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

Analytic combinatorics and dynamical systems

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.

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.

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

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

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.

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

The Artin Holomorphy Conjecture via Artin L-function regularity 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.