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.

Local Lean formalization permanently registered in Palomar (PALOMAR-2026-08-29-000004). Two-certificate trace-energy deduction for the 67.3316977142% simple critical-line zero research-draft candidate.

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

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.

Analytic number theory club notes and experiments

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

Evidence-first multi-agent research graph for advancing the verifiable frontier around the Riemann Hypothesis

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

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

A Topological Proof by Contradiction of Non-Trivial Zeros via Spectral Rigidity in Lean 4 & Comparator.

Code relating to the Bateman-Horn Conjecture

Research profile and selected work in analytic number theory

Route C of 4 — Act III Growth. RH via contradiction: |ζ|≤C(log t)² false via Littlewood 1924 Ω exp(c√(log t/log log t)). Zero repulsion 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. Opera Numerorum with A, B, D 35 brothers desert.

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.

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

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.