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Let $C$ be a \\textit{singular} irreducible projective curve of degree $d\\geq 5$ with the arithmetic genus $\\rho_a(C)$ in $\\p^r$ where $r\\ge 3$. If $M(I_C)$ is the regularity of the lexicographic generic initial ideal of $I_C$ in a polynomial ring $k[x_0,..., x_r]$ then we prove that $M(I_C)$ is $1+\\binom{d-1}{2}-\\rho_a(C)$ which is obtained from the monomial $$ x_{r-3} x_{r-1}\\,^{\\binom{d-1}{2}-\\rho_a(C)}, $$ provided that $\\dim\\Tan_p(C)=2$ for e","authors_text":"Jeaman Ahn, Sijong Kwak, YeongSeok Song","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-30T06:43:14Z","title":"Generic Initial ideals of Singular Curves in Graded Lexicographic Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0045","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a2bae28bab9becfc0f3110ef48e741b707742ac5a7fe75213b71a2cefa2ccdba","target":"record","created_at":"2026-05-18T04:16:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"eb53a8c7a4bed1ff0487b8bbc664c4528f66fc860bd4c401fd123bd6b240d826","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-30T06:43:14Z","title_canon_sha256":"76bb5dac9c41087792fbeb36014c455bbaf74c44a3116b9dfd573914dbf0a7ac"},"schema_version":"1.0","source":{"id":"1108.0045","kind":"arxiv","version":1}},"canonical_sha256":"9d4fd965d6a3a2cd5ca39d700b38ff868ced815565b32bf49ede80f0b40e2ce2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d4fd965d6a3a2cd5ca39d700b38ff868ced815565b32bf49ede80f0b40e2ce2","first_computed_at":"2026-05-18T04:16:31.785342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.785342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Uu4O8brj7DpO8QrQek6vuFN2nv79EEcpPZEyE4qqlaFnm+3U3/V56YLucvx7jkcRPbPrc+QC5ZKjaO3ZTLbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.785790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2bae28bab9becfc0f3110ef48e741b707742ac5a7fe75213b71a2cefa2ccdba","sha256:b3888ad9bf374d16f391bb41168f7981778110253fc30b69ccb50442aa75912f"],"state_sha256":"fd00855de65b54812717a58d6ebb2084c664d31462dc970860d53cd26b926b6f"}