{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L2GEJXQJOBWZBFDXSKG675MW22","short_pith_number":"pith:L2GEJXQJ","canonical_record":{"source":{"id":"1801.06125","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-18T16:58:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"837662b360b0fed96279ae5947c4cb7538c1e6c7785134c930877358ca31b355","abstract_canon_sha256":"e5d70374e19e76b97bd7d28f92203afe7d3697080c587b12ab741a70ed3215bb"},"schema_version":"1.0"},"canonical_sha256":"5e8c44de09706d909477928deff596d68a2b9f4f84a83944e08d50d54bc094f5","source":{"kind":"arxiv","id":"1801.06125","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06125","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06125v2","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06125","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"L2GEJXQJOBWZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L2GEJXQJOBWZBFDX","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L2GEJXQJ","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L2GEJXQJOBWZBFDXSKG675MW22","target":"record","payload":{"canonical_record":{"source":{"id":"1801.06125","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-18T16:58:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"837662b360b0fed96279ae5947c4cb7538c1e6c7785134c930877358ca31b355","abstract_canon_sha256":"e5d70374e19e76b97bd7d28f92203afe7d3697080c587b12ab741a70ed3215bb"},"schema_version":"1.0"},"canonical_sha256":"5e8c44de09706d909477928deff596d68a2b9f4f84a83944e08d50d54bc094f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:47.400478Z","signature_b64":"qiQxU4Y00eJmKUxboOdwDqSUSJmoHCtYOJ9uiOaHjUAL2USbjgs2XVFQZesWA0P680U6bw2smgTvAdwcgQ5mAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e8c44de09706d909477928deff596d68a2b9f4f84a83944e08d50d54bc094f5","last_reissued_at":"2026-05-18T00:09:47.399843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:47.399843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.06125","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":"2026-05-18T00:09:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UB/i20SB3f8mH3I1wvOOg2U6i0UcSGrO7CfZJ5eXT5N8ZpzQxBE9orZ5FquYnUwaMPFKCeaVSZ1UcWWzaC4ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:30:11.217695Z"},"content_sha256":"4ba95330f366250b12b6617eaeed88179ded6ec1c335856ffd3f8527cb5021fd","schema_version":"1.0","event_id":"sha256:4ba95330f366250b12b6617eaeed88179ded6ec1c335856ffd3f8527cb5021fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L2GEJXQJOBWZBFDXSKG675MW22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying braidings on fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Dmitri Nikshych","submitted_at":"2018-01-18T16:58:16Z","abstract_excerpt":"We show that braidings on a fusion category $\\mathcal{C}$ correspond to certain fusion subcategories of the center of $\\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06125","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":""},"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":"2026-05-18T00:09:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/uqHG3A0gRPYez4IpBHffsrfwv+7mi/eP1rHrSSUYR/NqPexoREjhErGxQ0nhVGIqk0rii2hP+12fx+ANvgHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:30:11.218030Z"},"content_sha256":"19736f739f12553765b0072296957f890503523314197016af2deac6ee409d6d","schema_version":"1.0","event_id":"sha256:19736f739f12553765b0072296957f890503523314197016af2deac6ee409d6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2GEJXQJOBWZBFDXSKG675MW22/bundle.json","state_url":"https://pith.science/pith/L2GEJXQJOBWZBFDXSKG675MW22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2GEJXQJOBWZBFDXSKG675MW22/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":"2026-06-02T02:30:11Z","links":{"resolver":"https://pith.science/pith/L2GEJXQJOBWZBFDXSKG675MW22","bundle":"https://pith.science/pith/L2GEJXQJOBWZBFDXSKG675MW22/bundle.json","state":"https://pith.science/pith/L2GEJXQJOBWZBFDXSKG675MW22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2GEJXQJOBWZBFDXSKG675MW22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L2GEJXQJOBWZBFDXSKG675MW22","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":"e5d70374e19e76b97bd7d28f92203afe7d3697080c587b12ab741a70ed3215bb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-18T16:58:16Z","title_canon_sha256":"837662b360b0fed96279ae5947c4cb7538c1e6c7785134c930877358ca31b355"},"schema_version":"1.0","source":{"id":"1801.06125","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06125","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06125v2","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06125","created_at":"2026-05-18T00:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"L2GEJXQJOBWZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L2GEJXQJOBWZBFDX","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L2GEJXQJ","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:19736f739f12553765b0072296957f890503523314197016af2deac6ee409d6d","target":"graph","created_at":"2026-05-18T00:09:47Z","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 show that braidings on a fusion category $\\mathcal{C}$ correspond to certain fusion subcategories of the center of $\\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories.","authors_text":"Dmitri Nikshych","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-18T16:58:16Z","title":"Classifying braidings on fusion categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06125","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":"sha256:4ba95330f366250b12b6617eaeed88179ded6ec1c335856ffd3f8527cb5021fd","target":"record","created_at":"2026-05-18T00:09:47Z","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":"e5d70374e19e76b97bd7d28f92203afe7d3697080c587b12ab741a70ed3215bb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-18T16:58:16Z","title_canon_sha256":"837662b360b0fed96279ae5947c4cb7538c1e6c7785134c930877358ca31b355"},"schema_version":"1.0","source":{"id":"1801.06125","kind":"arxiv","version":2}},"canonical_sha256":"5e8c44de09706d909477928deff596d68a2b9f4f84a83944e08d50d54bc094f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e8c44de09706d909477928deff596d68a2b9f4f84a83944e08d50d54bc094f5","first_computed_at":"2026-05-18T00:09:47.399843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:47.399843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qiQxU4Y00eJmKUxboOdwDqSUSJmoHCtYOJ9uiOaHjUAL2USbjgs2XVFQZesWA0P680U6bw2smgTvAdwcgQ5mAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:47.400478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06125","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ba95330f366250b12b6617eaeed88179ded6ec1c335856ffd3f8527cb5021fd","sha256:19736f739f12553765b0072296957f890503523314197016af2deac6ee409d6d"],"state_sha256":"541714d855eb9bd64b0d008dfc5d76012e4ed3cb9e00b03d1008b31593f70dc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WYI3domyhaVB80L58Qp2Fledako/8HFddUScPBSS/Lns8RxJLz4T9QxJLHH2rw3OdnqssFc5yBoT5+zW5eWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:30:11.219977Z","bundle_sha256":"afdee84ce4621325ed027c066a1f3527cc271206da9725b7e79851ede4975bc4"}}