{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HUQFERCDMMIO6PHESFWWER2RBH","short_pith_number":"pith:HUQFERCD","schema_version":"1.0","canonical_sha256":"3d205244436310ef3ce4916d62475109fd69383544a28adc7f8a27eb1ab49111","source":{"kind":"arxiv","id":"1809.07003","version":4},"attestation_state":"computed","paper":{"title":"Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Bin Gui","submitted_at":"2018-09-19T03:54:35Z","abstract_excerpt":"The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo for type $D$ affine VOAs. In this paper, we extend their results to affine VOAs of type $B$, $C$, and $G_2$. As a consequence, the modular tensor categories of these unitary vertex operator algebras are unitary."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.07003","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-19T03:54:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"172df7b9d6629a3743e9417fe2b8412f988864c772e92a41a0b1435f040ca478","abstract_canon_sha256":"2df42b2e9e2c461ba5f4eeb7cbcf8b8ddbceb9e7e0a2f0835ca36f12a8af62dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:16:31.287899Z","signature_b64":"rF11PG1himVQegsxW+QYAzYsE5qibFhE4LO5gPaLyLTfRVj12PhhGZu8t4JDSP8QVcz2+/41uNIcgY0r7E4eDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d205244436310ef3ce4916d62475109fd69383544a28adc7f8a27eb1ab49111","last_reissued_at":"2026-07-05T00:16:31.287468Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:16:31.287468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Bin Gui","submitted_at":"2018-09-19T03:54:35Z","abstract_excerpt":"The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo for type $D$ affine VOAs. In this paper, we extend their results to affine VOAs of type $B$, $C$, and $G_2$. As a consequence, the modular tensor categories of these unitary vertex operator algebras are unitary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07003","kind":"arxiv","version":4},"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/1809.07003/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.07003","created_at":"2026-07-05T00:16:31.287524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.07003v4","created_at":"2026-07-05T00:16:31.287524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07003","created_at":"2026-07-05T00:16:31.287524+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUQFERCDMMIO","created_at":"2026-07-05T00:16:31.287524+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUQFERCDMMIO6PHE","created_at":"2026-07-05T00:16:31.287524+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUQFERCD","created_at":"2026-07-05T00:16:31.287524+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.01008","citing_title":"Rational and non-rational two-dimensional conformal field theories arising from lattices","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH","json":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH.json","graph_json":"https://pith.science/api/pith-number/HUQFERCDMMIO6PHESFWWER2RBH/graph.json","events_json":"https://pith.science/api/pith-number/HUQFERCDMMIO6PHESFWWER2RBH/events.json","paper":"https://pith.science/paper/HUQFERCD"},"agent_actions":{"view_html":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH","download_json":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH.json","view_paper":"https://pith.science/paper/HUQFERCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.07003&json=true","fetch_graph":"https://pith.science/api/pith-number/HUQFERCDMMIO6PHESFWWER2RBH/graph.json","fetch_events":"https://pith.science/api/pith-number/HUQFERCDMMIO6PHESFWWER2RBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH/action/storage_attestation","attest_author":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH/action/author_attestation","sign_citation":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH/action/citation_signature","submit_replication":"https://pith.science/pith/HUQFERCDMMIO6PHESFWWER2RBH/action/replication_record"}},"created_at":"2026-07-05T00:16:31.287524+00:00","updated_at":"2026-07-05T00:16:31.287524+00:00"}