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We denote the $k$-th order jet scheme of the determinantal variety defined by $r$-minors in an $m \\times n$ matrix as $\\mathscr{L}^{m,n}_{r,k}$. For the special case where $m$, $n$, and $r$ are equal, and $m$ and $r$ are 3 while $k$ is 1, we establish a correspondence between the defining ideals of $\\mathscr{L}^{m,n}_{r,k}$ and abstract simpl"},"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":"2506.22898","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-28T14:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"df2cb2403d71d7bf1b9bfefc5efab514b44630ab5a633791e6261579f4a659f9","abstract_canon_sha256":"e88b22c59e8cea148fa20e2e3091a54bdc5ee1693f408e2aadea8427b58b5b0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:47.378175Z","signature_b64":"mjPsAv+KpbS0b9yhesTnMRZRwDsoNZ29G/mrJm9aJbiHRoOpmM3j0AW7Mm0vilXrYzFMwU4HfcFDADy6zQIEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f89f800436a44ce928bf344e0e1cf2a78f39500ba2d5c8dfed5b9c8c141c1d86","last_reissued_at":"2026-07-05T11:28:47.377638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:47.377638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On jet schemes of determinantal varieties","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Huaiqing Zuo, Yifan Chen","submitted_at":"2025-06-28T14:25:09Z","abstract_excerpt":"Determinantal varieties are important objects of study in algebraic geometry. 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