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the averaged fields converge almost surely to 1 in C(K) and their scaled fluctuations converge to the Gaussian process G(z) = 1/sqrt(pi) int 1_{B(z,1)}(u) dW_R(u).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The sequence f_n is constructed by iterated application of the Landau raising operator to the base Gaussian entire function f_0 while preserving the pointwise orthonormality condition E[e^{-|z|^2} f_n(z, bar z) bar f_{n'}(z, bar z)] = delta_{n n'}.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves interlacing-like zero pair correlations (repulsion at k=1, attraction at k=2, none for k>=3) and a functional CLT for averaged fields of iterated Gaussian entire functions, confirming signal-processing conjectures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Iterated orthonormal Gaussian entire functions produce zero processes with index-dependent short-range correlations and averaged fields converging almost surely to 1.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7bc59ce478aeee45e5f9ef7990572656f9725590a333aa8efb12e0985f09f65e"},"source":{"id":"2605.17296","kind":"arxiv","version":1},"verdict":{"id":"ee44e26e-86e0-466e-bdee-e2ca807451d3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:12:13.062058Z","strongest_claim":"The normalized pair correlations g_{n,n+k}(z,w) exhibit repulsion for k=1, attraction for k=2, and no short-range second-order correlation for k >= 3 as w -> z; the averaged fields converge almost surely to 1 in C(K) and their scaled fluctuations converge to the Gaussian process G(z) = 1/sqrt(pi) int 1_{B(z,1)}(u) dW_R(u).","one_line_summary":"Proves interlacing-like zero pair correlations (repulsion at k=1, attraction at k=2, none for k>=3) and a functional CLT for averaged fields of iterated Gaussian entire functions, confirming signal-processing conjectures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The sequence f_n is constructed by iterated application of the Landau raising operator to the base Gaussian entire function f_0 while preserving the pointwise orthonormality condition E[e^{-|z|^2} f_n(z, bar z) bar f_{n'}(z, bar z)] = delta_{n n'}.","pith_extraction_headline":"Iterated orthonormal Gaussian entire functions produce zero processes with index-dependent short-range correlations and averaged fields converging almost surely to 1."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17296/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.178012Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:21:25.512420Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.808085Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.763324Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e9e8087c95cc2250b63743e09dd94ca3f76ea71d54112952d41731b6dd598044"},"references":{"count":72,"sample":[{"doi":"","year":2010,"title":"L. 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