{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:QVYJINL4FDEWY6P7LUK2WNC5IF","short_pith_number":"pith:QVYJINL4","schema_version":"1.0","canonical_sha256":"857094357c28c96c79ff5d15ab345d414bd5f9cf2de380766cec2a1ae6baa961","source":{"kind":"arxiv","id":"math/9912146","version":1},"attestation_state":"computed","paper":{"title":"Decomposition of the vertex operator algebra V_{\\sqrt{2}D_l}","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"C. Dong, C. H. Lam, H. Yamada","submitted_at":"1999-12-17T19:15:32Z","abstract_excerpt":"We determine the decomposition of V_{\\sqrt{2}D_l} into a sum of irreducible T-modules for general l where D_l is the root lattice of type D_l and T is the tensor product of l+1 Virasoro vertex operator algebras with central charges c_{1}=1/2, c_{2}=7/10, c_{3}=4/5, and c_{i}=1 for 4\\le i\\le l+1."},"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":"math/9912146","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1999-12-17T19:15:32Z","cross_cats_sorted":[],"title_canon_sha256":"774e9285f9cd55e5eb850f2c2b9d61ce57b17310258bca0c5d455865c71724b2","abstract_canon_sha256":"9d58a68a3e3200f9d324a94ac24e2fd9c6a8c8c864b69a603ff64c54d88fb0c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:32.154607Z","signature_b64":"065onlxIm9IgZBFDpmhG1hTfOHOFspSdxLzBij1HrUjtBpU9D2afBuID5MKb9Y7OlT2OHMr7V9ffmH/u0eWMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"857094357c28c96c79ff5d15ab345d414bd5f9cf2de380766cec2a1ae6baa961","last_reissued_at":"2026-07-04T14:41:32.154279Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:32.154279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition of the vertex operator algebra V_{\\sqrt{2}D_l}","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"C. Dong, C. H. Lam, H. Yamada","submitted_at":"1999-12-17T19:15:32Z","abstract_excerpt":"We determine the decomposition of V_{\\sqrt{2}D_l} into a sum of irreducible T-modules for general l where D_l is the root lattice of type D_l and T is the tensor product of l+1 Virasoro vertex operator algebras with central charges c_{1}=1/2, c_{2}=7/10, c_{3}=4/5, and c_{i}=1 for 4\\le i\\le l+1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9912146","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/math/9912146/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":"math/9912146","created_at":"2026-07-04T14:41:32.154335+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9912146v1","created_at":"2026-07-04T14:41:32.154335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9912146","created_at":"2026-07-04T14:41:32.154335+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVYJINL4FDEW","created_at":"2026-07-04T14:41:32.154335+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVYJINL4FDEWY6P7","created_at":"2026-07-04T14:41:32.154335+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVYJINL4","created_at":"2026-07-04T14:41:32.154335+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF","json":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF.json","graph_json":"https://pith.science/api/pith-number/QVYJINL4FDEWY6P7LUK2WNC5IF/graph.json","events_json":"https://pith.science/api/pith-number/QVYJINL4FDEWY6P7LUK2WNC5IF/events.json","paper":"https://pith.science/paper/QVYJINL4"},"agent_actions":{"view_html":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF","download_json":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF.json","view_paper":"https://pith.science/paper/QVYJINL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9912146&json=true","fetch_graph":"https://pith.science/api/pith-number/QVYJINL4FDEWY6P7LUK2WNC5IF/graph.json","fetch_events":"https://pith.science/api/pith-number/QVYJINL4FDEWY6P7LUK2WNC5IF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF/action/storage_attestation","attest_author":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF/action/author_attestation","sign_citation":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF/action/citation_signature","submit_replication":"https://pith.science/pith/QVYJINL4FDEWY6P7LUK2WNC5IF/action/replication_record"}},"created_at":"2026-07-04T14:41:32.154335+00:00","updated_at":"2026-07-04T14:41:32.154335+00:00"}