{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IUNUWN36YQ4B77LPBGOUUPQD5R","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":"8eac3b682feadc7b12e9c106895755342e6a3bf0dca26dbe062a979798c617c1","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-02T08:17:28Z","title_canon_sha256":"4b41210c080e9ed6eaccf8267752fa5e341473f131a24025637d26de43bb84e0"},"schema_version":"1.0","source":{"id":"1711.00645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00645","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00645v2","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00645","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"IUNUWN36YQ4B","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IUNUWN36YQ4B77LP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IUNUWN36","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:ab5e2a4e68bcb76db822045627c535b85963b4933402faf3c9bb17353a922467","target":"graph","created_at":"2026-05-17T23:58:19Z","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 further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the $\\mathcal{C}$-based equivalences between two $G$-graded extensions of $\\mathcal{C}$. The main result of this paper (which follows from this classification) shows that there is an action of the group $\\operatorname{Aut}(G)\\times \\operatorname{Aut}_\\otimes(\\mathcal{C})$ on the set of all $G$-graded extensions of $\\mathcal{C}$, and further, any two extensions in the same orbit of this action are monoidally equivalent. As a warm up for the proof of our classification result we reprove the classification o","authors_text":"Cain Edie-Michell","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-02T08:17:28Z","title":"Equivalences of Graded Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00645","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":"sha256:8fa8c2bcdb74cfd17e806c7cea413ef15424c33e3adbff450774b52c6e810ed5","target":"record","created_at":"2026-05-17T23:58:19Z","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":"8eac3b682feadc7b12e9c106895755342e6a3bf0dca26dbe062a979798c617c1","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-02T08:17:28Z","title_canon_sha256":"4b41210c080e9ed6eaccf8267752fa5e341473f131a24025637d26de43bb84e0"},"schema_version":"1.0","source":{"id":"1711.00645","kind":"arxiv","version":2}},"canonical_sha256":"451b4b377ec4381ffd6f099d4a3e03ec752c3582bdd34e0676837e692fc351f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"451b4b377ec4381ffd6f099d4a3e03ec752c3582bdd34e0676837e692fc351f0","first_computed_at":"2026-05-17T23:58:19.564706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.564706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J4RQokszOBg12mCtvzLV+6dm/F8SVrJ7XoBVa7VxnPNMi2uv5bZAPJl3HpC54vyQFOT3n+ACN3FWJIJs/VjCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.565227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa8c2bcdb74cfd17e806c7cea413ef15424c33e3adbff450774b52c6e810ed5","sha256:ab5e2a4e68bcb76db822045627c535b85963b4933402faf3c9bb17353a922467"],"state_sha256":"3bc94bf509c66ef8193d3d9726fb3c4df9f6d15817d7a02055eeb3dc1f6b853d"}