{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LFTKWJWKLBVXGGXMGKIRCRDTH5","short_pith_number":"pith:LFTKWJWK","schema_version":"1.0","canonical_sha256":"5966ab26ca586b731aec32911144733f7823393e184cd6e63a9dcb1ed24e337a","source":{"kind":"arxiv","id":"2605.16773","version":1},"attestation_state":"computed","paper":{"title":"Shifted quantum toroidal algebra of type $\\mathfrak{gl}_{1|1}$ and the Pieri rule of the super Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials.","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hiroaki Kanno, Jun'ichi Shiraishi, Ryo Ohkawa","submitted_at":"2026-05-16T02:50:52Z","abstract_excerpt":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$. The action of the super charges of $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$ implies the Pieri rule of the super Macdonald polynomials. We can express the Pieri rule in terms of differential operators in the power sums $p_k$ and the fermionic power sums $\\pi_k$, which leads to the operators on the Fock space of a free boson and a free fermio"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.16773","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-05-16T02:50:52Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"336c4373eba708a41cad82521e6140bf73b6835e17686d7bd9c5a49c32afa7c6","abstract_canon_sha256":"41d4a3ba3a9a2f1707ffedc1846171b1e0459174c362cc7695e263815719847e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:21.226532Z","signature_b64":"pvtIZ7xC/JRx0dLbjRiiqE38YCtDxJsPleheLgSz2IYYHaZIvpDcZhPydB7NhyfLUuMqqoBEQ+XRkrKrfDUQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5966ab26ca586b731aec32911144733f7823393e184cd6e63a9dcb1ed24e337a","last_reissued_at":"2026-05-20T00:03:21.225429Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:21.225429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shifted quantum toroidal algebra of type $\\mathfrak{gl}_{1|1}$ and the Pieri rule of the super Macdonald polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials.","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hiroaki Kanno, Jun'ichi Shiraishi, Ryo Ohkawa","submitted_at":"2026-05-16T02:50:52Z","abstract_excerpt":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$. The action of the super charges of $\\mathcal{U}_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_{1|1})$ implies the Pieri rule of the super Macdonald polynomials. We can express the Pieri rule in terms of differential operators in the power sums $p_k$ and the fermionic power sums $\\pi_k$, which leads to the operators on the Fock space of a free boson and a free fermio"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The action of the super charges of U_{q,t}(widehat{widehat{gl}}_{1|1}) implies the Pieri rule of the super Macdonald polynomials.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module of the quantum toroidal algebra.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat hat 1|1), with the Pieri rule following from super charge actions and yielding supersymmetric Hamiltonians via anti-commutators.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8a739024c9c2ea42b8e12ee551ef1e2ee142b129081be758548410e85f63dc43"},"source":{"id":"2605.16773","kind":"arxiv","version":1},"verdict":{"id":"84585214-89b5-4e93-866c-c1995a5d3226","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:40:42.269394Z","strongest_claim":"The action of the super charges of U_{q,t}(widehat{widehat{gl}}_{1|1}) implies the Pieri rule of the super Macdonald polynomials.","one_line_summary":"Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat hat 1|1), with the Pieri rule following from super charge actions and yielding supersymmetric Hamiltonians via anti-commutators.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module of the quantum toroidal algebra.","pith_extraction_headline":"The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16773/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.088494Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:50:54.831534Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.308820Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.443147Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"db3dcbe469c029cd87622b613935605e86baa2ce956f6884286f53c6f2255536"},"references":{"count":23,"sample":[{"doi":"","year":1903,"title":"Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)","work_id":"b9fe044b-8445-4ff2-927e-da6b7046125d","ref_index":1,"cited_arxiv_id":"1903.07777","is_internal_anchor":true},{"doi":"","year":2012,"title":"Quantum Algebraic Approach to Refined Topological Vertex","work_id":"c3b03daf-8c5d-49ae-82af-85d7fe72df40","ref_index":2,"cited_arxiv_id":"1112.6074","is_internal_anchor":true},{"doi":"","year":1995,"title":"Collective fields, Calogero-Sutherland model and generalized matrix models","work_id":"5184381c-f0d2-41d5-a67e-a1846d04a964","ref_index":3,"cited_arxiv_id":"hep-th/9411053","is_internal_anchor":true},{"doi":"","year":1996,"title":"Quantum W(N) algebras and Macdonald polynomials,","work_id":"8c61d0d8-8053-4075-a990-198199f98328","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Macdonald polynomials in superspace: conjectural definition and positivity conjectures","work_id":"8d88c2db-643b-4dd5-809e-21ec394ca4fd","ref_index":5,"cited_arxiv_id":"1112.5188","is_internal_anchor":true}],"resolved_work":23,"snapshot_sha256":"dcd30317f7e65f205947f118ffa16266e055e5a7d021d64f22f8a6585422a775","internal_anchors":9},"formal_canon":{"evidence_count":3,"snapshot_sha256":"205d9da552ae71ec843ccdfcff81d217885906785868fe6e95faf648a988d5ed"},"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":"2605.16773","created_at":"2026-05-20T00:03:21.225607+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.16773v1","created_at":"2026-05-20T00:03:21.225607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16773","created_at":"2026-05-20T00:03:21.225607+00:00"},{"alias_kind":"pith_short_12","alias_value":"LFTKWJWKLBVX","created_at":"2026-05-20T00:03:21.225607+00:00"},{"alias_kind":"pith_short_16","alias_value":"LFTKWJWKLBVXGGXM","created_at":"2026-05-20T00:03:21.225607+00:00"},{"alias_kind":"pith_short_8","alias_value":"LFTKWJWK","created_at":"2026-05-20T00:03:21.225607+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":3,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5","json":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5.json","graph_json":"https://pith.science/api/pith-number/LFTKWJWKLBVXGGXMGKIRCRDTH5/graph.json","events_json":"https://pith.science/api/pith-number/LFTKWJWKLBVXGGXMGKIRCRDTH5/events.json","paper":"https://pith.science/paper/LFTKWJWK"},"agent_actions":{"view_html":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5","download_json":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5.json","view_paper":"https://pith.science/paper/LFTKWJWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.16773&json=true","fetch_graph":"https://pith.science/api/pith-number/LFTKWJWKLBVXGGXMGKIRCRDTH5/graph.json","fetch_events":"https://pith.science/api/pith-number/LFTKWJWKLBVXGGXMGKIRCRDTH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5/action/storage_attestation","attest_author":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5/action/author_attestation","sign_citation":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5/action/citation_signature","submit_replication":"https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5/action/replication_record"}},"created_at":"2026-05-20T00:03:21.225607+00:00","updated_at":"2026-05-20T00:03:21.225607+00:00"}