{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5YIF3K2KFTBMEDJ7RX73OD3D4Q","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":"a9c3bbff26d9347d41c0a87d3ffe87ed82a8aaf97246c04d0b2fff3427ef6db2","cross_cats_sorted":["math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-30T14:05:20Z","title_canon_sha256":"957bf587dd56ca74cc8f96d75c393e3cc3df80ef29e665fb93b90ee2a4096018"},"schema_version":"1.0","source":{"id":"2405.20075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.20075","created_at":"2026-07-05T08:25:24Z"},{"alias_kind":"arxiv_version","alias_value":"2405.20075v1","created_at":"2026-07-05T08:25:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.20075","created_at":"2026-07-05T08:25:24Z"},{"alias_kind":"pith_short_12","alias_value":"5YIF3K2KFTBM","created_at":"2026-07-05T08:25:24Z"},{"alias_kind":"pith_short_16","alias_value":"5YIF3K2KFTBMEDJ7","created_at":"2026-07-05T08:25:24Z"},{"alias_kind":"pith_short_8","alias_value":"5YIF3K2K","created_at":"2026-07-05T08:25:24Z"}],"graph_snapshots":[{"event_id":"sha256:e8de1df22e606096f2549ee2a95b55216ea10b95860511e240e53dc298546e46","target":"graph","created_at":"2026-07-05T08:25:24Z","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/2405.20075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This thesis explains the methods and algorithms we used to obtain explicit F symbols, R symbols, and pivotal coefficients of all multiplicity-free pivotal fusion categories up to rank 7. The thesis starts by introducing the concept of a unitary modular fusion system via two applications: modeling anyons for topological quantum computation and calculating braid group representations. Next, the notions of a pivotal, spherical, braided, ribbon, and modular fusion system are introduced. Unitarity and its implications on the pivotal structure are discussed as well. The next part of the thesis is de","authors_text":"Gert Vercleyen","cross_cats":["math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-30T14:05:20Z","title":"On Low-Rank Multiplicity-Free Fusion Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20075","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":"sha256:66853f2331468d23917779f1241efa6335a009beee2463e6f669f0b52a331e07","target":"record","created_at":"2026-07-05T08:25:24Z","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":"a9c3bbff26d9347d41c0a87d3ffe87ed82a8aaf97246c04d0b2fff3427ef6db2","cross_cats_sorted":["math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-30T14:05:20Z","title_canon_sha256":"957bf587dd56ca74cc8f96d75c393e3cc3df80ef29e665fb93b90ee2a4096018"},"schema_version":"1.0","source":{"id":"2405.20075","kind":"arxiv","version":1}},"canonical_sha256":"ee105dab4a2cc2c20d3f8dffb70f63e40f436a7d24f9ae785c4c2d6410f91197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee105dab4a2cc2c20d3f8dffb70f63e40f436a7d24f9ae785c4c2d6410f91197","first_computed_at":"2026-07-05T08:25:24.007182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:24.007182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"geRmdUl2hryv+A2llRXrTz2s7qR9k/c7+TXudCJ1KQ+iaHjykSBOKhkjaZVO+t/abfT7f+16ndq1/eTTPYUGDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:24.007793Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.20075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66853f2331468d23917779f1241efa6335a009beee2463e6f669f0b52a331e07","sha256:e8de1df22e606096f2549ee2a95b55216ea10b95860511e240e53dc298546e46"],"state_sha256":"7886ce228cb4114480758ce5bf7011a7d1ef610cd2ef08829220b5bbeed98309"}