A Complete and Unconditional Spectral-determinantal Proof of the Riemann Hypothesis: the Krein-hadamard-mosco Route
Year: 2025
Type: article
Abstract: Thispaperpresents acompleteandunconditional proof of theRiemannHypothesis, establishedthroughtheconvergenceofthreeclassicalapproaches: (I)aspectralproofbased ontheconstructionofaself-adjointSchrödingeroperatorHwhosespectrumcorresponds bijectivelytothezerosof ζ(s); (II)analgebraicproofutilizingDirichlet formtheoryand theKrein-Birmanformalismto identifythespectraldeterminantofHwiththecomplete functionξ(s); and(III)afractalproof thatregularizesthepotentialoveraprimalCantor set, guaranteeingthenecessaryanalytical estimatesunconditionally. The spectrum-zeros bijection,themainobstacleinpreviousattempts, isestablishedrigorouslythroughdeterminantal identityandvalidatedbyaquantuminterpretationviatheGutzwillertraceformula. Theproof is completedbyacontinuous interpolation(AppendixN)betweenthe fractal framework(wheretheproof isunconditional)andtheclassical real line,usingMoscoconvergenceofquadraticforms.Numericalverificationconfirmsthetheoreticalpredictionswith relativeerrorsoforder10−9andvalidatesGUEstatisticswithcorrelation>0.998.
Author: Rodrigues, Vinicius Ramos
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083673494
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