{"paper":{"title":"RH-Conditional Positivity in a Theta-Kernel Langevin Model","arxiv_id":"2611.04359","primary_cat":"math.PR","submitted_at":"2026-11-03T05:41:31+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":0.55,"id":"s0","own":false,"role":"background","text":"A classical Brownian-bridge representation of Riemann's xi function defines an even, rapidly confining probability density and a reversible Langevin model.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.26,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.32,"result":0.0,"background":0.55,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.0}},{"i":1,"p":0.96,"id":"s1","own":true,"role":"contribution","text":"Our principal physical observable is the transient variance after a quadratic-potential quench; we also analyze a tilted bridge-range response and a sixth-order cumulant gap.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.9,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.96,"interpretation":0.0}},{"i":2,"p":0.84,"id":"s2","own":true,"role":"result","text":"For a specified passive harmonic trap with bounded delayed residual feedback, we derive a non-vacuous finite-time variance-increase bound under explicit calibration and sampling assumptions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.9,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.84,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.13,"interpretation":0.0}},{"i":3,"p":0.77,"id":"s3","own":true,"role":"result","text":"An elementary global curvature estimate and de Bruijn's strip-contraction theorem give a direct proof of a strict susceptibility bound for every nonnegative quadratic tilt, without assuming the Riemann hypothesis.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.2,"quantitative":true,"quantitative_p":0.89,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.77,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.18,"interpretation":0.0}},{"i":4,"p":0.45,"id":"s4","own":false,"role":"background","text":"The inequality itself is a classical GHS consequence, valid more generally for every real quadratic tilt.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.15,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.25,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.26,"background":0.45,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.28}},{"i":5,"p":0.76,"id":"s5","own":true,"role":"result","text":"Reversibility then gives explicit finite-time response and deterministic-control action bounds (not thermodynamic energy).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.68,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.42,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.76,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.17}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"result","text":"The same curvature estimate gives monotone variance relaxation after an outward quadratic quench, with an exponential deficit bound.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.83,"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":7,"p":0.49,"id":"s7","own":true,"role":"interpretation","text":"At the undeformed density, all alternating zero-field cumulant signs and the displayed low-order cumulant gap are also unconditional; neither is an RH test.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.63,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.41,"background":0.0,"limitation":0.1,"future_work":0.0,"contribution":0.0,"interpretation":0.49}},{"i":8,"p":0.63,"id":"s8","own":false,"role":"result","text":"The genuinely stronger RH-conditional structure is a positive Stieltjes representation and positive semidefiniteness of divided-difference matrices of every size.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.49,"main_claim_p":0.43,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.63,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.15,"interpretation":0.21}},{"i":9,"p":0.48,"id":"s9","own":false,"role":"interpretation","text":"At the undeformed density that entire matrix hierarchy is equivalent to RH.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.3,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.44,"background":0.05,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.48}},{"i":10,"p":0.5,"id":"s10","own":true,"role":"limitation","text":"We separate these exact statements from finite-sample confidence bounds, numerical discretization evidence, and theoretical physical implementations.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.7,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.01,"background":0.0,"limitation":0.5,"future_work":0.0,"contribution":0.23,"interpretation":0.23}},{"i":11,"p":1.0,"id":"s11","own":true,"role":"limitation","text":"The work supplies neither a proof of RH nor a laboratory realization.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.66,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":1.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.62,"text":"The genuinely stronger RH-conditional structure is a positive Stieltjes representation and positive semidefiniteness of divided-difference matrices of every size.","location":"abstract s8","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":8804,"cost_usd_reported":0.0},"compiled_at":"2026-11-04","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.04,"states_limitation":0.97,"human_participants":0.01,"controlled_comparison":0.13,"randomized_assignment":0.02,"states_quantitative_result":0.75,"compares_with_prior_results":0.24,"mentions_code_or_data_availability":0.03},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.57,"text":"An elementary global curvature estimate and de Bruijn's strip-contraction theorem give a direct proof of a strict susceptibility bound for every nonnegative quadratic tilt, without assuming the Riemann hypothesis.","location":"abstract s3"}},"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":12,"sentences_in_abstract":12},"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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