{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QJDIW32Y32SUMEUR2U5NGYY235","short_pith_number":"pith:QJDIW32Y","canonical_record":{"source":{"id":"1708.09728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-31T14:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"667692a9fa1b09c5997e131f007201e18051b103b40822ac874a6e3eead8821a","abstract_canon_sha256":"6479d7d8fbbbec6e45a8d59a4f111b3023a9430b5bb2854d7862ba35d86bd118"},"schema_version":"1.0"},"canonical_sha256":"82468b6f58dea5461291d53ad3631adf78907bfdee8856a9bae654703af07d7c","source":{"kind":"arxiv","id":"1708.09728","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09728","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09728v1","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09728","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"QJDIW32Y32SU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJDIW32Y32SUMEUR","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJDIW32Y","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QJDIW32Y32SUMEUR2U5NGYY235","target":"record","payload":{"canonical_record":{"source":{"id":"1708.09728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-31T14:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"667692a9fa1b09c5997e131f007201e18051b103b40822ac874a6e3eead8821a","abstract_canon_sha256":"6479d7d8fbbbec6e45a8d59a4f111b3023a9430b5bb2854d7862ba35d86bd118"},"schema_version":"1.0"},"canonical_sha256":"82468b6f58dea5461291d53ad3631adf78907bfdee8856a9bae654703af07d7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:15.622475Z","signature_b64":"ZCk7qxyixOElTYm5+DVTTTlTRzW5GnEZnZQ06oZbWQuyZMZLuEYShGj+8NX5jZxMpmzYjJzdv2WU2jpRqkf2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82468b6f58dea5461291d53ad3631adf78907bfdee8856a9bae654703af07d7c","last_reissued_at":"2026-05-18T00:36:15.621730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:15.621730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.09728","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":"2026-05-18T00:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5whcqQU6NJTJ+ofe0UCffXrUp7aR5NxrxfRcUylfLG04/agnLWSqALmLFAs53nM1z/cs5fE2AbxIXNZWEhPACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:04.492421Z"},"content_sha256":"9fa08f409250311c748e298a072f9ab163a153b616e0f9c48e893d3a8df85627","schema_version":"1.0","event_id":"sha256:9fa08f409250311c748e298a072f9ab163a153b616e0f9c48e893d3a8df85627"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QJDIW32Y32SUMEUR2U5NGYY235","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Calogero-Moser space associated with dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (IMAG)","submitted_at":"2017-08-31T14:14:59Z","abstract_excerpt":"Using the geometry of the associated Calogero-Moser space, R. Rouquier and the author have attached to any finite complex reflection group $W$ several notions (Calogero-Moser left, right or two-sided cells, Calogero-Moser cellular characters), completing the notion of Calogero-Moser families defined by Gordon. If moreover $W$ is a Coxeter group, they conjectured that these notions coincide with the analogous notions defined using the Hecke algebra by Kazhdan and Lusztig (or Lusztig in the unequal parameters case). In the present paper, we aim to investigate these conjectures whenever $W$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09728","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":"2026-05-18T00:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaQiQYog5Ovmtd+zEHzW86jhr4syCqZ20r5KtI+bf36I7BLFHzFj4n9iCAEt+Hzugzw4i5FQE/1ceSBPDNZ6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:04.492783Z"},"content_sha256":"161a409aed42e70e4a15e22d701edf75eded1f7db638ea44452367163b24f683","schema_version":"1.0","event_id":"sha256:161a409aed42e70e4a15e22d701edf75eded1f7db638ea44452367163b24f683"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJDIW32Y32SUMEUR2U5NGYY235/bundle.json","state_url":"https://pith.science/pith/QJDIW32Y32SUMEUR2U5NGYY235/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJDIW32Y32SUMEUR2U5NGYY235/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":"2026-06-26T08:23:04Z","links":{"resolver":"https://pith.science/pith/QJDIW32Y32SUMEUR2U5NGYY235","bundle":"https://pith.science/pith/QJDIW32Y32SUMEUR2U5NGYY235/bundle.json","state":"https://pith.science/pith/QJDIW32Y32SUMEUR2U5NGYY235/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJDIW32Y32SUMEUR2U5NGYY235/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QJDIW32Y32SUMEUR2U5NGYY235","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":"6479d7d8fbbbec6e45a8d59a4f111b3023a9430b5bb2854d7862ba35d86bd118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-31T14:14:59Z","title_canon_sha256":"667692a9fa1b09c5997e131f007201e18051b103b40822ac874a6e3eead8821a"},"schema_version":"1.0","source":{"id":"1708.09728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09728","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09728v1","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09728","created_at":"2026-05-18T00:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"QJDIW32Y32SU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJDIW32Y32SUMEUR","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJDIW32Y","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:161a409aed42e70e4a15e22d701edf75eded1f7db638ea44452367163b24f683","target":"graph","created_at":"2026-05-18T00:36:15Z","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":"Using the geometry of the associated Calogero-Moser space, R. Rouquier and the author have attached to any finite complex reflection group $W$ several notions (Calogero-Moser left, right or two-sided cells, Calogero-Moser cellular characters), completing the notion of Calogero-Moser families defined by Gordon. If moreover $W$ is a Coxeter group, they conjectured that these notions coincide with the analogous notions defined using the Hecke algebra by Kazhdan and Lusztig (or Lusztig in the unequal parameters case). In the present paper, we aim to investigate these conjectures whenever $W$ is a ","authors_text":"C\\'edric Bonnaf\\'e (IMAG)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-31T14:14:59Z","title":"On the Calogero-Moser space associated with dihedral groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09728","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":"sha256:9fa08f409250311c748e298a072f9ab163a153b616e0f9c48e893d3a8df85627","target":"record","created_at":"2026-05-18T00:36:15Z","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":"6479d7d8fbbbec6e45a8d59a4f111b3023a9430b5bb2854d7862ba35d86bd118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-31T14:14:59Z","title_canon_sha256":"667692a9fa1b09c5997e131f007201e18051b103b40822ac874a6e3eead8821a"},"schema_version":"1.0","source":{"id":"1708.09728","kind":"arxiv","version":1}},"canonical_sha256":"82468b6f58dea5461291d53ad3631adf78907bfdee8856a9bae654703af07d7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82468b6f58dea5461291d53ad3631adf78907bfdee8856a9bae654703af07d7c","first_computed_at":"2026-05-18T00:36:15.621730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:15.621730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCk7qxyixOElTYm5+DVTTTlTRzW5GnEZnZQ06oZbWQuyZMZLuEYShGj+8NX5jZxMpmzYjJzdv2WU2jpRqkf2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:15.622475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fa08f409250311c748e298a072f9ab163a153b616e0f9c48e893d3a8df85627","sha256:161a409aed42e70e4a15e22d701edf75eded1f7db638ea44452367163b24f683"],"state_sha256":"a22fc44fd0b16d6539e39ab5a84622ced212004505817706dddd2cf1477ede14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pls6izISIf0zSOJvRqAymdEV82N9QD2dQKMf+arL36iTbptGNnEGFDuNmAzJxp/CSKGEQ7NWZ5zOU5mlE/QxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:23:04.494693Z","bundle_sha256":"c29e80b9ba209a789fc0225677c8e52ccb446f326e03ff7c6024f6e17a5c2ba2"}}