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Case ${N\\ge3}$ was obtained independently by Coand\\v{a} with a different choice of families of monomials [Coa09].\n  For ${(N,d,n)=(2,2,5)}$, there are $5$ monomials of degree~$2$ in $K[X_0,X_1,X_2]$ such that their syzygy bundle is semistable."},"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":"1008.2733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-16T18:32:34Z","cross_cats_sorted":[],"title_canon_sha256":"a764270bdfc009d04ebed9d1bd3409f1da1d0c4942b2d2d588c86841b6274cd2","abstract_canon_sha256":"e79bc49449d153afbe6e67f6bdddc52166016084ba953ceaa48eb0164e64d436"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.289251Z","signature_b64":"Xqy5xJbIqFr8p51UrS+9UBZfUjIA7ZVyCv04aCLhM9/bIgRkVfPDEBMO6vQpF6a5Rif2Wr9wwRyxZ5+s9d90Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3c0ebed8c5c12e6157a9bc496649b407a4b3695bf7702ad05b779252ce04b7","last_reissued_at":"2026-05-18T00:30:33.288585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.288585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of syzygy bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pedro Macias Marques, Rosa Mar\\'ia Mir\\'o-Roig","submitted_at":"2010-08-16T18:32:34Z","abstract_excerpt":"We show that given integers $N$, $d$ and $n$ such that ${N\\ge2}$, ${(N,d,n)\\ne(2,2,5)}$, and ${N+1\\le n\\le\\tbinom{d+N}{N}}$, there is a family of $n$ monomials in $K[X_0,\\ldots,X_N]$ of degree $d$ such that their syzygy bundle is stable. 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