{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H6GSNRQGDM72PSQ3TRYG3CQ3NY","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":"8c1c5e91750fb2c1ed472a570e338e68583ba4358a2bee7cc366669ecec0196a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T07:16:21Z","title_canon_sha256":"81670575951b6bcac24707a936954d7b070d044cc4d9344560655eb5cb0733bf"},"schema_version":"1.0","source":{"id":"2605.17296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17296","created_at":"2026-05-20T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17296v1","created_at":"2026-05-20T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17296","created_at":"2026-05-20T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"H6GSNRQGDM72","created_at":"2026-05-20T00:03:50Z"},{"alias_kind":"pith_short_16","alias_value":"H6GSNRQGDM72PSQ3","created_at":"2026-05-20T00:03:50Z"},{"alias_kind":"pith_short_8","alias_value":"H6GSNRQG","created_at":"2026-05-20T00:03:50Z"}],"graph_snapshots":[{"event_id":"sha256:6a933dc17d6989c53296a2d67853bb54a12481aebffae14e47917a545ee24d29","target":"graph","created_at":"2026-05-20T00:03:50Z","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":"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)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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'}."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Iterated orthonormal Gaussian entire functions produce zero processes with index-dependent short-range correlations and averaged fields converging almost surely to 1."}],"snapshot_sha256":"7bc59ce478aeee45e5f9ef7990572656f9725590a333aa8efb12e0985f09f65e"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2ddf4b981e6aabc53d30c13c679875e1b6c344237749720a75be186b3ee70e63"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"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"}],"endpoint":"/pith/2605.17296/integrity.json","findings":[],"snapshot_sha256":"e9e8087c95cc2250b63743e09dd94ca3f76ea71d54112952d41731b6dd598044","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the family of point processes $\\{\\mathcal{Z}_{f_{n}}\\}_{n=0}^{\\infty}$ of zeros of Gaussian random functions $\\{f_{n}(z,\\overline{z})\\}_{n=0}^{\\infty} $, arising from the Gaussian Entire Function \\[ f_{0}(z):=\\sum_{k=0}^{\\infty} \\zeta_{k} \\frac{z^{k}}{\\sqrt{k!}}, \\quad \\zeta_{k} \\sim N_{\\mathbb{C}}(0,1)\\text{ i.i.d.} \\] by iteration of the Landau raising operator, and orthonormal at each point in expectation in the sense that \\[ \\mathbb{E}\\left[ e^{-\\left\\vert z\\right\\vert^{2}}f_{n}(z,\\overline{z})\\overline{f_{n^{\\prime }}(z,\\overline{z})}\\right] ={\\delta }_{nn'}. \\] We first show ","authors_text":"Lu\\'is Daniel Abreu, Tomoyuki Shirai","cross_cats":["math-ph","math.CA","math.MP"],"headline":"Iterated orthonormal Gaussian entire functions produce zero processes with index-dependent short-range correlations and averaged fields converging almost surely to 1.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T07:16:21Z","title":"Zero correlations and averaged fields of orthonormal Gaussian functions"},"references":{"count":72,"internal_anchors":1,"resolved_work":72,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"L. D. Abreu,Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions. Appl. Comp. Harm. Anal., 29, 287–302, (2010)","work_id":"a9610efc-d776-4032-848f-300110fbd7ba","year":2010},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"L. D. Abreu, K. Gr¨ ochenig, J. L. Romero,On accumulated spectrograms. Trans. Amer. Math. Soc.368, 3629–3649, (2016)","work_id":"cd98b291-0055-455b-aedb-80f2e550ea4b","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"L. D. Abreu, K. Gr¨ ochenig, J. L. Romero,Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles. J. Stat. Phys., vol. 174, 5, 1104–1136, (2019)","work_id":"021c7556-07ee-4502-98e4-8e1dc6f213eb","year":2019},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"L. D. Abreu,Local maxima of white noise spectrograms and Gaussian Entire Functions. J. Fourier Anal. Appl., vol. 28, Article number: 88 (2022)","work_id":"377c97f7-1a44-4608-a050-60cb2706eacc","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"L. D. Abreu, D. Alpay, T. Georgiou, P. Jorgensen,Analytic continuation of time in Brownian motion. Stochastic distributions approach. J. Math. Anal. Appl., 130438, (2026)","work_id":"b6c3f6ea-9c2d-49b2-b855-cc000d210a97","year":2026}],"snapshot_sha256":"2b6adf7e604ba1da1dbcde14634a93e178644312da658f82b83997de0b5be057"},"source":{"id":"2605.17296","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T23:12:13.062058Z","id":"ee44e26e-86e0-466e-bdee-e2ca807451d3","model_set":{"reader":"grok-4.3"},"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","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.","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).","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'}."}},"verdict_id":"ee44e26e-86e0-466e-bdee-e2ca807451d3"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e5a5c1ce14d02d946040ce9d1e09dcf58444a2b41c552270405359b693f933f5","target":"record","created_at":"2026-05-20T00:03:50Z","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":"8c1c5e91750fb2c1ed472a570e338e68583ba4358a2bee7cc366669ecec0196a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T07:16:21Z","title_canon_sha256":"81670575951b6bcac24707a936954d7b070d044cc4d9344560655eb5cb0733bf"},"schema_version":"1.0","source":{"id":"2605.17296","kind":"arxiv","version":1}},"canonical_sha256":"3f8d26c6061b3fa7ca1b9c706d8a1b6e0d7c9667d036f732e083e5c579d6d52c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f8d26c6061b3fa7ca1b9c706d8a1b6e0d7c9667d036f732e083e5c579d6d52c","first_computed_at":"2026-05-20T00:03:50.783212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:50.783212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iMnPldvXARwJjXLMOuDI02kqSagayDAkvwagIYT90ef0kkYAAgAjAuLDNWouUYquiGdxe3tiymmDLcQgQTE+BA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:50.783908Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5a5c1ce14d02d946040ce9d1e09dcf58444a2b41c552270405359b693f933f5","sha256:6a933dc17d6989c53296a2d67853bb54a12481aebffae14e47917a545ee24d29"],"state_sha256":"4abaa31ea3612b9875e28fbe0cd4b2e3ca31db9b9de0c0d2321ee4c459adaa4b"}