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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"},"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":"1108.0045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-30T06:43:14Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"76bb5dac9c41087792fbeb36014c455bbaf74c44a3116b9dfd573914dbf0a7ac","abstract_canon_sha256":"eb53a8c7a4bed1ff0487b8bbc664c4528f66fc860bd4c401fd123bd6b240d826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:31.785790Z","signature_b64":"2Uu4O8brj7DpO8QrQek6vuFN2nv79EEcpPZEyE4qqlaFnm+3U3/V56YLucvx7jkcRPbPrc+QC5ZKjaO3ZTLbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d4fd965d6a3a2cd5ca39d700b38ff868ced815565b32bf49ede80f0b40e2ce2","last_reissued_at":"2026-05-18T04:16:31.785342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:31.785342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic Initial ideals of Singular Curves in Graded Lexicographic Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jeaman Ahn, Sijong Kwak, YeongSeok Song","submitted_at":"2011-07-30T06:43:14Z","abstract_excerpt":"In this paper, we are interested in the generic initial ideals of \\textit{singular} projective curves with respect to the graded lexicographic order. 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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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0045","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":"1108.0045","created_at":"2026-05-18T04:16:31.785415+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.0045v1","created_at":"2026-05-18T04:16:31.785415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0045","created_at":"2026-05-18T04:16:31.785415+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVH5SZOWUORM","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVH5SZOWUORM2XFD","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVH5SZOW","created_at":"2026-05-18T12:26:42.757692+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/TVH5SZOWUORM2XFDTVYAWOH7Q2","json":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2.json","graph_json":"https://pith.science/api/pith-number/TVH5SZOWUORM2XFDTVYAWOH7Q2/graph.json","events_json":"https://pith.science/api/pith-number/TVH5SZOWUORM2XFDTVYAWOH7Q2/events.json","paper":"https://pith.science/paper/TVH5SZOW"},"agent_actions":{"view_html":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2","download_json":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2.json","view_paper":"https://pith.science/paper/TVH5SZOW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.0045&json=true","fetch_graph":"https://pith.science/api/pith-number/TVH5SZOWUORM2XFDTVYAWOH7Q2/graph.json","fetch_events":"https://pith.science/api/pith-number/TVH5SZOWUORM2XFDTVYAWOH7Q2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2/action/storage_attestation","attest_author":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2/action/author_attestation","sign_citation":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2/action/citation_signature","submit_replication":"https://pith.science/pith/TVH5SZOWUORM2XFDTVYAWOH7Q2/action/replication_record"}},"created_at":"2026-05-18T04:16:31.785415+00:00","updated_at":"2026-05-18T04:16:31.785415+00:00"}