Research Papers
Peer-reviewed publications and preprints by Kerym Makraini on noncommutative algebra, the Riemann Hypothesis, spectral geometry, and quantum computing.
UNED National University of Distance Education, Madrid
AGE Quantum Gates Engine S.L., Melilla, Spain
Peer-Reviewed Publication
Emergent Lorentzian Spacetime and Gauge Dynamics from Twistorial Spectral Data
By Kerym Makraini
We introduce the Twistorial Spectral Quantum Vacuum Theory (TSQVT), a Lorentzian background-independent framework where spacetime and gauge fields emerge from twistorial spectral data on a Krein space. A spectral density ρ acts as order parameter: its condensed regime generates the conformal metric without prior geometric input.
Riemann Hypothesis Papers
View all →Spectral Properties of the Truncated Weil Operator & Numerical Verification of Weil Positivity
We study the truncated Weil operator A_Λ on L²([-log Λ, log Λ]), following Connes's programme for the Riemann Hypothesis. We establish spectral properties and provide numerical verification of Weil positivity conditions.
Spectral Detection of Automorphic & Arithmetic Zeros: Mayer–Ruelle Verification, Eisenstein Scattering, & Negative Diagnostics
Our methodological principle is that an operator construction for zeros of L-functions should be accepted only when it is anchored to a rigid mathematical identity—a theorem, not a numerical coincidence.
Spectral Persistence and Kreĭin Rigidity in the Weil–Connes Programme
We develop a conditional proof architecture for the Riemann Hypothesis within the Weil–Connes programme, structured around seven verifiable hypotheses (H1–H7) and five supporting lemmas (A–E). We introduce a trace–energy identity rendering Weil positivity structurally inevitable.
Recent Preprints
Spectral Properties of the Truncated Weil Operator & Numerical Verification of Weil Positivity
We study the truncated Weil operator A_Λ on L²([-log Λ, log Λ]), following Connes's programme for the Riemann Hypothesis. We establish spectral properties and provide numerical verification of Weil positivity conditions.
Spectral Detection of Automorphic & Arithmetic Zeros: Mayer–Ruelle Verification, Eisenstein Scattering, & Negative Diagnostics
Our methodological principle is that an operator construction for zeros of L-functions should be accepted only when it is anchored to a rigid mathematical identity—a theorem, not a numerical coincidence.
Spectral Persistence and Kreĭin Rigidity in the Weil–Connes Programme
We develop a conditional proof architecture for the Riemann Hypothesis within the Weil–Connes programme, structured around seven verifiable hypotheses (H1–H7) and five supporting lemmas (A–E). We introduce a trace–energy identity rendering Weil positivity structurally inevitable.
Geometric Transport and Trivialization of the Ground-State Bundle in the Weil-Connes Programme
We introduce a geometric framework for the Weil-Connes programme that addresses the critical hypotheses H3 (global simplicity of the minimal eigenvalue) and H7 (identification of the Mellin limit with Riemann's Xi function). The central object is the transport integral I(Λ), measuring cumulative distortion of the ground-state bundle.
Three Fermion Generations from Spectral Geometry: Dynamical, Algebraic, and Vacuum Constraints
We show that the number of fermion generations is constrained by spectral–geometric principles and satisfies the strict, model–independent bound N_gen ≤ 3. The KO–dimension 6 finite algebra A_F = C⊕H⊕M₃(C) admits exactly three minimal central idempotents.
Spectral Geometry of the Standard Model Algebra: Trace Structures and Gauge Unification
We present a complete derivation of the gauge unification condition sin²θ_W = 3/8 within the spectral geometry framework. Working with the finite algebra A_F = C⊕H⊕M₃(C), we compute trace invariants controlling spectral coefficients.
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