{"paper":{"title":"Ordered POVMs and Residual Collapse","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A residual transform on ordered POVM realizations produces a collapsed form with mutually orthogonal non-escape coordinates whose supports strongly sum to the identity.","cross_cats":["math-ph","math.MP","quant-ph","stat.ME"],"primary_cat":"math.FA","authors_text":"James Tian","submitted_at":"2026-05-17T18:39:47Z","abstract_excerpt":"Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effect obtained after all earlier tests have failed, and appends the remaining mass as a terminal outcome. Under natural hypotheses, iterating the transform produces a collapsed POVM whose non-escape coordinates are the parts of the original effects that survive all earlier tests. The resulting collapse map gives an equivalence relation on ordered POVM realizations. Its range and fibers are characterized. The range consi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting collapse map gives an equivalence relation on ordered POVM realizations. Its range consists of collapsed POVMs, whose non-escape coordinates are mutually orthogonal and whose support projections strongly sum to the identity. The fiber over a collapsed POVM consists of all ordered realizations with the same residually visible compressions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Under natural hypotheses, iterating the transform produces a collapsed POVM whose non-escape coordinates are the parts of the original effects that survive all earlier tests.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines a residual collapse map for ordered POVMs that produces collapsed POVMs with mutually orthogonal non-escape coordinates and characterizes the map's range and fibers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A residual transform on ordered POVM realizations produces a collapsed form with mutually orthogonal non-escape coordinates whose supports strongly sum to the identity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ce49a9ffe4cfc514dc9af51f9365f443ea8173c0e04c0cf07816d6cba0fd7c86"},"source":{"id":"2605.17592","kind":"arxiv","version":1},"verdict":{"id":"403c4eba-e2ae-4931-a58e-ecc5b241c7a1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:10:48.994543Z","strongest_claim":"The resulting collapse map gives an equivalence relation on ordered POVM realizations. Its range consists of collapsed POVMs, whose non-escape coordinates are mutually orthogonal and whose support projections strongly sum to the identity. The fiber over a collapsed POVM consists of all ordered realizations with the same residually visible compressions.","one_line_summary":"Defines a residual collapse map for ordered POVMs that produces collapsed POVMs with mutually orthogonal non-escape coordinates and characterizes the map's range and fibers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Under natural hypotheses, iterating the transform produces a collapsed POVM whose non-escape coordinates are the parts of the original effects that survive all earlier tests.","pith_extraction_headline":"A residual transform on ordered POVM realizations produces a collapsed form with mutually orthogonal non-escape coordinates whose supports strongly sum to the identity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17592/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.554518Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:21:44.295083Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.582524Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.511366Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b62328d4aebe97634fe911372124b298a08db8385af3a03e0a08237391c6e7dc"},"references":{"count":34,"sample":[{"doi":"","year":null,"title":"Takesaki, M. , date-added =. 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