zeta-function

Riemann R(x) prime counting function approximation using complex Zeta zeroes

Certified first 1,000 nontrivial zeros of the Riemann zeta function using a dual-evaluator (mpmath ζ + η‐series) contour method with strict Krawczyk isolation and automatic refinement.

Official repo for "The Genesis of e from Modular Substrate Theory". Certifies exact algebraic identities linking e, ln 2, and ζ(0) = -1/2 with Lean 4 (0 sorries). Features a high-precision Python suite showing robust D₆ dihedral phase quantization over 10,000 non-trivial Riemann zeros with extreme statistical significance (p ≈ 10⁻⁸³).

Computational validation of the modular Z/6Z structure in Riemann zeros. Includes the Reconstruction Theorem, logarithmic spectroscopy (12.69x SNR), and Python code to replicate phase resonance.

This repository presents Version 2.5 of a formally complete, structurally reinforced, and type-theoretically encoded resolution of the Riemann Hypothesis (RH), formulated through Collapse Theory and the AK High-Dimensional Projection Structural Framework (AK-HDPST v12.5).

"Spectral Determinant of a Cutoff-Regularized Hamiltonian and the Riemann Zeta Function" - preprint

Research project exploring operator-theoretic approaches to the Riemann Hypothesis, combining spectral theory and computational analysis. Includes English (main) and Portuguese versions.

探索生成论、差异性的跨学科框架 A transdisciplinary framework exploring generative worldview

Computational and mathematical research archive and proof-engineering workspace for experimental approaches to the Riemann Hypothesis, Li-Keiper positivity, and related spectral/arithmetic structures.

Riemann Hypothesis Numerical Toolkit & REST API Services. Riemann-Siegel formula, zero finding, Turing verification, GUE random matrix analysis, prime analytics. Computational exploration of the greatest unsolved problem in mathematics.

Exact zero expansion and unconditional infinite oscillation for one fixed reflected packet in the semilocal Weil form

Fixed-packet Weil-kernel zero expansions, exact growth criteria, and unconditional infinite oscillation

Fixed-parameter Galerkin, relative trace, smoothed spectral, and certified interlacing results for semilocal zeta operators

Standalone paper and reproducibility package for smoothed positive zeta spectral kernels and a scalar RH criterion

Jabri_lab — Jabri's Laboratory for Computational Proofs A public repository where every file contains one small idea, one computation, one proof. No bloated notebooks. No hidden parameters. Just focused experiments that you can run, check, and falsify. Structure: - Zx_5.ipynb : Test the Jabri identity on the 5th zero of ζ(s) - Zx_28.ipy

Dual-channel coupled PDE system seeded by ζ(s). Emergent fold on the critical line. Zero imposed constants — the field derives everything.

Función Zeta de Riemann programado en c++

Unified constructive and non-constructive proof of the Riemann Hypothesis. Prime density, ζ-function symmetry, and A-type structure ensure full consistency. リーマン予想に対する構成的・非構成的な統合証明。素数密度・ゼータ関数対称性・A型構成により完全整合を実現。

Repo with plots for Complex Analysis Course. Riemman Zeta function example.

Exact bottom-cluster and Feshbach reduction for the semilocal Weil prolate-proxy bridge, with reproducible code and audits.