{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AKHZGJGHJST5TBK62NVYG6EXUI","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":"6b291649de842d6fd0654200e0c0cd82a3d35e8dd35c157d198577a1e0c5cd75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-11T12:48:38Z","title_canon_sha256":"b899e57511c6ae44c3fb1f1668d4f254decbdf1de010089e01a80cce1fdde1aa"},"schema_version":"1.0","source":{"id":"2606.13296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13296","created_at":"2026-06-12T01:09:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13296v1","created_at":"2026-06-12T01:09:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13296","created_at":"2026-06-12T01:09:51Z"},{"alias_kind":"pith_short_12","alias_value":"AKHZGJGHJST5","created_at":"2026-06-12T01:09:51Z"},{"alias_kind":"pith_short_16","alias_value":"AKHZGJGHJST5TBK6","created_at":"2026-06-12T01:09:51Z"},{"alias_kind":"pith_short_8","alias_value":"AKHZGJGH","created_at":"2026-06-12T01:09:51Z"}],"graph_snapshots":[{"event_id":"sha256:914ccf11f1ac88bbf4fe16002375b4959f6a4ce8353cd34abad3fabae9d8f3e9","target":"graph","created_at":"2026-06-12T01:09:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.13296/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that an Artin group $A_\\Gamma$ of XXL type (with all defining integers satisfying $m_{ij}\\geq 5$) is isomorphic to the corresponding dual Artin group for any choice of Coxeter element. Our proof involves the set of Hurwitz words $Q$ which arise from the Hurwitz action on tuples of elements of the free group. We show that the canonical epimorphism from $A_\\Gamma$ to the dual Artin group is an isomorphism if and only if the projection from $A_\\Gamma$ to the Coxeter group is injective on the image of $Q$. Then, using geometric properties of $Q$ and the solution to the word problem for Cox","authors_text":"Sean O'Brien","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-11T12:48:38Z","title":"The dual Artin isomorphism for Artin groups of XXL type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13296","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":"sha256:72e8fbdd28b7dffcb736653c450a3f2a38f8c8a86bc3437967679a5d17b00fb3","target":"record","created_at":"2026-06-12T01:09:51Z","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":"6b291649de842d6fd0654200e0c0cd82a3d35e8dd35c157d198577a1e0c5cd75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-11T12:48:38Z","title_canon_sha256":"b899e57511c6ae44c3fb1f1668d4f254decbdf1de010089e01a80cce1fdde1aa"},"schema_version":"1.0","source":{"id":"2606.13296","kind":"arxiv","version":1}},"canonical_sha256":"028f9324c74ca7d9855ed36b837897a22e9b44d0b46d389cad1fd039bf93d7cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"028f9324c74ca7d9855ed36b837897a22e9b44d0b46d389cad1fd039bf93d7cb","first_computed_at":"2026-06-12T01:09:51.143125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:51.143125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wt5vt9j0VdR8lVtYPr/wdEyDTqSRX1m9RpyBRHYE/FMiTOn3gdDQDcpEhQSutX0oqRafkvT/mfOuXTGdu612Dw==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:51.143713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e8fbdd28b7dffcb736653c450a3f2a38f8c8a86bc3437967679a5d17b00fb3","sha256:914ccf11f1ac88bbf4fe16002375b4959f6a4ce8353cd34abad3fabae9d8f3e9"],"state_sha256":"a8470804ba868c68856fd2eea11d46ffe1a02db7c133369c4b677e1be4e13d29"}