{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:56BPUPYFKJVSDZDRQZHQ4T2B4K","short_pith_number":"pith:56BPUPYF","schema_version":"1.0","canonical_sha256":"ef82fa3f05526b21e471864f0e4f41e29915c2c48e6b5d7c1231e6bf53644986","source":{"kind":"arxiv","id":"1509.00830","version":1},"attestation_state":"computed","paper":{"title":"Permutation-equivariant quantum K-theory IV. $D_q$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Givental","submitted_at":"2015-09-02T19:38:52Z","abstract_excerpt":"In Part II, we saw how genus-0 permutation-equivariant quantum K-theory of a manifold with isolated fixed points of a torus action can be reduced via fixed point localization to permutation-equivariant quantum K-theory of the point. In Part III, we gave a complete description of genus-0 permutation-equivariant quantum K-theory of the point by means of adelic characterization. Here we apply the adelic characterization to introduce the action on this theory of a certain group of $q$-difference operators. This action will enable us to prove that toric $q$-hypergeometric functions represent K-theo"},"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":"1509.00830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-02T19:38:52Z","cross_cats_sorted":[],"title_canon_sha256":"df8076d46f3d94dcf477ec505b2d3a4db06b1c23da247dfd7fd7ae1e51808f5d","abstract_canon_sha256":"aaf96e3e6d9823e3b57eccf9761ded55848981f9edb0a91bd8dd2e3172ba6f62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:05.927270Z","signature_b64":"/VrHYueL4g/tUtxThC/41JT/v3AG6J1dON2RVELDWhYmlcXNkPqjB/ZxJpafVCYhtGk/5DUWh1IvGB9d/GKCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef82fa3f05526b21e471864f0e4f41e29915c2c48e6b5d7c1231e6bf53644986","last_reissued_at":"2026-05-18T01:34:05.926795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:05.926795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permutation-equivariant quantum K-theory IV. $D_q$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Givental","submitted_at":"2015-09-02T19:38:52Z","abstract_excerpt":"In Part II, we saw how genus-0 permutation-equivariant quantum K-theory of a manifold with isolated fixed points of a torus action can be reduced via fixed point localization to permutation-equivariant quantum K-theory of the point. In Part III, we gave a complete description of genus-0 permutation-equivariant quantum K-theory of the point by means of adelic characterization. Here we apply the adelic characterization to introduce the action on this theory of a certain group of $q$-difference operators. This action will enable us to prove that toric $q$-hypergeometric functions represent K-theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00830","kind":"arxiv","version":1},"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":"1509.00830","created_at":"2026-05-18T01:34:05.926859+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00830v1","created_at":"2026-05-18T01:34:05.926859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00830","created_at":"2026-05-18T01:34:05.926859+00:00"},{"alias_kind":"pith_short_12","alias_value":"56BPUPYFKJVS","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"56BPUPYFKJVSDZDR","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"56BPUPYF","created_at":"2026-05-18T12:29:05.191682+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/56BPUPYFKJVSDZDRQZHQ4T2B4K","json":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K.json","graph_json":"https://pith.science/api/pith-number/56BPUPYFKJVSDZDRQZHQ4T2B4K/graph.json","events_json":"https://pith.science/api/pith-number/56BPUPYFKJVSDZDRQZHQ4T2B4K/events.json","paper":"https://pith.science/paper/56BPUPYF"},"agent_actions":{"view_html":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K","download_json":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K.json","view_paper":"https://pith.science/paper/56BPUPYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00830&json=true","fetch_graph":"https://pith.science/api/pith-number/56BPUPYFKJVSDZDRQZHQ4T2B4K/graph.json","fetch_events":"https://pith.science/api/pith-number/56BPUPYFKJVSDZDRQZHQ4T2B4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K/action/storage_attestation","attest_author":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K/action/author_attestation","sign_citation":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K/action/citation_signature","submit_replication":"https://pith.science/pith/56BPUPYFKJVSDZDRQZHQ4T2B4K/action/replication_record"}},"created_at":"2026-05-18T01:34:05.926859+00:00","updated_at":"2026-05-18T01:34:05.926859+00:00"}