{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3HZBEPSFTN7MO2J6PN2RHDJEJY","short_pith_number":"pith:3HZBEPSF","schema_version":"1.0","canonical_sha256":"d9f2123e459b7ec7693e7b75138d244e35dc4377dcd98b6ce6da5d6b8cd400ff","source":{"kind":"arxiv","id":"1602.04687","version":2},"attestation_state":"computed","paper":{"title":"Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Ozren Perse, Paolo Papi, Pierluigi Moseneder Frajria, Victor G. Kac","submitted_at":"2016-02-15T14:11:58Z","abstract_excerpt":"We find all values of $k\\in \\mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\\mathfrak g,\\theta)$ is conformal, where $\\mathfrak g$ is a basic simple Lie superalgebra and $-\\theta$ its minimal root. In particular, it turns out that if $W_k(\\mathfrak g,\\theta)$ does not collapse to its affine part, then the possible values of these $k$ are either $-\\frac{2}{3} h^\\vee$ or $-\\frac{h^\\vee-1}{2}$, where $h^\\vee$ is the dual Coxeter number of $\\mathfrak g$ for the normalization $(\\theta,\\theta)=2$. As an application of our results, we presen"},"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":"1602.04687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-15T14:11:58Z","cross_cats_sorted":[],"title_canon_sha256":"457b5bbb59c0b597a295c8891b3faa243376e5a1968283f70f6712f6a2e1ddc2","abstract_canon_sha256":"f8f5fdfb7b7a0efe386b0ab17f9438c6a1584f9c3494ac694ccc33284b02b3a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:44.522662Z","signature_b64":"9W8lZ8/m/Ogr5KGVYlBQZh4i9JyPoSn+pwSrd+pRtaR4MQCiIz1Qs8pUgH9N81z1qLyGxc2YrZWtUHv+D2M4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f2123e459b7ec7693e7b75138d244e35dc4377dcd98b6ce6da5d6b8cd400ff","last_reissued_at":"2026-05-17T23:49:44.522030Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:44.522030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Ozren Perse, Paolo Papi, Pierluigi Moseneder Frajria, Victor G. Kac","submitted_at":"2016-02-15T14:11:58Z","abstract_excerpt":"We find all values of $k\\in \\mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\\mathfrak g,\\theta)$ is conformal, where $\\mathfrak g$ is a basic simple Lie superalgebra and $-\\theta$ its minimal root. In particular, it turns out that if $W_k(\\mathfrak g,\\theta)$ does not collapse to its affine part, then the possible values of these $k$ are either $-\\frac{2}{3} h^\\vee$ or $-\\frac{h^\\vee-1}{2}$, where $h^\\vee$ is the dual Coxeter number of $\\mathfrak g$ for the normalization $(\\theta,\\theta)=2$. As an application of our results, we presen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04687","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1602.04687","created_at":"2026-05-17T23:49:44.522127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04687v2","created_at":"2026-05-17T23:49:44.522127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04687","created_at":"2026-05-17T23:49:44.522127+00:00"},{"alias_kind":"pith_short_12","alias_value":"3HZBEPSFTN7M","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3HZBEPSFTN7MO2J6","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3HZBEPSF","created_at":"2026-05-18T12:29:55.572404+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/3HZBEPSFTN7MO2J6PN2RHDJEJY","json":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY.json","graph_json":"https://pith.science/api/pith-number/3HZBEPSFTN7MO2J6PN2RHDJEJY/graph.json","events_json":"https://pith.science/api/pith-number/3HZBEPSFTN7MO2J6PN2RHDJEJY/events.json","paper":"https://pith.science/paper/3HZBEPSF"},"agent_actions":{"view_html":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY","download_json":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY.json","view_paper":"https://pith.science/paper/3HZBEPSF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04687&json=true","fetch_graph":"https://pith.science/api/pith-number/3HZBEPSFTN7MO2J6PN2RHDJEJY/graph.json","fetch_events":"https://pith.science/api/pith-number/3HZBEPSFTN7MO2J6PN2RHDJEJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY/action/storage_attestation","attest_author":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY/action/author_attestation","sign_citation":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY/action/citation_signature","submit_replication":"https://pith.science/pith/3HZBEPSFTN7MO2J6PN2RHDJEJY/action/replication_record"}},"created_at":"2026-05-17T23:49:44.522127+00:00","updated_at":"2026-05-17T23:49:44.522127+00:00"}