{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:XWPWGLTLAQ6SQOZFIYNPEAYONK","short_pith_number":"pith:XWPWGLTL","schema_version":"1.0","canonical_sha256":"bd9f632e6b043d283b25461af2030e6a9f7527c5655e154f2cdbc9138ac3ef80","source":{"kind":"arxiv","id":"math/9803041","version":7},"attestation_state":"computed","paper":{"title":"Chiral de Rham complex","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arkady Vaintrob, Fyodor Malikov, Vadim Schechtman","submitted_at":"1998-03-11T13:37:33Z","abstract_excerpt":"The aim of this note is to define certain sheaves of vertex algebras on smooth manifolds. For each smooth complex algebraic (or analytic) manifold $X$, we construct a sheaf $\\Omega^{ch}_X$, called the {\\bf chiral de Rham complex} of $X$. It is a sheaf of vertex algebras in the Zarisky (or classical) topology, It comes equipped with a $\\BZ$-grading by {\\it fermionic charge}, and the {\\it chiral de Rham differential} $d_{DR}^{ch}$, which is an endomorphism of degree 1 such that $(d_{DR}^{ch})^2=0$. One has a canonical embedding of the usual de Rham complex $(\\Omega_X, d_{DR})\\hra (\\Omega_X^{ch},"},"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":"math/9803041","kind":"arxiv","version":7},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-03-11T13:37:33Z","cross_cats_sorted":[],"title_canon_sha256":"b7b432a82337f92102f5d6b7d388629fbf81abce003bf84ea4e1ec25a33873dd","abstract_canon_sha256":"8bb0037f07817caba70fead5420e77975f45eb56f6b38bc2b76b7e0ae2614176"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:10:09.072476Z","signature_b64":"uIajK+SW/D3M8VbRbWrwzUJDx8a2zz+IIUOiPd3Xd7rOtBNPaiNUVD7RcQgtXmN+3cmBufDPBpocU87dwm/MDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9f632e6b043d283b25461af2030e6a9f7527c5655e154f2cdbc9138ac3ef80","last_reissued_at":"2026-07-04T16:10:09.072054Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:10:09.072054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chiral de Rham complex","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arkady Vaintrob, Fyodor Malikov, Vadim Schechtman","submitted_at":"1998-03-11T13:37:33Z","abstract_excerpt":"The aim of this note is to define certain sheaves of vertex algebras on smooth manifolds. For each smooth complex algebraic (or analytic) manifold $X$, we construct a sheaf $\\Omega^{ch}_X$, called the {\\bf chiral de Rham complex} of $X$. It is a sheaf of vertex algebras in the Zarisky (or classical) topology, It comes equipped with a $\\BZ$-grading by {\\it fermionic charge}, and the {\\it chiral de Rham differential} $d_{DR}^{ch}$, which is an endomorphism of degree 1 such that $(d_{DR}^{ch})^2=0$. One has a canonical embedding of the usual de Rham complex $(\\Omega_X, d_{DR})\\hra (\\Omega_X^{ch},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803041","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9803041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/9803041","created_at":"2026-07-04T16:10:09.072121+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9803041v7","created_at":"2026-07-04T16:10:09.072121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803041","created_at":"2026-07-04T16:10:09.072121+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWPWGLTLAQ6S","created_at":"2026-07-04T16:10:09.072121+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWPWGLTLAQ6SQOZF","created_at":"2026-07-04T16:10:09.072121+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWPWGLTL","created_at":"2026-07-04T16:10:09.072121+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.24708","citing_title":"Vertex Superalgebras for Hypertoric Varieties and 3d Abelian Gauge Theories","ref_index":72,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK","json":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK.json","graph_json":"https://pith.science/api/pith-number/XWPWGLTLAQ6SQOZFIYNPEAYONK/graph.json","events_json":"https://pith.science/api/pith-number/XWPWGLTLAQ6SQOZFIYNPEAYONK/events.json","paper":"https://pith.science/paper/XWPWGLTL"},"agent_actions":{"view_html":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK","download_json":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK.json","view_paper":"https://pith.science/paper/XWPWGLTL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9803041&json=true","fetch_graph":"https://pith.science/api/pith-number/XWPWGLTLAQ6SQOZFIYNPEAYONK/graph.json","fetch_events":"https://pith.science/api/pith-number/XWPWGLTLAQ6SQOZFIYNPEAYONK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK/action/storage_attestation","attest_author":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK/action/author_attestation","sign_citation":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK/action/citation_signature","submit_replication":"https://pith.science/pith/XWPWGLTLAQ6SQOZFIYNPEAYONK/action/replication_record"}},"created_at":"2026-07-04T16:10:09.072121+00:00","updated_at":"2026-07-04T16:10:09.072121+00:00"}