{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RXJOHPXXFE2SSEIKDPI26B55SZ","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":"602ad6fd9eb1a4b63c5be1e413524902e248464984cf6699e430b14e0e083840","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-06-06T13:31:38Z","title_canon_sha256":"e9c5190e1e942e458cc32935e314cd7272d3cf4f218aad66928a62c5a8b35d3a"},"schema_version":"1.0","source":{"id":"2206.02611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.02611","created_at":"2026-07-05T04:29:19Z"},{"alias_kind":"arxiv_version","alias_value":"2206.02611v1","created_at":"2026-07-05T04:29:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.02611","created_at":"2026-07-05T04:29:19Z"},{"alias_kind":"pith_short_12","alias_value":"RXJOHPXXFE2S","created_at":"2026-07-05T04:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"RXJOHPXXFE2SSEIK","created_at":"2026-07-05T04:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"RXJOHPXX","created_at":"2026-07-05T04:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:54e32dd31762a25238808fdf6518c30366a6bfcf3bab5d8741b789993168601b","target":"graph","created_at":"2026-07-05T04:29:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.02611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In Mulevi\\v{c}ius-Runkel, arXiv:2002.00663, it was shown how a so-called orbifold datum $\\mathbb{A}$ in a given modular fusion category (MFC) $\\mathcal{C}$ produces a new MFC $\\mathcal{C}_{\\mathbb{A}}$. Examples of these associated MFCs include condensations, i.e. the categories $\\mathcal{C}_B^\\circ$ of local modules of a separable commutative algebra $B\\in\\mathcal{C}$. In this paper we prove that the relation $\\mathcal{C} \\sim \\mathcal{C}_{\\mathbb{A}}$ on MFCs is the same as Witt equivalence. This is achieved in part by providing one with an explicit construction for inverting condensations, ","authors_text":"Vincentas Mulevicius","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-06-06T13:31:38Z","title":"Condensation inversion and Witt equivalence via generalised orbifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.02611","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":"sha256:378f6d2999cf3a0048f3bfda5eb38de51ea55cd68cd20e269bde9c75f9fb5305","target":"record","created_at":"2026-07-05T04:29:19Z","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":"602ad6fd9eb1a4b63c5be1e413524902e248464984cf6699e430b14e0e083840","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-06-06T13:31:38Z","title_canon_sha256":"e9c5190e1e942e458cc32935e314cd7272d3cf4f218aad66928a62c5a8b35d3a"},"schema_version":"1.0","source":{"id":"2206.02611","kind":"arxiv","version":1}},"canonical_sha256":"8dd2e3bef7293529110a1bd1af07bd9652ed6c93b5588689a67c13627d9442b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dd2e3bef7293529110a1bd1af07bd9652ed6c93b5588689a67c13627d9442b4","first_computed_at":"2026-07-05T04:29:19.620324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:29:19.620324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jCfWKFegFOJv9v7QqTyLwV/t3257lUXAOmgxc6xFtpsqyRvWOIez/9MeKkcNrHypMIvLPHHfsLZPOxatfEp0Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:29:19.620754Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.02611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378f6d2999cf3a0048f3bfda5eb38de51ea55cd68cd20e269bde9c75f9fb5305","sha256:54e32dd31762a25238808fdf6518c30366a6bfcf3bab5d8741b789993168601b"],"state_sha256":"bcf96a66784942ef85a2323feab4666c448c7eea6e34ca8bd3112d29610a9712"}