{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NHRY3ML3DFI62HTXKNIQKWXTDO","short_pith_number":"pith:NHRY3ML3","schema_version":"1.0","canonical_sha256":"69e38db17b1951ed1e775351055af31b9695116c9034b9f694846a2d6d5aae07","source":{"kind":"arxiv","id":"1607.03524","version":3},"attestation_state":"computed","paper":{"title":"Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.RT"],"primary_cat":"math.KT","authors_text":"Seth Baldwin, Shrawan Kumar","submitted_at":"2016-07-12T21:32:06Z","abstract_excerpt":"We prove sign-alternation of the structure constants in the basis of structure sheaves of opposite Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite case to the general Kac-Moody case, and affirmatively answers a conjecture of Lam-Schilling-Shimozono regarding the signs of the structure constants in the case of the affine Grassmannian."},"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":"1607.03524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-12T21:32:06Z","cross_cats_sorted":["math.AG","math.AT","math.RT"],"title_canon_sha256":"b4e75753c61135ffae33d599d073dcde8bf1594e3982f309cb95826800cbfb2d","abstract_canon_sha256":"3caf88814a064f1950637adcfcb42a9454726945ce20a271952ca5ce3e42b35a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:20.782758Z","signature_b64":"RjVpKVw8DgdhZusiHavaWKLTonf6DnmZ/Zf0aY8ZkP2DLjzQM3GRRfKHJ70x+8q8gCqbLWMY9SsIwioja8itCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69e38db17b1951ed1e775351055af31b9695116c9034b9f694846a2d6d5aae07","last_reissued_at":"2026-05-18T00:47:20.782178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:20.782178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.RT"],"primary_cat":"math.KT","authors_text":"Seth Baldwin, Shrawan Kumar","submitted_at":"2016-07-12T21:32:06Z","abstract_excerpt":"We prove sign-alternation of the structure constants in the basis of structure sheaves of opposite Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite case to the general Kac-Moody case, and affirmatively answers a conjecture of Lam-Schilling-Shimozono regarding the signs of the structure constants in the case of the affine Grassmannian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03524","kind":"arxiv","version":3},"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":"1607.03524","created_at":"2026-05-18T00:47:20.782272+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.03524v3","created_at":"2026-05-18T00:47:20.782272+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03524","created_at":"2026-05-18T00:47:20.782272+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHRY3ML3DFI6","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHRY3ML3DFI62HTX","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHRY3ML3","created_at":"2026-05-18T12:30:32.724797+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/NHRY3ML3DFI62HTXKNIQKWXTDO","json":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO.json","graph_json":"https://pith.science/api/pith-number/NHRY3ML3DFI62HTXKNIQKWXTDO/graph.json","events_json":"https://pith.science/api/pith-number/NHRY3ML3DFI62HTXKNIQKWXTDO/events.json","paper":"https://pith.science/paper/NHRY3ML3"},"agent_actions":{"view_html":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO","download_json":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO.json","view_paper":"https://pith.science/paper/NHRY3ML3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.03524&json=true","fetch_graph":"https://pith.science/api/pith-number/NHRY3ML3DFI62HTXKNIQKWXTDO/graph.json","fetch_events":"https://pith.science/api/pith-number/NHRY3ML3DFI62HTXKNIQKWXTDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO/action/storage_attestation","attest_author":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO/action/author_attestation","sign_citation":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO/action/citation_signature","submit_replication":"https://pith.science/pith/NHRY3ML3DFI62HTXKNIQKWXTDO/action/replication_record"}},"created_at":"2026-05-18T00:47:20.782272+00:00","updated_at":"2026-05-18T00:47:20.782272+00:00"}