{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OWNY3OXVMEBNOVA5RAA7KLYNRY","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":"353b48122d85f1b9b2b6f28e1574cde95273ad8de3e59c5e467da045dc3e61f4","cross_cats_sorted":["hep-th","math-ph","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-01-22T14:11:57Z","title_canon_sha256":"aac9af7cd59111b1b0e1ae6e385704ea330379f17588589b66e0f60535b0fd82"},"schema_version":"1.0","source":{"id":"2101.10860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.10860","created_at":"2026-07-05T02:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"2101.10860v3","created_at":"2026-07-05T02:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.10860","created_at":"2026-07-05T02:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"OWNY3OXVMEBN","created_at":"2026-07-05T02:48:59Z"},{"alias_kind":"pith_short_16","alias_value":"OWNY3OXVMEBNOVA5","created_at":"2026-07-05T02:48:59Z"},{"alias_kind":"pith_short_8","alias_value":"OWNY3OXV","created_at":"2026-07-05T02:48:59Z"}],"graph_snapshots":[{"event_id":"sha256:009a142eccd02ca70c7de83f3d03661fb06b4a052cb2ad94401064c7bf7ecbfa","target":"graph","created_at":"2026-07-05T02:48:59Z","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/2101.10860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of uniqueness of universal formulae for (quantum) dimensions of simple Lie algebras is investigated. We present generic functions, which multiplied by a universal (quantum) dimension formula, preserve both its structure and its values at the points from Vogel's table. Connection of some of these functions with geometrical configurations, such as the famous Pappus-Brianchon-Pascal $(9_3)_1$ configuration of points and lines, is established. Particularly, the appropriate realizable configuration $(144_336_{12})$ (yet to be found) will provide a symmetric non-uniqueness factor for any","authors_text":"M.Y. Avetisyan, R.L. Mkrtchyan","cross_cats":["hep-th","math-ph","math.GR","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-01-22T14:11:57Z","title":"Uniqueness of universal dimensions and configurations of points and lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.10860","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:a5344f87c97e9addf87734913a1bdaed0da4d4a4cc630cc2f20ef7749bb415ff","target":"record","created_at":"2026-07-05T02:48:59Z","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":"353b48122d85f1b9b2b6f28e1574cde95273ad8de3e59c5e467da045dc3e61f4","cross_cats_sorted":["hep-th","math-ph","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-01-22T14:11:57Z","title_canon_sha256":"aac9af7cd59111b1b0e1ae6e385704ea330379f17588589b66e0f60535b0fd82"},"schema_version":"1.0","source":{"id":"2101.10860","kind":"arxiv","version":3}},"canonical_sha256":"759b8dbaf56102d7541d8801f52f0d8e1d7277a040bc24e2beff6e6c590df2e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"759b8dbaf56102d7541d8801f52f0d8e1d7277a040bc24e2beff6e6c590df2e1","first_computed_at":"2026-07-05T02:48:59.322022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:48:59.322022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"apI5i2+0oTNyQSocTAID9GY807Q/WFvu+zh+JflbckPcoXA0CvjERr+egeMmYpv4yGYgQSeYKqRfil/8p+bfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:48:59.322530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.10860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5344f87c97e9addf87734913a1bdaed0da4d4a4cc630cc2f20ef7749bb415ff","sha256:009a142eccd02ca70c7de83f3d03661fb06b4a052cb2ad94401064c7bf7ecbfa"],"state_sha256":"30e8eda8dcae72c3ad65bea2a0f9db40d7a7b7b6fece06491d152d49d43e3e5b"}