{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:36U7FQ5M4QBGF4B5IQAOMGYJ2H","short_pith_number":"pith:36U7FQ5M","canonical_record":{"source":{"id":"0909.0283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-01T22:03:20Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"fcd9571f2658480b6cdd914bbf90d101477483aa03da99aa20c395fb19d55cb8","abstract_canon_sha256":"1219ae196fd6777f3e9302b757ac766c4a62cee46f46abb9de33c70c0654e41a"},"schema_version":"1.0"},"canonical_sha256":"dfa9f2c3ace40262f03d4400e61b09d1fd4fd7ea06d05737af3309f4c971d049","source":{"kind":"arxiv","id":"0909.0283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0283","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0283v2","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0283","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"36U7FQ5M4QBG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"36U7FQ5M4QBGF4B5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"36U7FQ5M","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:36U7FQ5M4QBGF4B5IQAOMGYJ2H","target":"record","payload":{"canonical_record":{"source":{"id":"0909.0283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-01T22:03:20Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"fcd9571f2658480b6cdd914bbf90d101477483aa03da99aa20c395fb19d55cb8","abstract_canon_sha256":"1219ae196fd6777f3e9302b757ac766c4a62cee46f46abb9de33c70c0654e41a"},"schema_version":"1.0"},"canonical_sha256":"dfa9f2c3ace40262f03d4400e61b09d1fd4fd7ea06d05737af3309f4c971d049","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:22.903268Z","signature_b64":"MXVTeJQZtpS9mDUy/b9cwUSYzZOXdfak78qQoYu4GHtC2cHH7uAPi5Khr8clm4FDocixO3RKojSOnDay5p5tDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfa9f2c3ace40262f03d4400e61b09d1fd4fd7ea06d05737af3309f4c971d049","last_reissued_at":"2026-05-18T04:21:22.902813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:22.902813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.0283","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":"2026-05-18T04:21:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLxDh2tBaWb4oPYbbP6ywencURJpRX4i2Uu/wTkJgcEx4mAHzeoOpvCHbhtw8Q7gf6e7Mye6IDycWUzAO3G2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:16:06.110015Z"},"content_sha256":"f02ee3fcc0208ff9d283a4ac24f9795a1413dace8c1ee3aa7603ea3a3fa056f0","schema_version":"1.0","event_id":"sha256:f02ee3fcc0208ff9d283a4ac24f9795a1413dace8c1ee3aa7603ea3a3fa056f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:36U7FQ5M4QBGF4B5IQAOMGYJ2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine su(2) fusion rules from gerbe 2-isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Ingo Runkel, Rafal R. Suszek","submitted_at":"2009-09-01T22:03:20Z","abstract_excerpt":"We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rule coefficients are related to the existence of a 2-isomorphism between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2) determined by the corresponding three conjugacy classes. This construction is motivated by its application in the description of junctions of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0283","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":"2026-05-18T04:21:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RW3cjhqeTk4M6+10C60mE3HnQ1FtuxCXT+E00qmwmDt36IJKW1zEYe5xeM4Qau106YeP0x5HsEC85LRx2QtPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:16:06.110700Z"},"content_sha256":"8d38cea9348afae31022c1c20e1bd1bdafbcbe96c4695035a865216c947c9648","schema_version":"1.0","event_id":"sha256:8d38cea9348afae31022c1c20e1bd1bdafbcbe96c4695035a865216c947c9648"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/bundle.json","state_url":"https://pith.science/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/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":"2026-06-11T23:16:06Z","links":{"resolver":"https://pith.science/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H","bundle":"https://pith.science/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/bundle.json","state":"https://pith.science/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36U7FQ5M4QBGF4B5IQAOMGYJ2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:36U7FQ5M4QBGF4B5IQAOMGYJ2H","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":"1219ae196fd6777f3e9302b757ac766c4a62cee46f46abb9de33c70c0654e41a","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-01T22:03:20Z","title_canon_sha256":"fcd9571f2658480b6cdd914bbf90d101477483aa03da99aa20c395fb19d55cb8"},"schema_version":"1.0","source":{"id":"0909.0283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0283","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0283v2","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0283","created_at":"2026-05-18T04:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"36U7FQ5M4QBG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"36U7FQ5M4QBGF4B5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"36U7FQ5M","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:8d38cea9348afae31022c1c20e1bd1bdafbcbe96c4695035a865216c947c9648","target":"graph","created_at":"2026-05-18T04:21:22Z","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 give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rule coefficients are related to the existence of a 2-isomorphism between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2) determined by the corresponding three conjugacy classes. This construction is motivated by its application in the description of junctions of","authors_text":"Ingo Runkel, Rafal R. Suszek","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-01T22:03:20Z","title":"Affine su(2) fusion rules from gerbe 2-isomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0283","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:f02ee3fcc0208ff9d283a4ac24f9795a1413dace8c1ee3aa7603ea3a3fa056f0","target":"record","created_at":"2026-05-18T04:21:22Z","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":"1219ae196fd6777f3e9302b757ac766c4a62cee46f46abb9de33c70c0654e41a","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-01T22:03:20Z","title_canon_sha256":"fcd9571f2658480b6cdd914bbf90d101477483aa03da99aa20c395fb19d55cb8"},"schema_version":"1.0","source":{"id":"0909.0283","kind":"arxiv","version":2}},"canonical_sha256":"dfa9f2c3ace40262f03d4400e61b09d1fd4fd7ea06d05737af3309f4c971d049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfa9f2c3ace40262f03d4400e61b09d1fd4fd7ea06d05737af3309f4c971d049","first_computed_at":"2026-05-18T04:21:22.902813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:22.902813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MXVTeJQZtpS9mDUy/b9cwUSYzZOXdfak78qQoYu4GHtC2cHH7uAPi5Khr8clm4FDocixO3RKojSOnDay5p5tDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:22.903268Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f02ee3fcc0208ff9d283a4ac24f9795a1413dace8c1ee3aa7603ea3a3fa056f0","sha256:8d38cea9348afae31022c1c20e1bd1bdafbcbe96c4695035a865216c947c9648"],"state_sha256":"3cb6f451eea168a97164f4ecaf65063e69f163e6daa37500dd29c19f75f9d7b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lktlqBGUvur/kTp8trZkhjyRcCAnqNCiLDzOd36zotJT60xidmgU4AhFDPc+rALeFsEtHaWSu3EipoBq6ZZIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:16:06.114524Z","bundle_sha256":"6c9450e7733029460f14bfa73e42a28971d92881a37934288ca62515ed1d1b56"}}