{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WCBVP2YCHT5KILOEUGKQHNW7LB","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":"48facc946b00d0d21a1cdd3bf6e7a1c3b47fb559ce25e79ff4b75cae27524563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-10-09T20:41:09Z","title_canon_sha256":"13687a99186fe7a9f1e976d7cd162819fcc2a43a19070d9815c42adbffc7a67d"},"schema_version":"1.0","source":{"id":"1110.1882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1882","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1882v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1882","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"WCBVP2YCHT5K","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WCBVP2YCHT5KILOE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WCBVP2YC","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:db86a90abb9e1550b569f0acbe67d1c47ade36723cda015d1c9ccbdf501844eb","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"A characterization of vertex operator algebra V_{Z\\alpha}^+ with (\\alpha,\\alpha)/2 not being a perfect square is given in terms of dimensions of homogeneous subspaces of small weights. This result contributes to the classification of rational vertex operator algebras of central charge 1.","authors_text":"Chongying Dong, Cuipo Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-10-09T20:41:09Z","title":"A characterization of vertex operator algebras $V_{Z\\alpha}^{+}$: I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1882","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":"sha256:15eb583f86afa4878aeade7322f91a0fbeeb76d426f222d83b8e7daf0f240ac1","target":"record","created_at":"2026-05-18T04:11:19Z","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":"48facc946b00d0d21a1cdd3bf6e7a1c3b47fb559ce25e79ff4b75cae27524563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-10-09T20:41:09Z","title_canon_sha256":"13687a99186fe7a9f1e976d7cd162819fcc2a43a19070d9815c42adbffc7a67d"},"schema_version":"1.0","source":{"id":"1110.1882","kind":"arxiv","version":1}},"canonical_sha256":"b08357eb023cfaa42dc4a19503b6df5878855cf4175a1b1a7b2d4cc28fc60d87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b08357eb023cfaa42dc4a19503b6df5878855cf4175a1b1a7b2d4cc28fc60d87","first_computed_at":"2026-05-18T04:11:19.413708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.413708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IEnbyCmNEIv5P+PlmxtAvzD9KgEA2KgW+PWfmfO3x2cc7MIwdunmKJEK5Nrq9rGLsLH9+LFzlDzvRoAvaToDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.414159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15eb583f86afa4878aeade7322f91a0fbeeb76d426f222d83b8e7daf0f240ac1","sha256:db86a90abb9e1550b569f0acbe67d1c47ade36723cda015d1c9ccbdf501844eb"],"state_sha256":"a49626bd75d091afcc3a5172bd2a78e70f214c9d0349252ff9fb1df1b214823a"}