{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:E3LFOGBDZVXPPYWBQZKRRA2EBT","short_pith_number":"pith:E3LFOGBD","schema_version":"1.0","canonical_sha256":"26d6571823cd6ef7e2c186551883440ccc884227ae8703a784881ce3d7e9cd70","source":{"kind":"arxiv","id":"1801.08017","version":1},"attestation_state":"computed","paper":{"title":"Hall-Littlewood expansions of Schur delta operators at $t = 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, James Haglund, Mark Shimozono","submitted_at":"2018-01-24T15:20:12Z","abstract_excerpt":"For any Schur function $s_{\\nu}$, the associated {\\em delta operator} $\\Delta'_{s_{\\nu}}$ is a linear operator on the ring of symmetric functions which has the modified Macdonald polynomials as an eigenbasis. When $\\nu = (1^{n-1})$ is a column of length $n-1$, the symmetric function $\\Delta'_{e_{n-1}} e_n$ appears in the Shuffle Theorem of Carlsson-Mellit. More generally, when $\\nu = (1^{k-1})$ is any column the polynomial $\\Delta'_{e_{k-1}} e_n$ is the symmetric function side of the Delta Conjecture of Haglund-Remmel-Wilson. We give an expansion of $\\omega \\Delta'_{s_{\\nu}} e_n$ at $t = 0$ in"},"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":"1801.08017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T15:20:12Z","cross_cats_sorted":[],"title_canon_sha256":"6a03c6505ca2309191ddebb8f61641d0280f661af0c78a54dad546fc598a3ec9","abstract_canon_sha256":"ed5b59e8e8b5418ae68c420140f62e2e6cf9f16b314cc5204f312ca9f7087695"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:10.322190Z","signature_b64":"pVO8C/o9D8DXx406aKmdAXQQC9oDk1VfVIwLDyK3EPz1Yg6x71x0L5pTQQZKI91cYH38NdL3ynoswrpGuAj4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26d6571823cd6ef7e2c186551883440ccc884227ae8703a784881ce3d7e9cd70","last_reissued_at":"2026-05-18T00:25:10.321631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:10.321631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hall-Littlewood expansions of Schur delta operators at $t = 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, James Haglund, Mark Shimozono","submitted_at":"2018-01-24T15:20:12Z","abstract_excerpt":"For any Schur function $s_{\\nu}$, the associated {\\em delta operator} $\\Delta'_{s_{\\nu}}$ is a linear operator on the ring of symmetric functions which has the modified Macdonald polynomials as an eigenbasis. When $\\nu = (1^{n-1})$ is a column of length $n-1$, the symmetric function $\\Delta'_{e_{n-1}} e_n$ appears in the Shuffle Theorem of Carlsson-Mellit. More generally, when $\\nu = (1^{k-1})$ is any column the polynomial $\\Delta'_{e_{k-1}} e_n$ is the symmetric function side of the Delta Conjecture of Haglund-Remmel-Wilson. We give an expansion of $\\omega \\Delta'_{s_{\\nu}} e_n$ at $t = 0$ in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08017","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":"1801.08017","created_at":"2026-05-18T00:25:10.321707+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08017v1","created_at":"2026-05-18T00:25:10.321707+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08017","created_at":"2026-05-18T00:25:10.321707+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3LFOGBDZVXP","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3LFOGBDZVXPPYWB","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3LFOGBD","created_at":"2026-05-18T12:32:19.392346+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/E3LFOGBDZVXPPYWBQZKRRA2EBT","json":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT.json","graph_json":"https://pith.science/api/pith-number/E3LFOGBDZVXPPYWBQZKRRA2EBT/graph.json","events_json":"https://pith.science/api/pith-number/E3LFOGBDZVXPPYWBQZKRRA2EBT/events.json","paper":"https://pith.science/paper/E3LFOGBD"},"agent_actions":{"view_html":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT","download_json":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT.json","view_paper":"https://pith.science/paper/E3LFOGBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08017&json=true","fetch_graph":"https://pith.science/api/pith-number/E3LFOGBDZVXPPYWBQZKRRA2EBT/graph.json","fetch_events":"https://pith.science/api/pith-number/E3LFOGBDZVXPPYWBQZKRRA2EBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT/action/storage_attestation","attest_author":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT/action/author_attestation","sign_citation":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT/action/citation_signature","submit_replication":"https://pith.science/pith/E3LFOGBDZVXPPYWBQZKRRA2EBT/action/replication_record"}},"created_at":"2026-05-18T00:25:10.321707+00:00","updated_at":"2026-05-18T00:25:10.321707+00:00"}