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This paper reports, for a given parameter ideal $Q$ for $M$, a criterion for the equality ${\\mathrm{g}}_s(Q;M)=\\operatorname{hdeg}_Q(M)-{\\mathrm{e}}_Q^0(M)-{\\mathrm{T}}_Q^1(M)$, where ${\\mathrm{g}}_s(Q;M)$, ${\\mathrm{e}}_Q^0(M)$, ${\\mathrm{e}}_Q^1(M)$, and ${\\mathrm{T}}_Q^1(M)$ respectively denote the sectional genus, the multiplicity, the first Hilbert coefficient, and the Homological torsion of $M$ with respect to $Q$."},"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":"1404.4680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-18T02:46:00Z","cross_cats_sorted":[],"title_canon_sha256":"bcf55af349b012812bbd3534a6114e286c79ec06442d365453a52d04d9dbabf0","abstract_canon_sha256":"c42679bf158b12f44842b8a60a0f19676aa337cadc12bef7611021b33c87835a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:55.426749Z","signature_b64":"wDBDLKVTw5F0xoOiltlIQafxUNsGtnQBgakpFnA9o3EdJoT9k+vPyIYJK9s8sFakZSZuGWozgjKCHfu2G0njDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21f88b7c1951d3cc222d7b4ede523f8f1ad80cce67495e92583b77d31fa1cd12","last_reissued_at":"2026-05-18T02:53:55.425772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:55.425772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sectional genera of parameter ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuho Ozeki, Shiro Goto","submitted_at":"2014-04-18T02:46:00Z","abstract_excerpt":"Let $M$ be a finitely generated module over a Noetherian local ring. 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