{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G5N3HQ3J3J3EH6HXTODRIBT657","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":"54fc115de5f22e592c710e063eb5fe347c5830fac1cc66e0d3bf700b45231cd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-11T23:23:36Z","title_canon_sha256":"32336c1f9c4130e829f940e8fe57e8dca9fc7b23d72ae54d54f242cd50941ca5"},"schema_version":"1.0","source":{"id":"1712.04067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04067","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04067v2","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04067","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"G5N3HQ3J3J3E","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G5N3HQ3J3J3EH6HX","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G5N3HQ3J","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:c58d5d7b1044ae0d4ae0f4956f75a0ee65106c292cb20666830059a4af2cf9cb","target":"graph","created_at":"2026-05-17T23:54:03Z","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 investigate the notion of $k$-transitivity for the quantum permutation groups $G\\subset S_N^+$, with a brief review of the known $k=1,2$ results, and with a study of what happens at $k\\geq3$. We discuss then matrix modelling questions for the algebras $C(G)$, notably by introducing the related notions of double and triple flat matrix model. At the level of the examples, our main results concern the quantum groups coming from the complex Hadamard matrices, and from the Weyl matrices.","authors_text":"Teodor Banica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-11T23:23:36Z","title":"Higher transitive quantum groups: theory and models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04067","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:cfb70416da63a90307e84bd7a16e418110c5e34a0e1a00830dc1ec9121bc5978","target":"record","created_at":"2026-05-17T23:54:03Z","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":"54fc115de5f22e592c710e063eb5fe347c5830fac1cc66e0d3bf700b45231cd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-11T23:23:36Z","title_canon_sha256":"32336c1f9c4130e829f940e8fe57e8dca9fc7b23d72ae54d54f242cd50941ca5"},"schema_version":"1.0","source":{"id":"1712.04067","kind":"arxiv","version":2}},"canonical_sha256":"375bb3c369da7643f8f79b8714067eeff2f782d44736433bd3e8bc6b29cb0b2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"375bb3c369da7643f8f79b8714067eeff2f782d44736433bd3e8bc6b29cb0b2e","first_computed_at":"2026-05-17T23:54:03.161404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.161404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hJSxc3/rpHeVM7fVarO3Vc6kUIJDrJDJVNRPxaQEuhGNR30x4q+TT93z7zRAhw7013r0S+dycGx213chPzp+CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.161987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfb70416da63a90307e84bd7a16e418110c5e34a0e1a00830dc1ec9121bc5978","sha256:c58d5d7b1044ae0d4ae0f4956f75a0ee65106c292cb20666830059a4af2cf9cb"],"state_sha256":"a17f169999e3a227ea921b45c6f8b39c6ae06b1c96982982f1661f5e4b9457c7"}