{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BEQQRMGUIOSPVOVEC3L7AD7ILZ","short_pith_number":"pith:BEQQRMGU","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"},"canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","source":{"kind":"arxiv","id":"1712.06137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06137","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06137v1","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06137","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"BEQQRMGUIOSP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BEQQRMGUIOSPVOVE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BEQQRMGU","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BEQQRMGUIOSPVOVEC3L7AD7ILZ","target":"record","payload":{"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"},"canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","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"},"source_kind":"arxiv","source_id":"1712.06137","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":"2026-05-18T00:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N49JcXe8mb+vNGNpGKlSIkGgqsqbf4MOV3wFO3O0lD+hV0lh7yDUrPK2+7+rqd/pt0PAR2DAVZGede4g9UENDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:25:21.448361Z"},"content_sha256":"2d489aa86f8141c90ff0a3b6662c739616eafd2ee07ca27f6656450a06b4c15d","schema_version":"1.0","event_id":"sha256:2d489aa86f8141c90ff0a3b6662c739616eafd2ee07ca27f6656450a06b4c15d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BEQQRMGUIOSPVOVEC3L7AD7ILZ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qSygWjiuTUqOZWef47lrDwonKR9iNcDkOPZPaFr7kQEfGqEfUFsmbPeBJJ2bH7qjBFqeFXxD8uYxOZF5kUUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:25:21.448715Z"},"content_sha256":"f86410505a93264db262759f5b5d3bb1c0a4e370419aa7bd04d99d01d9028c34","schema_version":"1.0","event_id":"sha256:f86410505a93264db262759f5b5d3bb1c0a4e370419aa7bd04d99d01d9028c34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/bundle.json","state_url":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/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":"2026-07-02T11:25:21Z","links":{"resolver":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ","bundle":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/bundle.json","state":"https://pith.science/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEQQRMGUIOSPVOVEC3L7AD7ILZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BEQQRMGUIOSPVOVEC3L7AD7ILZ","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":"ac917b52cce14edfb69284d3cf6df9173eafbef92314a2e7a261a51204fbd971","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-17T16:35:24Z","title_canon_sha256":"364670faf3b76b132714c6ba10e2d61449048b331716948eff0c75d1a564159f"},"schema_version":"1.0","source":{"id":"1712.06137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06137","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06137v1","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06137","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"BEQQRMGUIOSP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BEQQRMGUIOSPVOVE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BEQQRMGU","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:f86410505a93264db262759f5b5d3bb1c0a4e370419aa7bd04d99d01d9028c34","target":"graph","created_at":"2026-05-18T00:00:59Z","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":"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 $n$.","authors_text":"O. Ogievetsky, V. Petrova","cross_cats":["math-ph","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-17T16:35:24Z","title":"Cyclotomic shuffles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06137","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":"sha256:2d489aa86f8141c90ff0a3b6662c739616eafd2ee07ca27f6656450a06b4c15d","target":"record","created_at":"2026-05-18T00:00:59Z","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":"ac917b52cce14edfb69284d3cf6df9173eafbef92314a2e7a261a51204fbd971","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-17T16:35:24Z","title_canon_sha256":"364670faf3b76b132714c6ba10e2d61449048b331716948eff0c75d1a564159f"},"schema_version":"1.0","source":{"id":"1712.06137","kind":"arxiv","version":1}},"canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"092108b0d443a4fabaa416d7f00fe85e6bd0d5584d0e701cd22fa74f903378be","first_computed_at":"2026-05-18T00:00:59.591188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:59.591188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXpmr+zUPssau8UMOrbu5pmv3s9QuDM0+1u0vlw2HiocJK3eCAZjebapr7wnA7uxEuejtldrvl0FXQLWnBIpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:59.591729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d489aa86f8141c90ff0a3b6662c739616eafd2ee07ca27f6656450a06b4c15d","sha256:f86410505a93264db262759f5b5d3bb1c0a4e370419aa7bd04d99d01d9028c34"],"state_sha256":"8cf1b64280daddc25f1a6d227c343f1b03a5308f35b74b30c081a0c99a4075e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MuhyIs55UWtES5MdCfpoDFexiizv+liaXDe8q9GhJjcXoqXbWvB7bI95m7frWzjcbYVInwYO/4EPux3f5UmLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T11:25:21.450688Z","bundle_sha256":"be1ebdd6c426e393de8d1ca9499058ee3b98912d5f961fff6cc8dda1582fd188"}}