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

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.

Code relating to the Bateman-Horn Conjecture

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.

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

nfield: A structural analysis engine for the collision invariant of the digit function, connecting long division to L-function special values. Source code, publications, and companion research notes.

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

The Artin Holomorphy Conjecture via Artin L-function regularity persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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

The Generalized Riemann Hypothesis via L-function zero persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Twin Prime Conjecture via prime-gap persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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.

Infinitely many n^2 + 1 primes via polynomial-prime persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Bateman-Horn Conjecture via prime-pattern density persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Grand Riemann Hypothesis via Artin-automorphic zero persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.