{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TCWKRTRYD6BQS4BCCQ3JT3CVYX","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":"cdca5fda85353ceea4b662abf5fdd9378ad97fe69c52fb476a5ab0f745527d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-09T01:42:19Z","title_canon_sha256":"2f85848d5a3bc9e4fc9214ac97dc285769e52ac914393b463f78da9369bd90c8"},"schema_version":"1.0","source":{"id":"1401.1879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1879","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1879v2","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1879","created_at":"2026-05-18T02:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"TCWKRTRYD6BQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TCWKRTRYD6BQS4BC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TCWKRTRY","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:0617e1f7af124bed1092135e6506f2aa72252e3c60c1585983fcf49b87472d39","target":"graph","created_at":"2026-05-18T02:39:01Z","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":"A fusion category of rank $4$ has either four self-dual objects or exactly two self-dual objects. We study fusion categories of rank $4$ with exactly two self-dual objects, giving nearly a complete classification of those based ring that admit pseudo-unitary categorification. More precisely, we show that if $\\mathcal{C}$ is such a fusion category, then its Grothendieck ring $K(\\mathcal{C})$ must be one of seven based rings, six of which have know categorifications. In doing so, we classify all based rings associated with near-group categories of the group $\\mathbb{Z}/3\\mathbb{Z}$.","authors_text":"Hannah K. Larson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-09T01:42:19Z","title":"Pseudo-unitary non-self-dual fusion categories of rank 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1879","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":"sha256:70b186907ccb54a5cdfabc98629dd304d6762965e7dbb868f9e9b5ce0c2cf755","target":"record","created_at":"2026-05-18T02:39:01Z","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":"cdca5fda85353ceea4b662abf5fdd9378ad97fe69c52fb476a5ab0f745527d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-09T01:42:19Z","title_canon_sha256":"2f85848d5a3bc9e4fc9214ac97dc285769e52ac914393b463f78da9369bd90c8"},"schema_version":"1.0","source":{"id":"1401.1879","kind":"arxiv","version":2}},"canonical_sha256":"98aca8ce381f83097022143699ec55c5fbe8400dcd135e4a7fc50dae40888e87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98aca8ce381f83097022143699ec55c5fbe8400dcd135e4a7fc50dae40888e87","first_computed_at":"2026-05-18T02:39:01.149282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:01.149282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IdTDLHno6Tx+/U6w8gYuEZbnQfoABbJpeQCIjRXT8x/Rf+n5Ub0GfLgcOxYEi8pjRZipCg6eBPd5rAkNWz7UCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:01.149724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70b186907ccb54a5cdfabc98629dd304d6762965e7dbb868f9e9b5ce0c2cf755","sha256:0617e1f7af124bed1092135e6506f2aa72252e3c60c1585983fcf49b87472d39"],"state_sha256":"c6b35974e020388347ae2be74e9e27ecb3bfd63f7bc9e3741ea5c30b0806aa03"}