{"paper":{"title":"Statistically characterized subgroups related to arithmetic-type sequence of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ayan Ghosh, Pratulananda Das, Tamim Aziz","submitted_at":"2026-05-15T19:32:26Z","abstract_excerpt":"Very recently, in [Das et al., J. Lond. Math. Soc., 2025], statistically characterized subgroups were studied for certain classes of non-arithmetic sequences. Subsequently, in [Das et al., Bull. Sci. Math., 2025], characterized subgroups were investigated for a class of arithmetic-type sequences that includes both arithmetic sequences and certain non-arithmetic sequences. Motivated by these developments, we study statistically characterized subgroups associated with a broader class of arithmetic-type sequences. In particular, all previously obtained cardinality related observations for statist"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"All previously obtained cardinality related observations for statistically characterized subgroups corresponding to arithmetic sequences as well as certain non-arithmetic sequences follow as special cases of our results. Moreover, we show that this broader class exhibits drastically different behavior and differs significantly from the previously studied special cases.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The paper assumes that the statistical characterization extends coherently to the broader class of arithmetic-type sequences without requiring new restrictions or producing contradictions with the special cases already studied.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Authors extend statistical subgroup characterizations to a broad class of arithmetic-type sequences, recovering earlier cardinality results as special cases while noting new qualitative differences.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0bf19333b0bc3148ace7132168e30d8e6fa4a27233aded70ee00071e603e3c89"},"source":{"id":"2605.16577","kind":"arxiv","version":1},"verdict":{"id":"64a9c4e6-11a5-4532-81d0-bfb0b3a45cd4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:02:53.035995Z","strongest_claim":"All previously obtained cardinality related observations for statistically characterized subgroups corresponding to arithmetic sequences as well as certain non-arithmetic sequences follow as special cases of our results. Moreover, we show that this broader class exhibits drastically different behavior and differs significantly from the previously studied special cases.","one_line_summary":"Authors extend statistical subgroup characterizations to a broad class of arithmetic-type sequences, recovering earlier cardinality results as special cases while noting new qualitative differences.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The paper assumes that the statistical characterization extends coherently to the broader class of arithmetic-type sequences without requiring new restrictions or producing contradictions with the special cases already studied.","pith_extraction_headline":"Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16577/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:31:19.445464Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:12:05.568476Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.857609Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.616048Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ea5c8e8246ef5c1628e7b5700a1e32316c4b77cd462cea3d7fdd03422161ed5b"},"references":{"count":41,"sample":[{"doi":"","year":1952,"title":"Arbault, Sur l’ensemble de convergence absolue d’une s´ erie trigonom´ etrique., Bull","work_id":"ab7872ed-0a09-426a-92f0-f9490ff6954f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"A. Arhangel’skii , M. Tkachenko, Topological Groups and Related Structures: An Introduc- tion to Topological Algebra, Atlantis Press, Paris, 2008","work_id":"c10f8948-f73e-48da-a500-eb18f3dcdef5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"L. Außenhofer, D. Dikranjan, Locally quasi-convex compatible topologies on locally compact abelian groups, Mathematische Zeitschrift, 296 (2020), 325-351","work_id":"bcdeaae9-3c80-4687-8f56-66afe4582a49","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"G. Barbieri, D. Dikranjan, A. Giordano Bruno, H. Weber, Dirichlet sets vs characterized subgroups, Topol. Appl. 231, 50–76 (2017)","work_id":"8a273848-2b28-4dcd-a824-e63e42fffa65","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. 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