Prior Work
About the Author
I'm a software engineer and polymath, not an academic mathematician. These are self-published explorations — not peer-reviewed papers. They represent several years of off-and-on investigation into the Collatz conjecture, each building on the last. The proof framework on this site is the culmination of that journey.
I share them here for transparency: so you can see how the ideas developed, and judge the work on its merits.
Writings
The Collatz Conjecture, Pythagorean Triples, and the Riemann Hypothesis
Unveiling a Novel Connection Through Dropping Times (2024)
The starting point. Introduces dropping sets, the affine orbit structure, orbital oddity, and an unexpected connection between Collatz dynamics and Pythagorean triples. This is where the dropping time framework — used throughout the proof — was first developed.
The Geometric Collatz Correspondence (2023)
Develops the geometric side: stopping classes, stopping signatures, and the modular classification of orbits. The residue class hierarchy introduced here is what the countdown mechanism later exploits.
The Collatz Conjecture: A New Perspective on an Old Problem (2024)
Proportional Power Ratios and the Base-6 Discovery
A more accessible exploration, published on Medium. This is where I stumbled onto the base-6 structure: the Proportional Power Ratio function maps Collatz orbits onto a circle where they trace out a near-perfect irrational rotation. I didn't know it at the time, but this was independently confirmed by Shakibaei Asli (2026) as a formal near-conjugacy. The 44-step spoke pattern in polar plots turned out to be the convergent of .
How They Connect to This Site
| Writing | Key Idea | Role in the Proof |
|---|---|---|
| Paper 1 (Pythagorean Triples) | Affine orbit structure, dropping sets | Foundation: the piecewise-linear maps underlying bit destruction |
| Paper 2 (Geometric Correspondence) | Stopping classes, modular classification | Framework: the residue class hierarchy the countdowns traverse |
| Medium article (PPR / Base-6) | Near-conjugacy to rotation by | Geometry: why orbits equidistribute and can't systematically dodge drops |
| This site (2026) | Countdown hierarchy, finite propagation | The proof: carry propagation consumes bits faster than orbits generate them |
Key References by Others
- Shakibaei Asli, B. (2026). An explicit near-conjugacy between the Collatz map and a circle rotation. arXiv:2601.04289
- Chang, E. Y. (2026). A structural reduction of the Collatz conjecture to one-bit orbit mixing. arXiv:2603.25753
- Terras, R. (1976). A stopping time problem on the positive integers. Acta Arithmetica, 30(3), 241-252.
- Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi.