{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:ZYXEWXQVS64ODJ7VJUYAIXIZQX","short_pith_number":"pith:ZYXEWXQV","canonical_record":{"source":{"id":"math/0101219","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-01-26T15:58:04Z","cross_cats_sorted":[],"title_canon_sha256":"bd076f3fe45f2328f1538c8a1f8302fa2e123208dffaf178ddd691e9b64732b9","abstract_canon_sha256":"8c75ea3359ba27dd86f52c8321a5ed2d153315b04cc3499a1c54dd67c32d4635"},"schema_version":"1.0"},"canonical_sha256":"ce2e4b5e1597b8e1a7f54d30045d1985d0b4607dc9c7a7922e5b977c675b610d","source":{"kind":"arxiv","id":"math/0101219","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101219","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101219v3","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101219","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZYXEWXQVS64O","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZYXEWXQVS64ODJ7V","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZYXEWXQV","created_at":"2026-07-04T14:35:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:ZYXEWXQVS64ODJ7VJUYAIXIZQX","target":"record","payload":{"canonical_record":{"source":{"id":"math/0101219","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-01-26T15:58:04Z","cross_cats_sorted":[],"title_canon_sha256":"bd076f3fe45f2328f1538c8a1f8302fa2e123208dffaf178ddd691e9b64732b9","abstract_canon_sha256":"8c75ea3359ba27dd86f52c8321a5ed2d153315b04cc3499a1c54dd67c32d4635"},"schema_version":"1.0"},"canonical_sha256":"ce2e4b5e1597b8e1a7f54d30045d1985d0b4607dc9c7a7922e5b977c675b610d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:02.723557Z","signature_b64":"iZYMu/nIrUq1Lrkywkf5kITAx5FFjO6r46AhdL3THAY7Es6ynh1UAc3zIaSPXREZdKkmH8bkMpz/qjKPcwj0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2e4b5e1597b8e1a7f54d30045d1985d0b4607dc9c7a7922e5b977c675b610d","last_reissued_at":"2026-07-04T14:35:02.723142Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:02.723142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0101219","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgAF6m0SGDb9HmkK+o7VKe2aNhN4Sr1gYxo3G2CWOov58Dwy6+8GOhSZVy3OhMCxT3z+WxlLqPjpNnTiDhpRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T22:56:14.519250Z"},"content_sha256":"86e4e2076f63aac27e76201656c94fec3aa56ba1da813ff609189d5ceffe7261","schema_version":"1.0","event_id":"sha256:86e4e2076f63aac27e76201656c94fec3aa56ba1da813ff609189d5ceffe7261"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:ZYXEWXQVS64ODJ7VJUYAIXIZQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alexander Kirillov Jr, Viktor Ostrik","submitted_at":"2001-01-26T15:58:04Z","abstract_excerpt":"The goal of this paper is to classify ``finite subgroups in U_q sl(2)'' where $q=e^{\\pi\\i/l}$ is a root of unity. We propose a definition of such a subgroup in terms of the category of representations of U_q sl(2); we show that this definition is a natural generalization of the notion of a subgroup in a reductive group, and that it is also related with extensions of the chiral (vertex operator) algebra corresponding to sl^(2) at level k=l-2. We show that ``finite subgroups in U_q sl(2)'' are classified by Dynkin diagrams of types A_n, D_{2n}, E_6, E_8 with Coxeter number equal to $l$, give a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101219","kind":"arxiv","version":3},"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/math/0101219/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":"2026-07-04T14:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LY52+jNNRCJciope7y7/3XzUgsj/SbqJebp9i00wPFYT/4RdHE0X6Im2ZWZU0hCP9fUaUTBT4IQ+peJIBXF0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T22:56:14.519739Z"},"content_sha256":"3c68717fec66e9121260d33ab3ac136bfa8a5217f7563edc34af3bc0af644aa3","schema_version":"1.0","event_id":"sha256:3c68717fec66e9121260d33ab3ac136bfa8a5217f7563edc34af3bc0af644aa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/bundle.json","state_url":"https://pith.science/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/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":"2026-07-31T22:56:14Z","links":{"resolver":"https://pith.science/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX","bundle":"https://pith.science/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/bundle.json","state":"https://pith.science/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYXEWXQVS64ODJ7VJUYAIXIZQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:ZYXEWXQVS64ODJ7VJUYAIXIZQX","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":"8c75ea3359ba27dd86f52c8321a5ed2d153315b04cc3499a1c54dd67c32d4635","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2001-01-26T15:58:04Z","title_canon_sha256":"bd076f3fe45f2328f1538c8a1f8302fa2e123208dffaf178ddd691e9b64732b9"},"schema_version":"1.0","source":{"id":"math/0101219","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101219","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101219v3","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101219","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZYXEWXQVS64O","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZYXEWXQVS64ODJ7V","created_at":"2026-07-04T14:35:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZYXEWXQV","created_at":"2026-07-04T14:35:02Z"}],"graph_snapshots":[{"event_id":"sha256:3c68717fec66e9121260d33ab3ac136bfa8a5217f7563edc34af3bc0af644aa3","target":"graph","created_at":"2026-07-04T14:35:02Z","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/math/0101219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of this paper is to classify ``finite subgroups in U_q sl(2)'' where $q=e^{\\pi\\i/l}$ is a root of unity. We propose a definition of such a subgroup in terms of the category of representations of U_q sl(2); we show that this definition is a natural generalization of the notion of a subgroup in a reductive group, and that it is also related with extensions of the chiral (vertex operator) algebra corresponding to sl^(2) at level k=l-2. We show that ``finite subgroups in U_q sl(2)'' are classified by Dynkin diagrams of types A_n, D_{2n}, E_6, E_8 with Coxeter number equal to $l$, give a d","authors_text":"Alexander Kirillov Jr, Viktor Ostrik","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2001-01-26T15:58:04Z","title":"On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101219","kind":"arxiv","version":3},"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":"sha256:86e4e2076f63aac27e76201656c94fec3aa56ba1da813ff609189d5ceffe7261","target":"record","created_at":"2026-07-04T14:35:02Z","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":"8c75ea3359ba27dd86f52c8321a5ed2d153315b04cc3499a1c54dd67c32d4635","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2001-01-26T15:58:04Z","title_canon_sha256":"bd076f3fe45f2328f1538c8a1f8302fa2e123208dffaf178ddd691e9b64732b9"},"schema_version":"1.0","source":{"id":"math/0101219","kind":"arxiv","version":3}},"canonical_sha256":"ce2e4b5e1597b8e1a7f54d30045d1985d0b4607dc9c7a7922e5b977c675b610d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce2e4b5e1597b8e1a7f54d30045d1985d0b4607dc9c7a7922e5b977c675b610d","first_computed_at":"2026-07-04T14:35:02.723142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:02.723142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZYMu/nIrUq1Lrkywkf5kITAx5FFjO6r46AhdL3THAY7Es6ynh1UAc3zIaSPXREZdKkmH8bkMpz/qjKPcwj0Bg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:02.723557Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101219","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e4e2076f63aac27e76201656c94fec3aa56ba1da813ff609189d5ceffe7261","sha256:3c68717fec66e9121260d33ab3ac136bfa8a5217f7563edc34af3bc0af644aa3"],"state_sha256":"c51f483c09f2c74b4b157417243aa3631121a3aaadef3dcf7b4894fa17b3b88b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flPv+4oNA5rBM7wguQXpbbuB+PtQF8e0YZyEoiAjWzLV67QrAoL+QOGhvt8xPLPcxKN1gW7kGBJnnuytVYlMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T22:56:14.524092Z","bundle_sha256":"7517a8b2b2fddd08d50814ad8e0e023f0c12a8289a4db7e66ca2b9261def6e6c"}}