fetch_events":"https://pith.science/api/pith-number/BEQQRMGUIOSPVOVEC3L7AD7ILZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/action/storage_attestation","attest_author":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/action/author_attestation","sign_citation":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/action/citation_signature","submit_replication":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/action/replication_record"}},"created_at":"2026-05-18T00:00:59.591264+00:00","updated_at":"2026-05-18T00:00:59.591264+00:00"}