{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NLNHD2UCENWOZAIHCSDV6VCSQI","short_pith_number":"pith:NLNHD2UC","schema_version":"1.0","canonical_sha256":"6ada71ea82236cec810714875f5452821043c6ecbe7526a5cd835d7bd172c7b9","source":{"kind":"arxiv","id":"1901.02397","version":2},"attestation_state":"computed","paper":{"title":"Ito's conjecture and the coset construction for ${\\mathcal W}^k(\\mathfrak{sl}(3|2))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Naoki Genra","submitted_at":"2019-01-08T16:45:11Z","abstract_excerpt":"Many ${\\mathcal W}$-(super)algebras which are defined by the generalized Drinfeld-Sokolov reduction are also known or expected to have coset realizations. For example, it was conjectured by Ito that the principal ${\\mathcal W}$-superalgebra ${\\mathcal W}^k(\\mathfrak{sl}(n+1|n))$ is isomorphic to the coset of $V^{l+1}(\\mathfrak{gl}_n)$ inside $V^{l}(\\mathfrak{sl}_{n+1}) \\otimes {\\mathcal E}(n)$ for generic values of $l$. Here ${\\mathcal E}(n)$ denotes the rank $n$ $bc$-system, which carries an action of $V^1(\\mathfrak{gl}_n)$, and $k$ and $l$ are related by $(k + 1) (l + n + 1) = 1$. This conje"},"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":"1901.02397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-01-08T16:45:11Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"626e8c6936eb630e1c07b53078a0e4febe8f6996c04ab77ea2d139151f03590c","abstract_canon_sha256":"28ca5ba6fab631b3f0591b4fb2bbdc0f1196744e5e8442060983001a2aaa6ea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:53:11.461010Z","signature_b64":"2Uh/wXh4K1PSWSPydnQ25TcaY6cduHIZgjaq9eYjmuPQ64NH0mUjVgqb5JRPi7ywtd+eppxBKYNfLzpNOSfnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ada71ea82236cec810714875f5452821043c6ecbe7526a5cd835d7bd172c7b9","last_reissued_at":"2026-07-04T23:53:11.460579Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:53:11.460579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ito's conjecture and the coset construction for ${\\mathcal W}^k(\\mathfrak{sl}(3|2))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Naoki Genra","submitted_at":"2019-01-08T16:45:11Z","abstract_excerpt":"Many ${\\mathcal W}$-(super)algebras which are defined by the generalized Drinfeld-Sokolov reduction are also known or expected to have coset realizations. For example, it was conjectured by Ito that the principal ${\\mathcal W}$-superalgebra ${\\mathcal W}^k(\\mathfrak{sl}(n+1|n))$ is isomorphic to the coset of $V^{l+1}(\\mathfrak{gl}_n)$ inside $V^{l}(\\mathfrak{sl}_{n+1}) \\otimes {\\mathcal E}(n)$ for generic values of $l$. Here ${\\mathcal E}(n)$ denotes the rank $n$ $bc$-system, which carries an action of $V^1(\\mathfrak{gl}_n)$, and $k$ and $l$ are related by $(k + 1) (l + n + 1) = 1$. This conje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02397","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.02397/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":"1901.02397","created_at":"2026-07-04T23:53:11.460627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02397v2","created_at":"2026-07-04T23:53:11.460627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02397","created_at":"2026-07-04T23:53:11.460627+00:00"},{"alias_kind":"pith_short_12","alias_value":"NLNHD2UCENWO","created_at":"2026-07-04T23:53:11.460627+00:00"},{"alias_kind":"pith_short_16","alias_value":"NLNHD2UCENWOZAIH","created_at":"2026-07-04T23:53:11.460627+00:00"},{"alias_kind":"pith_short_8","alias_value":"NLNHD2UC","created_at":"2026-07-04T23:53:11.460627+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.20750","citing_title":"Universal $2$-parameter $\\mathcal{N}=2$ supersymmetric $\\mathcal{W}_{\\infty}$-algebra","ref_index":63,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI","json":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI.json","graph_json":"https://pith.science/api/pith-number/NLNHD2UCENWOZAIHCSDV6VCSQI/graph.json","events_json":"https://pith.science/api/pith-number/NLNHD2UCENWOZAIHCSDV6VCSQI/events.json","paper":"https://pith.science/paper/NLNHD2UC"},"agent_actions":{"view_html":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI","download_json":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI.json","view_paper":"https://pith.science/paper/NLNHD2UC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02397&json=true","fetch_graph":"https://pith.science/api/pith-number/NLNHD2UCENWOZAIHCSDV6VCSQI/graph.json","fetch_events":"https://pith.science/api/pith-number/NLNHD2UCENWOZAIHCSDV6VCSQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI/action/storage_attestation","attest_author":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI/action/author_attestation","sign_citation":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI/action/citation_signature","submit_replication":"https://pith.science/pith/NLNHD2UCENWOZAIHCSDV6VCSQI/action/replication_record"}},"created_at":"2026-07-04T23:53:11.460627+00:00","updated_at":"2026-07-04T23:53:11.460627+00:00"}