A Fresh Thermodynamic Lens on the Collatz Conjecture: The Collatz conjecture remains one of mathematics’ most deceptively simple unsolved problems: start with any positive integer, repeatedly apply “divide by 2 if even, or 3n+1 if odd,” and you’ll e...

White Paper1 The Musical Fingerprint of the Collatz Conjecture: Listening for the 4-2-1 Loop. Mathematics is full of simple puzzles, but none are as notorious as the Collatz Conjecture. Pick a number: if it’s even, halve it; if odd, triple it and a...

White Paper:1 https://jmullings.github.io/TheAnalystsProblem/HPHCERTIFICATION.html We present the third instalment of a systematic operator-theoretic programme toward the Riemann Hypothesis. Building on prior works establishing an algebraic singula...

Euler–Maclaurin Control: In this volume, we formalize one of the most delicate bridges in analytic number theory: the transition from discrete arithmetic sums to continuous analytic structure. The Euler–Maclaurin framework is deployed not as a class...

Presenting "The Analyst's Problem: Hilbert Operator"... My paper develops a functional-analytic framework for encoding smoothed Dirichlet energy associated with the Riemann zeta function into a single compact, self-adjoint operator on a separable Hi...

AI Slop or Not? Certifying the Sech⁴ Kernel Against Bochner's and Mercer's Theorems I posted three equations to social media with one question underneath: does kH perfectly satisfy Bochner's and Mercer's theorems? Half the responses assumed it was A...

Welcome to Volume VI of The Analyst’s Problem. In this interactive 3D demonstration we bring together three deep mathematical threads: The Large Sieve – the fundamental inequality that bounds Dirichlet polynomials and underpins modern analytic numbe...

https://jmullings.github.io/riemann-hypothesis-singularity-proof/RHBDNEQUIV.html...

Dirichlet Polynomial Control & ARC Reasoning Engine for AGI! In Volumes I–IV, The Analyst’s Problem built a mathematical engine around Dirichlet polynomials, Toeplitz energy, and a spectral “bridge” inspired by the Riemann Hypothesis. Volume V takes...

The mathematics are proven. The engine is built. Now, you can run it yourself. This is the official application for The Analyst's Problem: Volume IV. It's not just a simulation; it's a live, physical encoding of the true architecture. This engine dy...

Welcome to Volume III of The Analyst's Problem: Diagonal Dominance. In this video, we dive deep into the spectral defence simulation I've built to demonstrate how advanced mathematical concepts can entirely replace traditional video game mechanics. ...

RHPRIMESDUALITY1 1: https://jmullings.github.io/riemann-hypothesis-singularity-proof/RHPRIMESDUALITY.html Build your own Mathematical Unification: PT ≡ ZT ≡ QT Using exact Fourier-pair Gaussian kernels, the arithmetic sum of primes T is strictl...

The Riemann Hypothesis has stood unsolved for over 160 years. One of the reasons it has been so resistant is that the mathematical space it lives in is inherently unstable — it bends, dips below zero, and breaks the matrix structures that would other...

The Riemann Hypothesis has stood unsolved for over 160 years — not because mathematicians haven't tried, but because the problem sits inside an ocean of chaos: infinite series, complex zeros, and analytic interference that obscures any clear path for...

Dive into the deep mathematics of the Riemann Hypothesis with this interactive 3D visualization of the critical line! In this video, we explore the de Bruijn–Newman - MKM Equivalence Operator, bridging the gap between classical analytic number theo...

"The primes are the zeros." What if you could generate the exact distribution of prime numbers using nothing but the infinite spectrum of Riemann zeros? In this video, we visualize one of the deepest mysteries in mathematics: the exact spectral du...

We've all seen it! The post in the early hours of the morning! I've done this, I've found that - “I solved the Riemann Hypothesis!” You take a quick peek! Another one. Another late-night manifesto. Another graph that looks convincing. You’ve been...

What does it mean for something in this world to be “real”? Do zeros in general really exist, or are they artefacts of how we choose to look at a number, functions or the absence of a set? Does the “critical line” in the Riemann Hypothesis even exist...

Just Browsing: https://jmullings.github.io/WhatsThePoint/ThreePoints.html1 A true Mathematician: https://github.com/jmullings/WhatsThePoint/blob/main/ThreePoints.py2 Want to expand your perspective - then read-on: It could be argued, We define an ...

A Slice of Pi: Transcendental Indexing The quest to compute Pi has long been the Mount Everest of computational mathematics. For decades, the approach was straightforward: calculate digits sequentially, store them on massive hard drives, and pray t...