{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PSXKHXAWVUJXK4ENGZVE2BSCYZ","short_pith_number":"pith:PSXKHXAW","schema_version":"1.0","canonical_sha256":"7caea3dc16ad1375708d366a4d0642c65201acbcf336c10020d04263ddcfc900","source":{"kind":"arxiv","id":"1609.03506","version":1},"attestation_state":"computed","paper":{"title":"The Elliptic Hall algebra and the deformed Khovanov Heisenberg category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, Anthony Licata, Joshua Sussan, Peter Samuelson, Sabin Cautis","submitted_at":"2016-09-12T17:56:06Z","abstract_excerpt":"We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined by Licata and Savage. We also show that as an algebra, it is isomorphic to \"half\" of a central extension of the elliptic Hall algebra of Burban and Schiffmann, specialized at $\\sigma = \\bar\\sigma^{-1} = q$. A key step in the proof may be of independent interest: we show that the sum (over $n$) of the Hochschild homologies of the positive affine Hecke algebras $\\mathrm{AH}_n^+$ is again an algebra, and that this algebra injects into both the elliptic Hall algebra and the trace of the"},"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":"1609.03506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-09-12T17:56:06Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"578299265bd9db1cf4a4af1e127a00fe718211401256a2742b83b24136e765ee","abstract_canon_sha256":"d01863da8bc261adeeaad1c2bc380085f7e68282c6389de2a1a50292c109951a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:37.292075Z","signature_b64":"hUpCUCBP4Cfj4udvOwPjdxCeigXHzX1w03KMntzy/yPAPSV+RSdi0KznJprT1evIM7B4kKJpymrszEOTQvmiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7caea3dc16ad1375708d366a4d0642c65201acbcf336c10020d04263ddcfc900","last_reissued_at":"2026-05-18T00:00:37.291456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:37.291456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Elliptic Hall algebra and the deformed Khovanov Heisenberg category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, Anthony Licata, Joshua Sussan, Peter Samuelson, Sabin Cautis","submitted_at":"2016-09-12T17:56:06Z","abstract_excerpt":"We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined by Licata and Savage. We also show that as an algebra, it is isomorphic to \"half\" of a central extension of the elliptic Hall algebra of Burban and Schiffmann, specialized at $\\sigma = \\bar\\sigma^{-1} = q$. A key step in the proof may be of independent interest: we show that the sum (over $n$) of the Hochschild homologies of the positive affine Hecke algebras $\\mathrm{AH}_n^+$ is again an algebra, and that this algebra injects into both the elliptic Hall algebra and the trace of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03506","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":"1609.03506","created_at":"2026-05-18T00:00:37.291555+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.03506v1","created_at":"2026-05-18T00:00:37.291555+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03506","created_at":"2026-05-18T00:00:37.291555+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSXKHXAWVUJX","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSXKHXAWVUJXK4EN","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSXKHXAW","created_at":"2026-05-18T12:30:39.010887+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/PSXKHXAWVUJXK4ENGZVE2BSCYZ","json":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ.json","graph_json":"https://pith.science/api/pith-number/PSXKHXAWVUJXK4ENGZVE2BSCYZ/graph.json","events_json":"https://pith.science/api/pith-number/PSXKHXAWVUJXK4ENGZVE2BSCYZ/events.json","paper":"https://pith.science/paper/PSXKHXAW"},"agent_actions":{"view_html":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ","download_json":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ.json","view_paper":"https://pith.science/paper/PSXKHXAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.03506&json=true","fetch_graph":"https://pith.science/api/pith-number/PSXKHXAWVUJXK4ENGZVE2BSCYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PSXKHXAWVUJXK4ENGZVE2BSCYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ/action/storage_attestation","attest_author":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ/action/author_attestation","sign_citation":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ/action/citation_signature","submit_replication":"https://pith.science/pith/PSXKHXAWVUJXK4ENGZVE2BSCYZ/action/replication_record"}},"created_at":"2026-05-18T00:00:37.291555+00:00","updated_at":"2026-05-18T00:00:37.291555+00:00"}