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However, there is no objective way to assess which of these discrete eigenvalues are artefacts o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The estimator ˆP(λ), which can be obtained by reprocessing our finite data sample, allows us to test statistically for the location of the true eigenvalues and gives a rigorous way to assess whether extracted patterns are signal or noise.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The central premise that reprocessing the finite data sample yields an unbiased estimator for the sampling pseudospectrum of the underlying infinite-data operator, without additional assumptions on the distribution of sampling errors or the structure of the true operator.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces a sampling pseudospectrum P(λ) and estimator ˆP(λ) obtained by reprocessing finite data to statistically test the location of true eigenvalues versus sampling artifacts in data-driven matrices.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A sampling pseudospectrum estimator lets users test statistically whether eigenvalues from finite data are genuine or sampling artifacts.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"efb401973bf6d212cb389319ccf9c4c9a7e2001607909a386210d30e5a73a339"},"source":{"id":"2605.15234","kind":"arxiv","version":1},"verdict":{"id":"1c7d8dcf-ae87-49f0-a664-08adce3e3357","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:32:55.864793Z","strongest_claim":"The estimator ˆP(λ), which can be obtained by reprocessing our finite data sample, allows us to test statistically for the location of the true eigenvalues and gives a rigorous way to assess whether extracted patterns are signal or noise.","one_line_summary":"Introduces a sampling pseudospectrum P(λ) and estimator ˆP(λ) obtained by reprocessing finite data to statistically test the location of true eigenvalues versus sampling artifacts in data-driven matrices.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The central premise that reprocessing the finite data sample yields an unbiased estimator for the sampling pseudospectrum of the underlying infinite-data operator, without additional assumptions on the distribution of sampling errors or the structure of the true operator.","pith_extraction_headline":"A sampling pseudospectrum estimator lets users test statistically whether eigenvalues from finite data are genuine or sampling artifacts."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15234/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:18.602282Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:50:37.724493Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.178057Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.827479Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"219c6edecc721a368dc381b66ac7879ec424b260cba9721fecf4d3ed4c172cc5"},"references":{"count":31,"sample":[{"doi":"","year":2011,"title":"A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones","work_id":"3b638ff6-2e3c-414e-99be-6ca4bb52d38b","ref_index":1,"cited_arxiv_id":"1112.5968","is_internal_anchor":true},{"doi":"","year":2096,"title":"Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the koopman operator.SIAM Journal on Applied Dynamical Systems, 16(4):2096–2126, 2017","work_id":"bc790c71-667a-4760-8921-f13884125998","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"Arnold.Random dynamical systems","work_id":"311ba272-bce1-481e-93c0-76c021e51222","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"VivianeBaladi.Dynamical zeta functions and dynamical determinants for hyperbolic maps. 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