{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JVS2HND7OQKNQN64IA54S6HYWM","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":"ac6a3ccc8c3b6003e240adf37ba44b88b87957ddbc4437c4dc15f0e41fbd7311","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-09-06T11:01:10Z","title_canon_sha256":"e4397365d0300ab6fe8100f18cff3ea30bc98afee6fa9eec122a984cc1b5776b"},"schema_version":"1.0","source":{"id":"1909.02816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02816","created_at":"2026-07-05T03:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02816v2","created_at":"2026-07-05T03:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02816","created_at":"2026-07-05T03:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"JVS2HND7OQKN","created_at":"2026-07-05T03:15:06Z"},{"alias_kind":"pith_short_16","alias_value":"JVS2HND7OQKNQN64","created_at":"2026-07-05T03:15:06Z"},{"alias_kind":"pith_short_8","alias_value":"JVS2HND7","created_at":"2026-07-05T03:15:06Z"}],"graph_snapshots":[{"event_id":"sha256:366a7691563b1a667f13d7c6f9a734a844cb3ec69f09c6c71f1adac685e32034","target":"graph","created_at":"2026-07-05T03:15:06Z","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/1909.02816/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A $G$-graded extension of a fusion category $\\mathcal{C}$ yields a categorical action of $G$ on the center $Z(\\mathcal C)$. If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the action. We then apply this to find closed formulas for the fusion rules of extensions of some group theoretical categories and of cyclic permutation crossed extensions of modular categories.","authors_text":"Corey Jones, Marcel Bischoff","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-09-06T11:01:10Z","title":"Computing fusion rules for spherical G-extensions of fusion categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02816","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":"sha256:36afc812b200ec2d1f4dd9935b6294be1a3fcf3ba0ec387e0dacb022e780996d","target":"record","created_at":"2026-07-05T03:15:06Z","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":"ac6a3ccc8c3b6003e240adf37ba44b88b87957ddbc4437c4dc15f0e41fbd7311","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-09-06T11:01:10Z","title_canon_sha256":"e4397365d0300ab6fe8100f18cff3ea30bc98afee6fa9eec122a984cc1b5776b"},"schema_version":"1.0","source":{"id":"1909.02816","kind":"arxiv","version":2}},"canonical_sha256":"4d65a3b47f7414d837dc403bc978f8b32082f2414efe6e3f5f0c47cdaece2ef6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d65a3b47f7414d837dc403bc978f8b32082f2414efe6e3f5f0c47cdaece2ef6","first_computed_at":"2026-07-05T03:15:06.464837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:15:06.464837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptKvdFuzElg9Wq2Bz3sGI79JFTHCVr/8CrYPwuzf82FvvBnVxNKaXwXT52RcZEZptyylUEGktUeF1QYlP2BTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:15:06.465261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.02816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36afc812b200ec2d1f4dd9935b6294be1a3fcf3ba0ec387e0dacb022e780996d","sha256:366a7691563b1a667f13d7c6f9a734a844cb3ec69f09c6c71f1adac685e32034"],"state_sha256":"8a4892005889a846a1426035c358ebddc12aa5812f0f12680325ec342a0a3577"}