{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NO5SP7ZRHOGMZQOKMQWNBTC52Q","short_pith_number":"pith:NO5SP7ZR","schema_version":"1.0","canonical_sha256":"6bbb27ff313b8cccc1ca642cd0cc5dd433c09585a204d08a854ef37ef553fe64","source":{"kind":"arxiv","id":"1404.5240","version":2},"attestation_state":"computed","paper":{"title":"The affine Yangian of $\\mathfrak{gl}_1$ revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Tsymbaliuk","submitted_at":"2014-04-21T16:41:00Z","abstract_excerpt":"The affine Yangian of $\\mathfrak{gl}_1$ has recently appeared simultaneously in the work of Maulik-Okounkov and Schiffmann-Vasserot in connection with the Alday-Gaiotto-Tachikawa conjecture. While the former presentation is purely geometric, the latter algebraic presentation is quite involved. In this article, we provide a simple loop realization of this algebra which can be viewed as an \"additivization\" of the quantum toroidal algebra of $\\mathfrak{gl}_1$ in the same way as the Yangian $Y_h(\\mathfrak{g})$ is an \"additivization\" of the quantum loop algebra $U_q(L\\mathfrak{g})$ for a simple Lie"},"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":"1404.5240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-21T16:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"85b39f8f06f03722fd9e12bd71466dca84b68f43929f99b2d617c626d9b9a6ff","abstract_canon_sha256":"e8e279caf39f0d8f7085a112ccbf3f8782863a7728d00cbc19cc70b6a45e8ac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.391960Z","signature_b64":"anfQ2GICu7EBw7621KalUm/cBokagXeVg1toy7BiRX/MT/6IKi+Imx7RnbsaLPIDAc9mFWcE5rNfz0z3s4TWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bbb27ff313b8cccc1ca642cd0cc5dd433c09585a204d08a854ef37ef553fe64","last_reissued_at":"2026-05-17T23:54:27.391427Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.391427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The affine Yangian of $\\mathfrak{gl}_1$ revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Tsymbaliuk","submitted_at":"2014-04-21T16:41:00Z","abstract_excerpt":"The affine Yangian of $\\mathfrak{gl}_1$ has recently appeared simultaneously in the work of Maulik-Okounkov and Schiffmann-Vasserot in connection with the Alday-Gaiotto-Tachikawa conjecture. While the former presentation is purely geometric, the latter algebraic presentation is quite involved. In this article, we provide a simple loop realization of this algebra which can be viewed as an \"additivization\" of the quantum toroidal algebra of $\\mathfrak{gl}_1$ in the same way as the Yangian $Y_h(\\mathfrak{g})$ is an \"additivization\" of the quantum loop algebra $U_q(L\\mathfrak{g})$ for a simple Lie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5240","kind":"arxiv","version":2},"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":"1404.5240","created_at":"2026-05-17T23:54:27.391526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5240v2","created_at":"2026-05-17T23:54:27.391526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5240","created_at":"2026-05-17T23:54:27.391526+00:00"},{"alias_kind":"pith_short_12","alias_value":"NO5SP7ZRHOGM","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NO5SP7ZRHOGMZQOK","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NO5SP7ZR","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.07255","citing_title":"Non-commutative creation operators for symmetric polynomials","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q","json":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q.json","graph_json":"https://pith.science/api/pith-number/NO5SP7ZRHOGMZQOKMQWNBTC52Q/graph.json","events_json":"https://pith.science/api/pith-number/NO5SP7ZRHOGMZQOKMQWNBTC52Q/events.json","paper":"https://pith.science/paper/NO5SP7ZR"},"agent_actions":{"view_html":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q","download_json":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q.json","view_paper":"https://pith.science/paper/NO5SP7ZR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5240&json=true","fetch_graph":"https://pith.science/api/pith-number/NO5SP7ZRHOGMZQOKMQWNBTC52Q/graph.json","fetch_events":"https://pith.science/api/pith-number/NO5SP7ZRHOGMZQOKMQWNBTC52Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q/action/storage_attestation","attest_author":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q/action/author_attestation","sign_citation":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q/action/citation_signature","submit_replication":"https://pith.science/pith/NO5SP7ZRHOGMZQOKMQWNBTC52Q/action/replication_record"}},"created_at":"2026-05-17T23:54:27.391526+00:00","updated_at":"2026-05-17T23:54:27.391526+00:00"}