{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PFZOCQBKR5S3X5IMSG4X7GJ45W","short_pith_number":"pith:PFZOCQBK","canonical_record":{"source":{"id":"1201.0585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-03T07:33:32Z","cross_cats_sorted":[],"title_canon_sha256":"3722bfd731e2bec8e4e3aaf687a24c1f8860e533abc16f955d9c97d0815c51d6","abstract_canon_sha256":"253f34cf9c7c3cc30fd4409662b17e7899736a82ed1077946304db60224b36a1"},"schema_version":"1.0"},"canonical_sha256":"7972e1402a8f65bbf50c91b97f993cedb9138e800be07499d423a6c0ccfa01d2","source":{"kind":"arxiv","id":"1201.0585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0585","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0585v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0585","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"PFZOCQBKR5S3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PFZOCQBKR5S3X5IM","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PFZOCQBK","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PFZOCQBKR5S3X5IMSG4X7GJ45W","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-03T07:33:32Z","cross_cats_sorted":[],"title_canon_sha256":"3722bfd731e2bec8e4e3aaf687a24c1f8860e533abc16f955d9c97d0815c51d6","abstract_canon_sha256":"253f34cf9c7c3cc30fd4409662b17e7899736a82ed1077946304db60224b36a1"},"schema_version":"1.0"},"canonical_sha256":"7972e1402a8f65bbf50c91b97f993cedb9138e800be07499d423a6c0ccfa01d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.191161Z","signature_b64":"0Grrn9wIVKJ42z7wz2um/CxwLLmtFmBgoWhjRz+1G/ZjpuvPpHQ+dEEwwW9LBp9PspMLA9sSUjN2o11d2aYoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7972e1402a8f65bbf50c91b97f993cedb9138e800be07499d423a6c0ccfa01d2","last_reissued_at":"2026-05-18T04:05:17.190659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.190659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0585","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alEI5wcU/YOXL1CA8722V4gHbWWvN2M27bBfNt89e7biK73nJq7SzKAblFMH00cm9iC4Q2Jl7nAzjW92eXNdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:20:51.864162Z"},"content_sha256":"c81f3642d7d1055fa51070b45f79d9ae5e9a907bac4472242d79efa18c67b9b8","schema_version":"1.0","event_id":"sha256:c81f3642d7d1055fa51070b45f79d9ae5e9a907bac4472242d79efa18c67b9b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PFZOCQBKR5S3X5IMSG4X7GJ45W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calogero-Moser versus Kazhdan-Lusztig cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (I3M), Rapha\\\"el Rouquier (MI)","submitted_at":"2012-01-03T07:33:32Z","abstract_excerpt":"In 1979, Kazhdan and Lusztig developed a combinatorial theory associated with Coxeter groups. They defined in particular partitions of the group in left and two-sided cells. In 1983, Lusztig generalized this theory to Hecke algebras of Coxeter groups with unequal parameters. We propose a definition of left cells and two-sided cells for complex reflection groups, based on ramification theory for Calogero-Moser spaces. These spaces have been defined via rational Cherednik algebras by Etingof and Ginzburg. We conjecture that these coincide with Kazhdan-Lusztig cells, for real reflection groups. C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0585","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFNRo/vo0/Ru+bYb77OvzduVVA8ifeS54wcxtI5CwIRHLkc3cp7cS9FQR8PRB4f+GdQ93uSFMdzF8PK3m+8JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:20:51.864819Z"},"content_sha256":"afe06de63c1d2edab23603be123459c19db7d45ad97d889f2dccb107406230ff","schema_version":"1.0","event_id":"sha256:afe06de63c1d2edab23603be123459c19db7d45ad97d889f2dccb107406230ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/bundle.json","state_url":"https://pith.science/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/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":"2026-05-31T06:20:51Z","links":{"resolver":"https://pith.science/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W","bundle":"https://pith.science/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/bundle.json","state":"https://pith.science/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFZOCQBKR5S3X5IMSG4X7GJ45W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PFZOCQBKR5S3X5IMSG4X7GJ45W","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":"253f34cf9c7c3cc30fd4409662b17e7899736a82ed1077946304db60224b36a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-03T07:33:32Z","title_canon_sha256":"3722bfd731e2bec8e4e3aaf687a24c1f8860e533abc16f955d9c97d0815c51d6"},"schema_version":"1.0","source":{"id":"1201.0585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0585","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0585v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0585","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"PFZOCQBKR5S3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PFZOCQBKR5S3X5IM","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PFZOCQBK","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:afe06de63c1d2edab23603be123459c19db7d45ad97d889f2dccb107406230ff","target":"graph","created_at":"2026-05-18T04:05:17Z","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":"In 1979, Kazhdan and Lusztig developed a combinatorial theory associated with Coxeter groups. They defined in particular partitions of the group in left and two-sided cells. In 1983, Lusztig generalized this theory to Hecke algebras of Coxeter groups with unequal parameters. We propose a definition of left cells and two-sided cells for complex reflection groups, based on ramification theory for Calogero-Moser spaces. These spaces have been defined via rational Cherednik algebras by Etingof and Ginzburg. We conjecture that these coincide with Kazhdan-Lusztig cells, for real reflection groups. C","authors_text":"C\\'edric Bonnaf\\'e (I3M), Rapha\\\"el Rouquier (MI)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-03T07:33:32Z","title":"Calogero-Moser versus Kazhdan-Lusztig cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0585","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:c81f3642d7d1055fa51070b45f79d9ae5e9a907bac4472242d79efa18c67b9b8","target":"record","created_at":"2026-05-18T04:05:17Z","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":"253f34cf9c7c3cc30fd4409662b17e7899736a82ed1077946304db60224b36a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-03T07:33:32Z","title_canon_sha256":"3722bfd731e2bec8e4e3aaf687a24c1f8860e533abc16f955d9c97d0815c51d6"},"schema_version":"1.0","source":{"id":"1201.0585","kind":"arxiv","version":1}},"canonical_sha256":"7972e1402a8f65bbf50c91b97f993cedb9138e800be07499d423a6c0ccfa01d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7972e1402a8f65bbf50c91b97f993cedb9138e800be07499d423a6c0ccfa01d2","first_computed_at":"2026-05-18T04:05:17.190659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.190659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Grrn9wIVKJ42z7wz2um/CxwLLmtFmBgoWhjRz+1G/ZjpuvPpHQ+dEEwwW9LBp9PspMLA9sSUjN2o11d2aYoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.191161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c81f3642d7d1055fa51070b45f79d9ae5e9a907bac4472242d79efa18c67b9b8","sha256:afe06de63c1d2edab23603be123459c19db7d45ad97d889f2dccb107406230ff"],"state_sha256":"b9f55c723c28ee0236db704cd978dddc2d8c7ec7a271bf03bb029ee474c39723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OonRqI3Glu2tcfrJuLKXE290xtD68WYV4I4WBNLH9mnHx8Xzw/1LaBCdEhvGUMh/92+xfv6Pm7JuEOYCb1xBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:20:51.868205Z","bundle_sha256":"698c0de3f935480b4e46947f927493fd9890e86ef63ae4994c11f7edd889372c"}}