{"paper":{"title":"Moment problems on compacts of characters of an unital commutative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Nonnegative functionals on Archimedean cones admit integral representations without semiring or quadratic-module assumptions.","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dragu Atanasiu","submitted_at":"2026-05-15T16:10:03Z","abstract_excerpt":"In this note we consider linear functionals on an unital commutative R-algebra. We give an integral representation of a nonnegative functional on an Archimedean cone where we do not assume that this cone is a semiring or a quadratic module. We also give a solution of the moment problem on a product of intervals and determine conditions for a functional to be a moment functional on a compact of characters."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give an integral representation of a nonnegative functional on an Archimedean cone where we do not assume that this cone is a semiring or a quadratic module.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cone under consideration is Archimedean; this property is invoked to obtain the integral representation once the semiring and quadratic-module assumptions are dropped.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Provides integral representation of nonnegative functionals on Archimedean cones without semiring or quadratic module assumptions and solves moment problems on compacts of characters.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonnegative functionals on Archimedean cones admit integral representations without semiring or quadratic-module assumptions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0f6e46e8c6d7b0585cc49c2ee939148ab5a8053c3c2b97f3fad6c55d2cf7a369"},"source":{"id":"2605.16124","kind":"arxiv","version":1},"verdict":{"id":"77029e3b-5fc8-460c-b7dc-824c1ec3d9fc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:37:31.184980Z","strongest_claim":"We give an integral representation of a nonnegative functional on an Archimedean cone where we do not assume that this cone is a semiring or a quadratic module.","one_line_summary":"Provides integral representation of nonnegative functionals on Archimedean cones without semiring or quadratic module assumptions and solves moment problems on compacts of characters.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cone under consideration is Archimedean; this property is invoked to obtain the integral representation once the semiring and quadratic-module assumptions are dropped.","pith_extraction_headline":"Nonnegative functionals on Archimedean cones admit integral representations without semiring or quadratic-module assumptions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16124/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.961224Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:44.927872Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:33.382354Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.470831Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"126011a1ce54806e76bb77f3bd26331d3146d410809630b0b6a2f822a92e3d12"},"references":{"count":27,"sample":[{"doi":"","year":1987,"title":"Atanasiu, Dragu , TITLE =. 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