{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SMVJ55NJDMACZTMYIA34JX4TJZ","short_pith_number":"pith:SMVJ55NJ","schema_version":"1.0","canonical_sha256":"932a9ef5a91b002ccd984037c4df934e736fa06a34e4e8db09b8b832a840496d","source":{"kind":"arxiv","id":"1801.05914","version":5},"attestation_state":"computed","paper":{"title":"The De Bruijn-Newman constant is non-negative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brad Rodgers, Terence Tao","submitted_at":"2018-01-18T02:47:14Z","abstract_excerpt":"For each $t \\in {\\bf R}$, define the entire function $$ H_t(x) := \\int_0^\\infty e^{tu^2} \\Phi(u) \\cos(xu)\\ du$$ where $\\Phi$ is the super-exponentially decaying function $$ \\Phi(u) := \\sum_{n=1}^\\infty (2\\pi^2 n^4 e^{9u} - 3\\pi n^2 e^{5u} ) \\exp(-\\pi n^2 e^{4u} ).$$ Newman showed that there exists a finite constant $\\Lambda$ (the \\emph{de Bruijn-Newman constant}) such that the zeroes of $H_t$ are all real precisely when $t \\geq \\Lambda$. The Riemann hypothesis is the equivalent to the assertion $\\Lambda \\leq 0$, and Newman conjectured the complementary bound $\\Lambda \\geq 0$.\n  In this paper w"},"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":"1801.05914","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-18T02:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"a1c723724fdf7f50cd25344106d9b48625013dc8078853c24e73d6983da8d427","abstract_canon_sha256":"15da96e43f10ff316b44d467f52ac14afa44f04fbe51a65ee4508eb5633c8dd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:54:48.165580Z","signature_b64":"QR6pAVL0h2797ay7Z+pMUTkZhG2mdHnK/4yFtw+Kt0A70/bjuXMTJD73dez1Abq8mNgbaMszS2qHCurUVK+dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"932a9ef5a91b002ccd984037c4df934e736fa06a34e4e8db09b8b832a840496d","last_reissued_at":"2026-07-05T02:54:48.165148Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:54:48.165148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The De Bruijn-Newman constant is non-negative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brad Rodgers, Terence Tao","submitted_at":"2018-01-18T02:47:14Z","abstract_excerpt":"For each $t \\in {\\bf R}$, define the entire function $$ H_t(x) := \\int_0^\\infty e^{tu^2} \\Phi(u) \\cos(xu)\\ du$$ where $\\Phi$ is the super-exponentially decaying function $$ \\Phi(u) := \\sum_{n=1}^\\infty (2\\pi^2 n^4 e^{9u} - 3\\pi n^2 e^{5u} ) \\exp(-\\pi n^2 e^{4u} ).$$ Newman showed that there exists a finite constant $\\Lambda$ (the \\emph{de Bruijn-Newman constant}) such that the zeroes of $H_t$ are all real precisely when $t \\geq \\Lambda$. The Riemann hypothesis is the equivalent to the assertion $\\Lambda \\leq 0$, and Newman conjectured the complementary bound $\\Lambda \\geq 0$.\n  In this paper w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05914","kind":"arxiv","version":5},"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/1801.05914/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":"1801.05914","created_at":"2026-07-05T02:54:48.165207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05914v5","created_at":"2026-07-05T02:54:48.165207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05914","created_at":"2026-07-05T02:54:48.165207+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMVJ55NJDMAC","created_at":"2026-07-05T02:54:48.165207+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMVJ55NJDMACZTMY","created_at":"2026-07-05T02:54:48.165207+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMVJ55NJ","created_at":"2026-07-05T02:54:48.165207+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/SMVJ55NJDMACZTMYIA34JX4TJZ","json":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ.json","graph_json":"https://pith.science/api/pith-number/SMVJ55NJDMACZTMYIA34JX4TJZ/graph.json","events_json":"https://pith.science/api/pith-number/SMVJ55NJDMACZTMYIA34JX4TJZ/events.json","paper":"https://pith.science/paper/SMVJ55NJ"},"agent_actions":{"view_html":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ","download_json":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ.json","view_paper":"https://pith.science/paper/SMVJ55NJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05914&json=true","fetch_graph":"https://pith.science/api/pith-number/SMVJ55NJDMACZTMYIA34JX4TJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SMVJ55NJDMACZTMYIA34JX4TJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ/action/storage_attestation","attest_author":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ/action/author_attestation","sign_citation":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ/action/citation_signature","submit_replication":"https://pith.science/pith/SMVJ55NJDMACZTMYIA34JX4TJZ/action/replication_record"}},"created_at":"2026-07-05T02:54:48.165207+00:00","updated_at":"2026-07-05T02:54:48.165207+00:00"}