{"paper":{"title":"A semigroup-theoretic linkage theory for relative ideals: principal and canonical links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Relative ideals in numerical semigroups admit two parallel linkage theories, one via semigroup translates and one via canonical ideal translates.","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ignacio Ojeda","submitted_at":"2026-04-15T23:26:48Z","abstract_excerpt":"We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical ideal."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical ideal.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the classical notions of liaison and linkage admit a faithful translation to the setting of relative ideals in numerical semigroups while preserving essential algebraic properties such as symmetry or linkage invariants.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new linkage theory for relative ideals in numerical semigroups is introduced via two notions: principal links using semigroup translates and canonical links using canonical ideal translates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Relative ideals in numerical semigroups admit two parallel linkage theories, one via semigroup translates and one via canonical ideal translates.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"937573a8d0b7b64b9c63b061cd8bea315eec6f7a0c7aeb09905cd2d847a083e8"},"source":{"id":"2604.14478","kind":"arxiv","version":2},"verdict":{"id":"017b60f4-c848-41ec-9daa-39e0339b68c0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T11:16:08.419582Z","strongest_claim":"We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical ideal.","one_line_summary":"A new linkage theory for relative ideals in numerical semigroups is introduced via two notions: principal links using semigroup translates and canonical links using canonical ideal translates.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the classical notions of liaison and linkage admit a faithful translation to the setting of relative ideals in numerical semigroups while preserving essential algebraic properties such as symmetry or linkage invariants.","pith_extraction_headline":"Relative ideals in numerical semigroups admit two parallel linkage theories, one via semigroup translates and one via canonical ideal translates."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.14478/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}