{"paper":{"title":"Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dumitru I. Stamate, Francesco Strazzanti","submitted_at":"2026-01-27T14:08:26Z","abstract_excerpt":"Given the integers $0<r_1<\\dots<r_k$, we consider the shifted family of semigroups $M_n=\\langle n, n+r_1,\\dots, n+r_k\\rangle$, where $n>0$. For sufficiently large $n$, we prove that if $M_n$ is nearly Gorenstein or almost symmetric, then so is $M_{n+r_k}$. A key ingredient is to relate the pseudo-Frobenius elements of $M_n$ and $M_{n+r_k}$, correcting a wrong claim in the literature. Moreover, we derive explicit formulas for the Frobenius and pseudo-Frobenius numbers of $M_{n+r_k}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19629","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.19629/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"}