Research Projects

Pick a question. We'll prove the answer.

Awkronos formalizes mathematics nobody has formalized before. Every theorem is machine-checked in Lean 4. Every result gets its own interactive page. You pick the question. We do the math.

Eight projects shipped so far, spanning gemstone optics, quantum photonics, behavioral finance, streaming algebra, curling physics, college counseling, longevity science, and combinatorial optimization. Each one started with a single question from a single person.

2,222
Theorems proved
8
Projects shipped
0
Unchecked axioms
49K
Lines of Lean 4

Shipped projects

Every project is live. Click to see the math.

Jill — Gemstone Optics

Why does a moissanite flash more fire than a diamond? What makes an opal shimmer? The physics of light inside gems, proved from Maxwell's equations to optimal cut geometry.
477 thm
0 sorry

Audrey — The Mathematics of Curling

Why does a curling stone curl? Hertz contact mechanics, ice friction, the cubic late-curl law. From the hack to the button, every force formalized.
490 thm
0 sorry

Kristi — Combinatorial Optimization

The Travelling Salesman Problem, Christofides' algorithm, matroid intersection, KKO decomposition. The hardest problems in computer science, made rigorous.
569 thm
18 sorry

Eisler — Quantum Photonics

Perovskite solar cells, directed superradiance, orientation optimization. Thirteen published papers from a UCLA lab, formalized for the first time.
292 thm
0 sorry

Becky — Behavioral Finance

Prospect theory, loss aversion, compound growth. The mathematics behind why we make the financial decisions we do.
195 thm
0 sorry

Robert — Streaming Algebra

Welford's algorithm, Chan-Golub-LeVeque merge, monoid laws. One-pass statistics over infinite streams, proved associative.
57 thm
0 sorry

Erika — College Counseling

Prerequisite chains, GPA thresholds, quarter-to-semester conversion. The admissions math for a community college nursing program, kernel-checked.
95 thm
0 sorry

Katie — Five Habits for a Long Good Life

Gompertz survival curves, hazard ratios from real clinical trials, adherence-weighted optimization. Which habits matter most, and in what order?
47 thm
0 sorry

How it works

1

You bring a question. It can be anything with a number in it. A physics problem, a financial model, a biological system, a game, a sport, a bet you want to settle. If there is math underneath, we can formalize it.

2

We scope and prove. We read the literature, write the Lean 4 theorems, and machine-check every claim. The Lean kernel trusts nothing. If the proof compiles, it is correct.

3

We build the page. An interactive scrollytelling site at yourname.awkronos.com that walks through the mathematics. Charts, animations, the full proof chain. Designed to make anyone lean forward.

4

You own it. The theorems, the code, the page. Full ownership. An Ed25519-signed certificate attests the proof hash. The page stays in the archive permanently.

Investment

Scoped individually based on the depth of the mathematics.

Personal question
$5K -- 15K
Published work formalization
$10K -- 25K
Lab-scale (multiple papers)
$25K -- 100K
Proprietary algorithm verification
$100K -- 300K
Grant or federal scope
$250K -- 1M

The first conversation is always free. We scope together, then you decide.

What's your question?

Every project in the archive started with someone saying "I've always wondered..." or "nobody has ever proved..." or "can you formalize this paper?" Tell us yours.