{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VBYADCGWU52L4GBZ6CMZVZQ5FL","short_pith_number":"pith:VBYADCGW","canonical_record":{"source":{"id":"1411.1778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T21:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"6cc550d60d519c1f7db5244100c06454627feba2bfddec8ebbd56d2b8863e4de","abstract_canon_sha256":"2cd2a4af2b37e9cc606a20ac5ae1ce838ac08aee4c8f4571abe7082f4a00171a"},"schema_version":"1.0"},"canonical_sha256":"a8700188d6a774be1839f0999ae61d2aeef5f3e04b9fcf15c0dfcf650f09a8ae","source":{"kind":"arxiv","id":"1411.1778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1778","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1778v1","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1778","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"VBYADCGWU52L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VBYADCGWU52L4GBZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VBYADCGW","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VBYADCGWU52L4GBZ6CMZVZQ5FL","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T21:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"6cc550d60d519c1f7db5244100c06454627feba2bfddec8ebbd56d2b8863e4de","abstract_canon_sha256":"2cd2a4af2b37e9cc606a20ac5ae1ce838ac08aee4c8f4571abe7082f4a00171a"},"schema_version":"1.0"},"canonical_sha256":"a8700188d6a774be1839f0999ae61d2aeef5f3e04b9fcf15c0dfcf650f09a8ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:26.021031Z","signature_b64":"ogghrSMhK1+CikAFarKTtN+MW+ZAM+SSu/ASVni7qRmN8ryO4oJpFrxzOBch+vTXnV28yOMBVR5TJw465XkQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8700188d6a774be1839f0999ae61d2aeef5f3e04b9fcf15c0dfcf650f09a8ae","last_reissued_at":"2026-05-18T02:38:26.020532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:26.020532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1778","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":"2026-05-18T02:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1lNcMrPCQmOYXYUZmMmo9yzJ5cAETvFge/J02+yHILXewSvgCFvhR1T1UFHZARfuCda/d1wAbCGuh9lUBVXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:49:48.169225Z"},"content_sha256":"20e9216d8584750079eba04129f9c010e956b80e4e03e376f96e5b6d4a3743d7","schema_version":"1.0","event_id":"sha256:20e9216d8584750079eba04129f9c010e956b80e4e03e376f96e5b6d4a3743d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VBYADCGWU52L4GBZ6CMZVZQ5FL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher topological complexity of Artin type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Sergey Yuzvinsky","submitted_at":"2014-11-06T21:40:36Z","abstract_excerpt":"We calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple combinatorial criterion of arrangements sufficed for the cohomological low bound for TC$_s$ to coincide with the dimensional upper bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1778","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":"2026-05-18T02:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1T3WJHCjO3t7hmab17LhCdc7R6nk15I9IjorQq9ffukOFlxcuyBF/Czhd1F5TZzP0iJ7VjG3stDIsBdxufMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:49:48.169648Z"},"content_sha256":"d76eaf419ba8efb4c33252ec0bd4fc2631cc3a7d6b013221f2e61b16b0712483","schema_version":"1.0","event_id":"sha256:d76eaf419ba8efb4c33252ec0bd4fc2631cc3a7d6b013221f2e61b16b0712483"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/bundle.json","state_url":"https://pith.science/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/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":"2026-06-20T07:49:48Z","links":{"resolver":"https://pith.science/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL","bundle":"https://pith.science/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/bundle.json","state":"https://pith.science/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBYADCGWU52L4GBZ6CMZVZQ5FL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VBYADCGWU52L4GBZ6CMZVZQ5FL","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":"2cd2a4af2b37e9cc606a20ac5ae1ce838ac08aee4c8f4571abe7082f4a00171a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T21:40:36Z","title_canon_sha256":"6cc550d60d519c1f7db5244100c06454627feba2bfddec8ebbd56d2b8863e4de"},"schema_version":"1.0","source":{"id":"1411.1778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1778","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1778v1","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1778","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"VBYADCGWU52L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VBYADCGWU52L4GBZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VBYADCGW","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:d76eaf419ba8efb4c33252ec0bd4fc2631cc3a7d6b013221f2e61b16b0712483","target":"graph","created_at":"2026-05-18T02:38:26Z","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 calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple combinatorial criterion of arrangements sufficed for the cohomological low bound for TC$_s$ to coincide with the dimensional upper bound.","authors_text":"Sergey Yuzvinsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T21:40:36Z","title":"Higher topological complexity of Artin type groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1778","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":"sha256:20e9216d8584750079eba04129f9c010e956b80e4e03e376f96e5b6d4a3743d7","target":"record","created_at":"2026-05-18T02:38:26Z","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":"2cd2a4af2b37e9cc606a20ac5ae1ce838ac08aee4c8f4571abe7082f4a00171a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T21:40:36Z","title_canon_sha256":"6cc550d60d519c1f7db5244100c06454627feba2bfddec8ebbd56d2b8863e4de"},"schema_version":"1.0","source":{"id":"1411.1778","kind":"arxiv","version":1}},"canonical_sha256":"a8700188d6a774be1839f0999ae61d2aeef5f3e04b9fcf15c0dfcf650f09a8ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8700188d6a774be1839f0999ae61d2aeef5f3e04b9fcf15c0dfcf650f09a8ae","first_computed_at":"2026-05-18T02:38:26.020532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:26.020532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ogghrSMhK1+CikAFarKTtN+MW+ZAM+SSu/ASVni7qRmN8ryO4oJpFrxzOBch+vTXnV28yOMBVR5TJw465XkQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:26.021031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20e9216d8584750079eba04129f9c010e956b80e4e03e376f96e5b6d4a3743d7","sha256:d76eaf419ba8efb4c33252ec0bd4fc2631cc3a7d6b013221f2e61b16b0712483"],"state_sha256":"0946a667d1bd1954df2dcf3cbe12b4d029b0f5928b6609c9b6fcacf4c9b80a96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOHJMc2/B0QNAsAYqbYMWX8VPyzfKDYHsAd2C5AVzmQO/MIGzDY+XYHYeSGUI9QdSob+CxCqvqwvZaVE42FLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:49:48.171583Z","bundle_sha256":"60f1ee64c5637663f8c18753bbe961d9be617f05da37a7c6abf6f74166906e8d"}}