{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VJN2QN62O2WHWIVTSTU6EWU54Z","short_pith_number":"pith:VJN2QN62","schema_version":"1.0","canonical_sha256":"aa5ba837da76ac7b22b394e9e25a9de664814ee3e0ffafb2d055cf7636e8b1ff","source":{"kind":"arxiv","id":"2211.01578","version":4},"attestation_state":"computed","paper":{"title":"Pieri-type multiplication formula for quantum Grothendieck polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.QA","authors_text":"Daisuke Sagaki, Satoshi Naito","submitted_at":"2022-11-03T04:18:18Z","abstract_excerpt":"The purpose of this paper is to prove a Pieri-type multiplication formula for quantum Grothendieck polynomials, which was conjectured by Lenart-Maeno. This formula would enable us to compute explicitly the quantum product of two arbitrary (opposite) Schubert classes in the (small) quantum $K$-theory ring $QK(Fl_{n})$ of the (full) flag manifold $Fl_{n}$ of type $A_{n-1}$ on the basis of the fact that quantum Grothendieck polynomials represent (opposite) Schubert classes in $QK(Fl_{n})$."},"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":"2211.01578","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-11-03T04:18:18Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"93dc0a6fffc0eeef598e0847e50f9b6c7f6e772be4b93de573cbb040d6cbfdcd","abstract_canon_sha256":"4cbdb88e4e07613e06a77618b5152a057382e88c63ef1c47253e165c54270e61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:16.605989Z","signature_b64":"mCnGFuz2tZhha67LDv8NjgJD06zT/jjpfU+D4SYl1CoMS2VGtElOlx9Ue1d4Ne4RQrCL8b5N14T8tsAnvnnWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa5ba837da76ac7b22b394e9e25a9de664814ee3e0ffafb2d055cf7636e8b1ff","last_reissued_at":"2026-07-05T08:36:16.605523Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:16.605523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pieri-type multiplication formula for quantum Grothendieck polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.QA","authors_text":"Daisuke Sagaki, Satoshi Naito","submitted_at":"2022-11-03T04:18:18Z","abstract_excerpt":"The purpose of this paper is to prove a Pieri-type multiplication formula for quantum Grothendieck polynomials, which was conjectured by Lenart-Maeno. This formula would enable us to compute explicitly the quantum product of two arbitrary (opposite) Schubert classes in the (small) quantum $K$-theory ring $QK(Fl_{n})$ of the (full) flag manifold $Fl_{n}$ of type $A_{n-1}$ on the basis of the fact that quantum Grothendieck polynomials represent (opposite) Schubert classes in $QK(Fl_{n})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.01578","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/2211.01578/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":"2211.01578","created_at":"2026-07-05T08:36:16.605589+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.01578v4","created_at":"2026-07-05T08:36:16.605589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.01578","created_at":"2026-07-05T08:36:16.605589+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJN2QN62O2WH","created_at":"2026-07-05T08:36:16.605589+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJN2QN62O2WHWIVT","created_at":"2026-07-05T08:36:16.605589+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJN2QN62","created_at":"2026-07-05T08:36:16.605589+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.12351","citing_title":"Toward quantum Pieri rule for $F\\ell_n$ via Seidel representation","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z","json":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z.json","graph_json":"https://pith.science/api/pith-number/VJN2QN62O2WHWIVTSTU6EWU54Z/graph.json","events_json":"https://pith.science/api/pith-number/VJN2QN62O2WHWIVTSTU6EWU54Z/events.json","paper":"https://pith.science/paper/VJN2QN62"},"agent_actions":{"view_html":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z","download_json":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z.json","view_paper":"https://pith.science/paper/VJN2QN62","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.01578&json=true","fetch_graph":"https://pith.science/api/pith-number/VJN2QN62O2WHWIVTSTU6EWU54Z/graph.json","fetch_events":"https://pith.science/api/pith-number/VJN2QN62O2WHWIVTSTU6EWU54Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z/action/storage_attestation","attest_author":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z/action/author_attestation","sign_citation":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z/action/citation_signature","submit_replication":"https://pith.science/pith/VJN2QN62O2WHWIVTSTU6EWU54Z/action/replication_record"}},"created_at":"2026-07-05T08:36:16.605589+00:00","updated_at":"2026-07-05T08:36:16.605589+00:00"}