{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GJHFWLKGYPLFEMQ4DB7EROFK6B","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":"a4f48c62d8767795ceed1d674c4e62c8ac9077b8165dbfcc29cf4125faea5539","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2007-01-29T19:00:46Z","title_canon_sha256":"40df3873b83891cf29c27fae7427144fabf90109efd456ee21e8fb87be64a1dd"},"schema_version":"1.0","source":{"id":"math/0701859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701859","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701859v2","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701859","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"GJHFWLKGYPLF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GJHFWLKGYPLFEMQ4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GJHFWLKG","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:b8b47b9cf73f60ec7bed7429fea5133d2d6e2717e7110149412e9fc65ec3d470","target":"graph","created_at":"2026-05-17T23:52:34Z","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 consider the hypercube in $\\mathbb R^n$, and show that its quantum symmetry group is a $q$-deformation of $O_n$ at $q=-1$. Then we consider the graph formed by $n$ segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted $H_n^+$, enlarges Wang's series $S_n^+,O_n^+,U_n^+$.","authors_text":"Benoit Collins, Julien Bichon, Teodor Banica","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2007-01-29T19:00:46Z","title":"The hyperoctahedral quantum group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701859","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":"sha256:66a5e4747461e17bbc8195de3effd513cbe7519d56965d0a9c10f34324ea0064","target":"record","created_at":"2026-05-17T23:52:34Z","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":"a4f48c62d8767795ceed1d674c4e62c8ac9077b8165dbfcc29cf4125faea5539","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2007-01-29T19:00:46Z","title_canon_sha256":"40df3873b83891cf29c27fae7427144fabf90109efd456ee21e8fb87be64a1dd"},"schema_version":"1.0","source":{"id":"math/0701859","kind":"arxiv","version":2}},"canonical_sha256":"324e5b2d46c3d652321c187e48b8aaf0551d8092943266cb276a6c3d5ac627e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"324e5b2d46c3d652321c187e48b8aaf0551d8092943266cb276a6c3d5ac627e2","first_computed_at":"2026-05-17T23:52:34.609976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:34.609976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mmdsP0jTg14weu3pmjZagucbx7AvQ4ZUxB4BLkXfhtQjcuUl9cNWhbqK9Nr3PeAAOChQGaCtmDBaenNra+9zCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:34.610447Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66a5e4747461e17bbc8195de3effd513cbe7519d56965d0a9c10f34324ea0064","sha256:b8b47b9cf73f60ec7bed7429fea5133d2d6e2717e7110149412e9fc65ec3d470"],"state_sha256":"113a1e104d5836abf2fc2b809b5549a7fa8414e290eb7879acf7e796e3825e74"}