{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AST542L72PQRPBZ7UFVJEX4L3O","short_pith_number":"pith:AST542L7","schema_version":"1.0","canonical_sha256":"04a7de697fd3e117873fa16a925f8bdbb61abbd56d2984c76642bf41bd0965cf","source":{"kind":"arxiv","id":"2608.08682","version":1},"attestation_state":"computed","paper":{"title":"A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\\xi$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonathan Holland","submitted_at":"2026-08-09T12:58:52Z","abstract_excerpt":"Let \\[\n  \\xi\\!\\left(\\frac12+z\\right)\n  =\\sum_{n\\geq 0}\\frac{\\gamma(n)}{n!}z^{2n},\n  \\qquad\n  J^{d,n}(X)\n  =\\sum_{j=0}^{d}\\binom dj\\gamma(n+j)X^j . \\] The Riemann hypothesis is equivalent to the hyperbolicity of $J^{d,n}$ for every $d,n\\geq0$. We prove that there is an absolute constant $K>0$ such that \\[\n  n^3\\log^2(n+2)\\geq Kd^5\n  \\quad\\Longrightarrow\\quad\n  J^{d,n}\\ \\text{is hyperbolic}. \\] Along every sequence with $n,d\\to\\infty$ in this region, the empirical measure of the naturally centered and scaled zeros also converges to Wigner's semicircle law. This gives a simultaneous degree--deriv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.08682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-08-09T12:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"a07a5a0f41dfba92dd0df44ea3d8dd59ae1e1eb1d013483f1c6f572d6f4a5222","abstract_canon_sha256":"7b4907e589e56192eaf8dfde01dd40703286d0e89ab722aca6bcdb715e1a52d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:24:59.553902Z","signature_b64":"sXS0AZREsuzMRWQBFd/GwgramLCMSypgietiG3mBzPl2G0a5bQAwZs5BRzLEUhXZReLBv3C3RbYZxSfckkpTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04a7de697fd3e117873fa16a925f8bdbb61abbd56d2984c76642bf41bd0965cf","last_reissued_at":"2026-08-11T01:24:59.551548Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:24:59.551548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\\xi$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonathan Holland","submitted_at":"2026-08-09T12:58:52Z","abstract_excerpt":"Let \\[\n  \\xi\\!\\left(\\frac12+z\\right)\n  =\\sum_{n\\geq 0}\\frac{\\gamma(n)}{n!}z^{2n},\n  \\qquad\n  J^{d,n}(X)\n  =\\sum_{j=0}^{d}\\binom dj\\gamma(n+j)X^j . \\] The Riemann hypothesis is equivalent to the hyperbolicity of $J^{d,n}$ for every $d,n\\geq0$. We prove that there is an absolute constant $K>0$ such that \\[\n  n^3\\log^2(n+2)\\geq Kd^5\n  \\quad\\Longrightarrow\\quad\n  J^{d,n}\\ \\text{is hyperbolic}. \\] Along every sequence with $n,d\\to\\infty$ in this region, the empirical measure of the naturally centered and scaled zeros also converges to Wigner's semicircle law. This gives a simultaneous degree--deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08682","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08682/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.08682","created_at":"2026-08-11T01:24:59.552317+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.08682v1","created_at":"2026-08-11T01:24:59.552317+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08682","created_at":"2026-08-11T01:24:59.552317+00:00"},{"alias_kind":"pith_short_12","alias_value":"AST542L72PQR","created_at":"2026-08-11T01:24:59.552317+00:00"},{"alias_kind":"pith_short_16","alias_value":"AST542L72PQRPBZ7","created_at":"2026-08-11T01:24:59.552317+00:00"},{"alias_kind":"pith_short_8","alias_value":"AST542L7","created_at":"2026-08-11T01:24:59.552317+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O","json":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O.json","graph_json":"https://pith.science/api/pith-number/AST542L72PQRPBZ7UFVJEX4L3O/graph.json","events_json":"https://pith.science/api/pith-number/AST542L72PQRPBZ7UFVJEX4L3O/events.json","paper":"https://pith.science/paper/AST542L7"},"agent_actions":{"view_html":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O","download_json":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O.json","view_paper":"https://pith.science/paper/AST542L7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.08682&json=true","fetch_graph":"https://pith.science/api/pith-number/AST542L72PQRPBZ7UFVJEX4L3O/graph.json","fetch_events":"https://pith.science/api/pith-number/AST542L72PQRPBZ7UFVJEX4L3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O/action/storage_attestation","attest_author":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O/action/author_attestation","sign_citation":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O/action/citation_signature","submit_replication":"https://pith.science/pith/AST542L72PQRPBZ7UFVJEX4L3O/action/replication_record"}},"created_at":"2026-08-11T01:24:59.552317+00:00","updated_at":"2026-08-11T01:24:59.552317+00:00"}