{"paper":{"title":"A certified classical-strip comparison for the de Bruijn-Newman constant","arxiv_id":"2610.18214","primary_cat":"math.NT","submitted_at":"2026-10-13T11:46:18+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.69,"id":"s0","own":true,"role":"contribution","text":"We give a directed comparison beginning with the classical zero strip \\(\\lvert\\Ima z\\rvert\\le1\\) for the de Bruijn--Newman heat deformation.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.79,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.89,"role_probabilities":{"gap":0.0,"method":0.11,"result":0.0,"background":0.2,"limitation":0.0,"future_work":0.0,"contribution":0.69,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":true,"role":"result","text":"Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply \\[ \\Lambda\\le\\frac{148611789321711}{10^{15}} =0.148611789321711<0.148612.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.89,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"method","text":"\\] The construction uses Raymond's finite source data and 57 fixed translated kernels, independently checked by rational Bernstein certificates.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.67,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.95,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.42,"id":"s3","own":true,"role":"contribution","text":"An explicit finite Weyl estimate improves the positive first-head tail and its centred logarithmic moment.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.76,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.39,"result":0.19,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.42,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":true,"role":"method","text":"A centred cone transfer retains the original physical error allowances, exceptional debit and additive cone reserve, and charges the change in existing phase-surplus credits.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.53,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.96,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.01}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"method","text":"Directed tail enclosures are regenerated at 192 and 256 bits; a separate exact-rational auditor accepts all 19,023 comparison steps.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.99,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":6,"p":0.98,"id":"s6","own":true,"role":"result","text":"The controlled decrease from the complete two-source comparison is \\(0.000021760452379\\).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":7,"p":0.76,"id":"s7","own":true,"role":"contribution","text":"We also prove a compatible matched logarithmic tail transfer and identify the finite requirements for stronger exponent pairs.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.14,"background":0.0,"limitation":0.0,"future_work":0.1,"contribution":0.76,"interpretation":0.0}},{"i":8,"p":0.77,"id":"s8","own":true,"role":"result","text":"A supplementary section records Raymond's ceiling below \\(0.116398\\) under the distinct \\(7/8\\) zero-free hypothesis.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.58,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.77,"background":0.04,"limitation":0.02,"future_work":0.01,"contribution":0.16,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply \\[ \\Lambda\\le\\frac{148611789321711}{10^{15}} =0.148611789321711<0.148612.","location":"abstract s1","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":7043,"cost_usd_reported":0.0},"compiled_at":"2026-10-14","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.05,"states_limitation":0.34,"human_participants":0.01,"controlled_comparison":0.38,"randomized_assignment":0.01,"states_quantitative_result":0.98,"compares_with_prior_results":0.82,"mentions_code_or_data_availability":0.07},"evidential_basis":{"p":0.79,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.79,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.21}},"contribution_type":{"p":0.99,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.01,"theoretical_result":0.99,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.67,"text":"Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply \\[ \\Lambda\\le\\frac{148611789321711}{10^{15}} =0.148611789321711<0.148612.","location":"abstract s1"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":9,"sentences_in_abstract":9},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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