{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:O7SOCCIZINXDW7BX57IXY4PT77","short_pith_number":"pith:O7SOCCIZ","canonical_record":{"source":{"id":"2412.15019","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-12-19T16:31:06Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"027d3f6906214d79cdef25c9f406723f29a07f3ed87d57955cd5357fc59fcb6e","abstract_canon_sha256":"da05bd537c3fef879f008b8faac95f450729be3b7b631fb449c8e602e1394628"},"schema_version":"1.0"},"canonical_sha256":"77e4e10919436e3b7c37efd17c71f3ffe4af7185b984515cf8ee282c4c651225","source":{"kind":"arxiv","id":"2412.15019","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15019","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15019v2","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15019","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"O7SOCCIZINXD","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_16","alias_value":"O7SOCCIZINXDW7BX","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_8","alias_value":"O7SOCCIZ","created_at":"2026-07-05T11:09:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:O7SOCCIZINXDW7BX57IXY4PT77","target":"record","payload":{"canonical_record":{"source":{"id":"2412.15019","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-12-19T16:31:06Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"027d3f6906214d79cdef25c9f406723f29a07f3ed87d57955cd5357fc59fcb6e","abstract_canon_sha256":"da05bd537c3fef879f008b8faac95f450729be3b7b631fb449c8e602e1394628"},"schema_version":"1.0"},"canonical_sha256":"77e4e10919436e3b7c37efd17c71f3ffe4af7185b984515cf8ee282c4c651225","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:05.655039Z","signature_b64":"zss46Cd29IjVwua/aURfB2WhopKaOlfiY5dUaMs3YimHffQk/RMXSaLIL+ua2VGP3w2jGbjxMLDkERooJuLcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77e4e10919436e3b7c37efd17c71f3ffe4af7185b984515cf8ee282c4c651225","last_reissued_at":"2026-07-05T11:09:05.654561Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:05.654561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.15019","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:09:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWDj+AMMQ31cNk9DoGVOMZTfAseTMap3P7LrAZPWwqYFJA8cKQxruy0z1+aSUAzUMKmYXL9IBfR5nO8G8FlXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:35:26.794543Z"},"content_sha256":"f65318a0327466576becd633bcc4c7d32e1d55f30e21eb0507c383eb5d6fdd2f","schema_version":"1.0","event_id":"sha256:f65318a0327466576becd633bcc4c7d32e1d55f30e21eb0507c383eb5d6fdd2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:O7SOCCIZINXDW7BX57IXY4PT77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact Semisimple Tensor 2-Categories are Morita Connected","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Sean Sanford, Thibault D. D\\'ecoppet","submitted_at":"2024-12-19T16:31:06Z","abstract_excerpt":"In arXiv:2211.04917, it was shown that, over an algebraically closed field of characteristic zero, every fusion 2-category is Morita equivalent to a connected fusion 2-category, that is, one arising from a braided fusion 1-category. This result has recently allowed for a complete classification of fusion 2-categories. Here we establish that compact semisimple tensor 2-categories, which generalize fusion 2-categories to an arbitrary field of characteristic zero, also enjoy this ``Morita connectedness'' property. In order to do so, we generalize to an arbitrary field of characteristic zero many "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15019","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.15019/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:09:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30ztEzkkLM4FTEitm3dVpznh/KDUPY8i6B5yDxBBizHmQRWmT688sPls19yAPWsJ//0yQtKpJT7dw6mZiYnkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:35:26.795409Z"},"content_sha256":"5d06bdfc0e30f169e9b0926fd7c8d992937ca4500da2b900a3376577773d7376","schema_version":"1.0","event_id":"sha256:5d06bdfc0e30f169e9b0926fd7c8d992937ca4500da2b900a3376577773d7376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7SOCCIZINXDW7BX57IXY4PT77/bundle.json","state_url":"https://pith.science/pith/O7SOCCIZINXDW7BX57IXY4PT77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7SOCCIZINXDW7BX57IXY4PT77/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T02:35:26Z","links":{"resolver":"https://pith.science/pith/O7SOCCIZINXDW7BX57IXY4PT77","bundle":"https://pith.science/pith/O7SOCCIZINXDW7BX57IXY4PT77/bundle.json","state":"https://pith.science/pith/O7SOCCIZINXDW7BX57IXY4PT77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7SOCCIZINXDW7BX57IXY4PT77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:O7SOCCIZINXDW7BX57IXY4PT77","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":"da05bd537c3fef879f008b8faac95f450729be3b7b631fb449c8e602e1394628","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-12-19T16:31:06Z","title_canon_sha256":"027d3f6906214d79cdef25c9f406723f29a07f3ed87d57955cd5357fc59fcb6e"},"schema_version":"1.0","source":{"id":"2412.15019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15019","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15019v2","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15019","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"O7SOCCIZINXD","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_16","alias_value":"O7SOCCIZINXDW7BX","created_at":"2026-07-05T11:09:05Z"},{"alias_kind":"pith_short_8","alias_value":"O7SOCCIZ","created_at":"2026-07-05T11:09:05Z"}],"graph_snapshots":[{"event_id":"sha256:5d06bdfc0e30f169e9b0926fd7c8d992937ca4500da2b900a3376577773d7376","target":"graph","created_at":"2026-07-05T11:09:05Z","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/2412.15019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In arXiv:2211.04917, it was shown that, over an algebraically closed field of characteristic zero, every fusion 2-category is Morita equivalent to a connected fusion 2-category, that is, one arising from a braided fusion 1-category. This result has recently allowed for a complete classification of fusion 2-categories. Here we establish that compact semisimple tensor 2-categories, which generalize fusion 2-categories to an arbitrary field of characteristic zero, also enjoy this ``Morita connectedness'' property. In order to do so, we generalize to an arbitrary field of characteristic zero many ","authors_text":"Sean Sanford, Thibault D. D\\'ecoppet","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-12-19T16:31:06Z","title":"Compact Semisimple Tensor 2-Categories are Morita Connected"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15019","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:f65318a0327466576becd633bcc4c7d32e1d55f30e21eb0507c383eb5d6fdd2f","target":"record","created_at":"2026-07-05T11:09:05Z","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":"da05bd537c3fef879f008b8faac95f450729be3b7b631fb449c8e602e1394628","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-12-19T16:31:06Z","title_canon_sha256":"027d3f6906214d79cdef25c9f406723f29a07f3ed87d57955cd5357fc59fcb6e"},"schema_version":"1.0","source":{"id":"2412.15019","kind":"arxiv","version":2}},"canonical_sha256":"77e4e10919436e3b7c37efd17c71f3ffe4af7185b984515cf8ee282c4c651225","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77e4e10919436e3b7c37efd17c71f3ffe4af7185b984515cf8ee282c4c651225","first_computed_at":"2026-07-05T11:09:05.654561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:05.654561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zss46Cd29IjVwua/aURfB2WhopKaOlfiY5dUaMs3YimHffQk/RMXSaLIL+ua2VGP3w2jGbjxMLDkERooJuLcBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:05.655039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.15019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f65318a0327466576becd633bcc4c7d32e1d55f30e21eb0507c383eb5d6fdd2f","sha256:5d06bdfc0e30f169e9b0926fd7c8d992937ca4500da2b900a3376577773d7376"],"state_sha256":"015aa632d77175de1cf97b9639c37482e2217a3f7fbfec9ddd88e9e3d8bb1ee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ADKUf+w2+zB+2Uqt50aJFfRPhJrF5r9x/Qk2HdHtBHXHxl2jkg57nvdDqfjyf9xJ8TUDbLg8DF08jQ6Jm9vBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:35:26.801894Z","bundle_sha256":"7fd11b8e554f20c31b775be839eda6f6be61bf8f1b5ed2ca5827678fd757b7cb"}}