{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BL333LER4UVBV7UIDMOIZOFLKW","short_pith_number":"pith:BL333LER","canonical_record":{"source":{"id":"1909.02076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-04T20:01:33Z","cross_cats_sorted":["hep-th","math.MP","math.RT"],"title_canon_sha256":"ef1de71a2fa74e39678ad26f919ffe35281b8866eb3446069ef1d8044bbc7486","abstract_canon_sha256":"e99c2bf3b41134f16bcf3be320b70e0a3e7ef3d37c69302b85987deeb5964b83"},"schema_version":"1.0"},"canonical_sha256":"0af7bdac91e52a1afe881b1c8cb8ab559552dc09f381389337cbdf7724585e19","source":{"kind":"arxiv","id":"1909.02076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02076","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02076v1","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02076","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"BL333LER4UVB","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"BL333LER4UVBV7UI","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"BL333LER","created_at":"2026-07-05T00:02:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BL333LER4UVBV7UIDMOIZOFLKW","target":"record","payload":{"canonical_record":{"source":{"id":"1909.02076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-04T20:01:33Z","cross_cats_sorted":["hep-th","math.MP","math.RT"],"title_canon_sha256":"ef1de71a2fa74e39678ad26f919ffe35281b8866eb3446069ef1d8044bbc7486","abstract_canon_sha256":"e99c2bf3b41134f16bcf3be320b70e0a3e7ef3d37c69302b85987deeb5964b83"},"schema_version":"1.0"},"canonical_sha256":"0af7bdac91e52a1afe881b1c8cb8ab559552dc09f381389337cbdf7724585e19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:30.043857Z","signature_b64":"uhvG51mXY0sVgn8aMGNKRYMB5vBybRFRWOwseHfCN7nZcmDfN/Luq8Tvwx9Nmd5VpXrOdYA7W9akch4v2cJFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0af7bdac91e52a1afe881b1c8cb8ab559552dc09f381389337cbdf7724585e19","last_reissued_at":"2026-07-05T00:02:30.043386Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:30.043386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.02076","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lb4MGAsbjVNqUJI2IaTZ3+a70f9UW8X/gK1lBz00j64zmFW1wGMAGGbGtCETzk1h4ZTIE6V+LoVrd/qvN32wCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:13:02.229133Z"},"content_sha256":"087d5012da8c76ab79c7542bbd48160f9a5da06c9220fdeedc61f69e275bbb9d","schema_version":"1.0","event_id":"sha256:087d5012da8c76ab79c7542bbd48160f9a5da06c9220fdeedc61f69e275bbb9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BL333LER4UVBV7UIDMOIZOFLKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On universal quantum dimensions of certain two-parameter series of representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"M.Y. Avetisyan, R.L. Mkrtchyan","submitted_at":"2019-09-04T20:01:33Z","abstract_excerpt":"We present the universal, in Vogel's sense, expression for the quantum dimension of Cartan product of an arbitrary number of adjoint and $X_2$ representations of simple Lie algebras. The same formula mysteriously gives quantum dimensions of some other representations of the same Lie algebra under permutations of universal parameters. We list these representations for exceptional algebras and stable versions for classical algebras, when the rank of the classical algebra is sufficiently large w.r.t. the powers of representations. We show that universal formulae can have singularities on Vogel's "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02076","kind":"arxiv","version":1},"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/1909.02076/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":"2026-07-05T00:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+qj75i8le4krkOXHx2ymipXCKr+iH93y7kjDs1FxZ9syC/YiDZs+x2HfRHSq8MpFv3p1XmuwTan0oH5Rd8mAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:13:02.229769Z"},"content_sha256":"61ad8e0bb00fa50882ce6dbfa48dbb5ceb44dbd9497f64a57496eafe52af0bfb","schema_version":"1.0","event_id":"sha256:61ad8e0bb00fa50882ce6dbfa48dbb5ceb44dbd9497f64a57496eafe52af0bfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BL333LER4UVBV7UIDMOIZOFLKW/bundle.json","state_url":"https://pith.science/pith/BL333LER4UVBV7UIDMOIZOFLKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BL333LER4UVBV7UIDMOIZOFLKW/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":"2026-08-09T07:13:02Z","links":{"resolver":"https://pith.science/pith/BL333LER4UVBV7UIDMOIZOFLKW","bundle":"https://pith.science/pith/BL333LER4UVBV7UIDMOIZOFLKW/bundle.json","state":"https://pith.science/pith/BL333LER4UVBV7UIDMOIZOFLKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BL333LER4UVBV7UIDMOIZOFLKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BL333LER4UVBV7UIDMOIZOFLKW","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":"e99c2bf3b41134f16bcf3be320b70e0a3e7ef3d37c69302b85987deeb5964b83","cross_cats_sorted":["hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-04T20:01:33Z","title_canon_sha256":"ef1de71a2fa74e39678ad26f919ffe35281b8866eb3446069ef1d8044bbc7486"},"schema_version":"1.0","source":{"id":"1909.02076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02076","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02076v1","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02076","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"BL333LER4UVB","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"BL333LER4UVBV7UI","created_at":"2026-07-05T00:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"BL333LER","created_at":"2026-07-05T00:02:30Z"}],"graph_snapshots":[{"event_id":"sha256:61ad8e0bb00fa50882ce6dbfa48dbb5ceb44dbd9497f64a57496eafe52af0bfb","target":"graph","created_at":"2026-07-05T00:02:30Z","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/1909.02076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the universal, in Vogel's sense, expression for the quantum dimension of Cartan product of an arbitrary number of adjoint and $X_2$ representations of simple Lie algebras. The same formula mysteriously gives quantum dimensions of some other representations of the same Lie algebra under permutations of universal parameters. We list these representations for exceptional algebras and stable versions for classical algebras, when the rank of the classical algebra is sufficiently large w.r.t. the powers of representations. We show that universal formulae can have singularities on Vogel's ","authors_text":"M.Y. Avetisyan, R.L. Mkrtchyan","cross_cats":["hep-th","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-04T20:01:33Z","title":"On universal quantum dimensions of certain two-parameter series of representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02076","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":"sha256:087d5012da8c76ab79c7542bbd48160f9a5da06c9220fdeedc61f69e275bbb9d","target":"record","created_at":"2026-07-05T00:02:30Z","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":"e99c2bf3b41134f16bcf3be320b70e0a3e7ef3d37c69302b85987deeb5964b83","cross_cats_sorted":["hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-09-04T20:01:33Z","title_canon_sha256":"ef1de71a2fa74e39678ad26f919ffe35281b8866eb3446069ef1d8044bbc7486"},"schema_version":"1.0","source":{"id":"1909.02076","kind":"arxiv","version":1}},"canonical_sha256":"0af7bdac91e52a1afe881b1c8cb8ab559552dc09f381389337cbdf7724585e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0af7bdac91e52a1afe881b1c8cb8ab559552dc09f381389337cbdf7724585e19","first_computed_at":"2026-07-05T00:02:30.043386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:02:30.043386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uhvG51mXY0sVgn8aMGNKRYMB5vBybRFRWOwseHfCN7nZcmDfN/Luq8Tvwx9Nmd5VpXrOdYA7W9akch4v2cJFBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:02:30.043857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.02076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:087d5012da8c76ab79c7542bbd48160f9a5da06c9220fdeedc61f69e275bbb9d","sha256:61ad8e0bb00fa50882ce6dbfa48dbb5ceb44dbd9497f64a57496eafe52af0bfb"],"state_sha256":"fc2c033d095610daf2f3ca8c6390ab1ae55c10bd13a8a74864966543f62935d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K4apMaZSeBYQU7fNGjw87VTdMGYJ6OHIppSv73H3x8WNfKqyt+MfX05ekz7DQcFerR86u/SF9+Sx24qhS7DuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:13:02.235289Z","bundle_sha256":"8fc92b175761391424d514be4bedc08501e1bb9fe7ffa8f051ad360a39b4bfd1"}}