{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NMGW7YO7U6JRNMUGYM6GITMKOQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fb30d0d28a21c6253887be6c92e7c808fae47c2a4c2174a61b9d7a04e072262e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T19:32:26Z","title_canon_sha256":"5b4b56eefeac400f6e48c635e3503cd27337c2307bb3513385a738ba8b21f245"},"schema_version":"1.0","source":{"id":"2605.16577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16577","created_at":"2026-05-20T00:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16577v1","created_at":"2026-05-20T00:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16577","created_at":"2026-05-20T00:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"NMGW7YO7U6JR","created_at":"2026-05-20T00:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"NMGW7YO7U6JRNMUG","created_at":"2026-05-20T00:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"NMGW7YO7","created_at":"2026-05-20T00:02:30Z"}],"graph_snapshots":[{"event_id":"sha256:3c8aff8ea4ea6317b973d7b54db2f8bbde476c3c3d2e00f82d1617c71d750df3","target":"graph","created_at":"2026-05-20T00:02:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior."}],"snapshot_sha256":"0bf19333b0bc3148ace7132168e30d8e6fa4a27233aded70ee00071e603e3c89"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2848f263ced5490819e832a5c980d2638a459bfa51a1668e0c945efa7ed0241e"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"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"}],"endpoint":"/pith/2605.16577/integrity.json","findings":[],"snapshot_sha256":"ea5c8e8246ef5c1628e7b5700a1e32316c4b77cd462cea3d7fdd03422161ed5b","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Ayan Ghosh, Pratulananda Das, Tamim Aziz","cross_cats":[],"headline":"Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T19:32:26Z","title":"Statistically characterized subgroups related to arithmetic-type sequence of integers"},"references":{"count":41,"internal_anchors":0,"resolved_work":41,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Arbault, Sur l’ensemble de convergence absolue d’une s´ erie trigonom´ etrique., Bull","work_id":"ab7872ed-0a09-426a-92f0-f9490ff6954f","year":1952},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"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","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"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","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"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","year":2017},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328(1) (2007), 715–729","work_id":"49fce91f-0ea3-4b38-8a74-d50d7c4531f6","year":2007}],"snapshot_sha256":"e37b15776cbc6efdfaade3f682537a14ec769b89b0712c9c8ef8860140cf36ac"},"source":{"id":"2605.16577","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T21:02:53.035995Z","id":"64a9c4e6-11a5-4532-81d0-bfb0b3a45cd4","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"64a9c4e6-11a5-4532-81d0-bfb0b3a45cd4"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cfc19cf615a48657a27752461cf181fa2849feddf938118f34380cc1b017b97e","target":"record","created_at":"2026-05-20T00:02:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fb30d0d28a21c6253887be6c92e7c808fae47c2a4c2174a61b9d7a04e072262e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T19:32:26Z","title_canon_sha256":"5b4b56eefeac400f6e48c635e3503cd27337c2307bb3513385a738ba8b21f245"},"schema_version":"1.0","source":{"id":"2605.16577","kind":"arxiv","version":1}},"canonical_sha256":"6b0d6fe1dfa79316b286c33c644d8a740eb5d5251bd6bdde2ba21dc47f202ac3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b0d6fe1dfa79316b286c33c644d8a740eb5d5251bd6bdde2ba21dc47f202ac3","first_computed_at":"2026-05-20T00:02:30.637281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:30.637281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t61/OtqI2lBQyx98uUo0cZ8a5wNDQ4W3yYWBH5kJ8NfWNd5D4sjbOXATjXITHLAFO3PYmGWc4lU1qjkcTCf2AA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:30.638247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfc19cf615a48657a27752461cf181fa2849feddf938118f34380cc1b017b97e","sha256:3c8aff8ea4ea6317b973d7b54db2f8bbde476c3c3d2e00f82d1617c71d750df3"],"state_sha256":"7e15d54e8bdb87a06f03e321cac16e3bc95c675058ececa2db515cc2c5838b0d"}