{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BLCSNCRLF6YFMR4K6IJE5BQQVQ","short_pith_number":"pith:BLCSNCRL","canonical_record":{"source":{"id":"1404.5430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-22T09:09:01Z","cross_cats_sorted":[],"title_canon_sha256":"72a65268e8d423a75483eb5b09ef983acc13502ded300bae7ed8b0423c730a19","abstract_canon_sha256":"619f06dbd8e9503e0ca77b99bf1944feb32c3edd7c59fca13a6bda993d0c1eda"},"schema_version":"1.0"},"canonical_sha256":"0ac5268a2b2fb056478af2124e8610ac0c328b0ce2062865f5c0c99c8277ec88","source":{"kind":"arxiv","id":"1404.5430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5430","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5430v2","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5430","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"BLCSNCRLF6YF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BLCSNCRLF6YFMR4K","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BLCSNCRL","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BLCSNCRLF6YFMR4K6IJE5BQQVQ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-22T09:09:01Z","cross_cats_sorted":[],"title_canon_sha256":"72a65268e8d423a75483eb5b09ef983acc13502ded300bae7ed8b0423c730a19","abstract_canon_sha256":"619f06dbd8e9503e0ca77b99bf1944feb32c3edd7c59fca13a6bda993d0c1eda"},"schema_version":"1.0"},"canonical_sha256":"0ac5268a2b2fb056478af2124e8610ac0c328b0ce2062865f5c0c99c8277ec88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:47.947164Z","signature_b64":"B+Br9CIppzW/MQi4YVacrrVn154Aj0zhq87AE6Dw5Ny3jxDqobl40f7gQOR9O+b7fquBrQRrKvMmBaPz17g7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac5268a2b2fb056478af2124e8610ac0c328b0ce2062865f5c0c99c8277ec88","last_reissued_at":"2026-05-18T02:28:47.946755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:47.946755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5430","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJzIF2vxN1L3doB8atAOMJldFtPTwwK/2w4AoZ3kc/bpVTOjCHHJA6chLL3SToj/aaf/bFy0vuB5Z54r3VstCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:47:51.727965Z"},"content_sha256":"690d1c6d3facc09981633d6491474e5d93c13fbecad0fbecc47fccb1e19f87ed","schema_version":"1.0","event_id":"sha256:690d1c6d3facc09981633d6491474e5d93c13fbecad0fbecc47fccb1e19f87ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BLCSNCRLF6YFMR4K6IJE5BQQVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Braid groups of imprimitive complex reflection groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eon-Kyung Lee, Ruth Corran, Sang-Jin Lee","submitted_at":"2014-04-22T09:09:01Z","abstract_excerpt":"We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \\ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group $B(de,e,r)$ is a semidirect product of the braid group of affine type $\\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5430","kind":"arxiv","version":2},"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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PU+qZVSi536q+w5P7ETq22bu7/Pz7m+a1+g25C01IodkSlOF3IFTfv0/8t+Owz1GabWuPvYr1748nD7grtt+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:47:51.728644Z"},"content_sha256":"70d58e2462c2009271533ada86208cd606b9ddbda720b60a268cb52af0ac814f","schema_version":"1.0","event_id":"sha256:70d58e2462c2009271533ada86208cd606b9ddbda720b60a268cb52af0ac814f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/bundle.json","state_url":"https://pith.science/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/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":"2026-05-31T15:47:51Z","links":{"resolver":"https://pith.science/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ","bundle":"https://pith.science/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/bundle.json","state":"https://pith.science/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLCSNCRLF6YFMR4K6IJE5BQQVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BLCSNCRLF6YFMR4K6IJE5BQQVQ","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":"619f06dbd8e9503e0ca77b99bf1944feb32c3edd7c59fca13a6bda993d0c1eda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-22T09:09:01Z","title_canon_sha256":"72a65268e8d423a75483eb5b09ef983acc13502ded300bae7ed8b0423c730a19"},"schema_version":"1.0","source":{"id":"1404.5430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5430","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5430v2","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5430","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"BLCSNCRLF6YF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BLCSNCRLF6YFMR4K","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BLCSNCRL","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:70d58e2462c2009271533ada86208cd606b9ddbda720b60a268cb52af0ac814f","target":"graph","created_at":"2026-05-18T02:28:47Z","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 obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \\ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group $B(de,e,r)$ is a semidirect product of the braid group of affine type $\\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $","authors_text":"Eon-Kyung Lee, Ruth Corran, Sang-Jin Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-22T09:09:01Z","title":"Braid groups of imprimitive complex reflection groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5430","kind":"arxiv","version":2},"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":"sha256:690d1c6d3facc09981633d6491474e5d93c13fbecad0fbecc47fccb1e19f87ed","target":"record","created_at":"2026-05-18T02:28:47Z","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":"619f06dbd8e9503e0ca77b99bf1944feb32c3edd7c59fca13a6bda993d0c1eda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-22T09:09:01Z","title_canon_sha256":"72a65268e8d423a75483eb5b09ef983acc13502ded300bae7ed8b0423c730a19"},"schema_version":"1.0","source":{"id":"1404.5430","kind":"arxiv","version":2}},"canonical_sha256":"0ac5268a2b2fb056478af2124e8610ac0c328b0ce2062865f5c0c99c8277ec88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac5268a2b2fb056478af2124e8610ac0c328b0ce2062865f5c0c99c8277ec88","first_computed_at":"2026-05-18T02:28:47.946755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:47.946755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+Br9CIppzW/MQi4YVacrrVn154Aj0zhq87AE6Dw5Ny3jxDqobl40f7gQOR9O+b7fquBrQRrKvMmBaPz17g7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:47.947164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:690d1c6d3facc09981633d6491474e5d93c13fbecad0fbecc47fccb1e19f87ed","sha256:70d58e2462c2009271533ada86208cd606b9ddbda720b60a268cb52af0ac814f"],"state_sha256":"341899a5e3910e81c51324ce609b0189caef5e9108ecad185dbcde93e200a395"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZGlEy0++YVbrZbUUNd8mgZfVbE2Ol11jaeJVGkkiGs6t+M0rvwWlDOYpV8zPxHU4StFjs6yOXIJCDaqyYFhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:47:51.732925Z","bundle_sha256":"d6058f30a7f3d522736f5949c9e7ddca2d418725c145709034fab540e0565c38"}}