analytic-number-theory

Investigates deterministic prime-gap interiors using the Divisor Normalization Identity (DNI). Establishes the Gap Winner Rule (GWR) the raw-Z maximizer is always the leftmost min-d(n) carrier. Validates the No-Later-Simpler-Composite Theorem with zero violations through 10^18. Documents hierarchical first-arrival laws and square-phase terminal.

Repository for the FermulerPy core package. Fermulerpy is useful for problems related to various fields of Number Theory.

Analytic combinatorics and dynamical systems

A Lean 4 formalization of the ternary (weak) Goldbach theorem, with an explicit audited finite and computational trust boundary.

slides accompanying the blog and YouTube channel

Analytic number theory club notes and experiments

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.

This repository contains a modular Python toolkit for studying the Riemann-Zeta function on the critical line and certifying its non-trivial zeros.

Route C of 3: RH via growth contradiction on X₀(143) g=13. Littlewood 1924 Ω: |ζ(1/2+it)|=Ω(exp(c log t/log log t)) contradicts |ζ|≤C(log t)² → Ingham Deuring-Heilbronn c1=0.209>0.2 β>0.9 closed at p5 → S₄={2,3,19,191} C=11.422>2√13 → GRH → H₄ 12/11 → RH. Lean 4.12 0 sorry. Companion to Route A & B.

Code relating to the Bateman-Horn Conjecture

Reproducible proofs for P vs NP, Yang-Mills Mass Gap, and Riemann Hypothesis using parameter-free Jabri Identity Zₜ=1. Zero fitted parameters. Python code, data, and Zenodo DOI included. Author: Abdulla Al-Jabri.

Nine-paper series introducing Constitutional Forcing — a mechanism by which algebraic structure uniquely determines governing constants across prime arithmetic, information theory, and fluid dynamics. θₖ = (2ᵏ − k)/2ᵏ. Khayyam Wakil, ARC Institute of Knowware, 2026.

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

Backward parabolic positivity barriers for the Xi flow, with symbolic and numeric checks supporting a proof of the Riemann Hypothesis.

Closed-form nth-prime estimator built on invariant-normalization logic, with deterministic refinement and exact benchmarks across a contract grid spanning n = 10^2 to 10^24.

A constructive and AI-assisted approach to the Riemann Hypothesis, focusing on structured classification and critical line constraints.

Audited fixed-shift Mobius and OSTT research package with Lean formalization.

Machine-checked (Lean) conditional reduction of the Riemann Hypothesis to explicit analytic assumptions (A, B, C) with reproducible certificates.

From a multiplication table to Riemann's zeros — a code-verified, bilingual (EN/TR) re-derivation of three centuries of number theory, with its refuted hypotheses kept.

🔍 Certify and explore the first 1,000 nontrivial zeros of the Riemann zeta function with a reliable, reproducible dataset for research and analysis.