{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DTRDGALE6JMD2DESIX7QRME7BR","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":"049f32fcec4b5f9dbadedfd5457015d61baead96cafced3b2863beabead503f1","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-14T13:59:16Z","title_canon_sha256":"e6c952cf63f2474e5a390474cfa805adfa189bf68ad48cc5b07f37ac2af7f5ab"},"schema_version":"1.0","source":{"id":"1602.04456","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04456","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04456v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04456","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"DTRDGALE6JMD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTRDGALE6JMD2DES","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTRDGALE","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:d5eb20c6a5524512b06a3e8a050693695abd74830a8ab5a7e387cca7aa4a800b","target":"graph","created_at":"2026-05-18T01:04:46Z","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 study the matrix models $\\pi:C(S_N^+)\\to M_N(C(X))$ which are flat, in the sense that the standard generators of $C(S_N^+)$ are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at $N=4$, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of $C(S_N^+)$, inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.","authors_text":"Ion Nechita, Teodor Banica","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-14T13:59:16Z","title":"Flat matrix models for quantum permutation groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04456","kind":"arxiv","version":3},"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":"sha256:3014ea30d12ccbfd16bfda85fb1496cc3d036556c1f3656e6949ce625f27775c","target":"record","created_at":"2026-05-18T01:04:46Z","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":"049f32fcec4b5f9dbadedfd5457015d61baead96cafced3b2863beabead503f1","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-14T13:59:16Z","title_canon_sha256":"e6c952cf63f2474e5a390474cfa805adfa189bf68ad48cc5b07f37ac2af7f5ab"},"schema_version":"1.0","source":{"id":"1602.04456","kind":"arxiv","version":3}},"canonical_sha256":"1ce2330164f2583d0c9245ff08b09f0c61e1ea2946ddac57fc734829b8a74084","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ce2330164f2583d0c9245ff08b09f0c61e1ea2946ddac57fc734829b8a74084","first_computed_at":"2026-05-18T01:04:46.546270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.546270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bMFa9qbSX6XTeA8G4EmjlhUcp3ZsXlycRelgRjopX8+/RGT/+tNoBu8D6jUukcUIRuT61RrhNbvQ1SDtr/gVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.546929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04456","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3014ea30d12ccbfd16bfda85fb1496cc3d036556c1f3656e6949ce625f27775c","sha256:d5eb20c6a5524512b06a3e8a050693695abd74830a8ab5a7e387cca7aa4a800b"],"state_sha256":"4217778f79e9e1fa3ba4dd923e0e49c10b1bda76c0e66a21ae9e7bb5fab8046c"}