SUNDRIFTサンドリフト
One night.
Drift until dawn.
A browser driving game through a cherry-blossom mountain pass and the neon streets of Tokyo. Bank a drift, move the clock, chase the sunrise.
Download the source ↓INDEPENDENT WORK / MATH · CODE · MOTION
LIAM
KRUER.
Proofs. Play.
Possibilities.
Mathematical work, games, and things
built along the way. Welcome to my corner.
MOVE TO LIGHT · DRAG TO ROTATE
01 / GAMES & INTERACTIVE WORLDS
Game source ↓After hours.
Full throttle.
A growing shelf of games and interactive worlds.
First stop: the streets of Sundrift.
DESIGNED & ITERATED WITH AI-ASSISTED TOOLS
Geometry, textures, and sound generated in code. Built with Claude Code for the 404 game jam.
THE GAME SHELF [01]
One world so far. Room for the next.
02 / PAPERS & FORMALIZATIONS
A WORKING COLLECTION / 2026The math
archive.
Twelve manuscripts. Questions in geometry, combinatorics, and number theory. Browse a first page, read the work here, or take the files with you.
Showing all 12 papers
PAPER / 01Discrete geometry
Unit distances in convex polygons
How many equal-length connections can a convex polygon contain? A collaborative manuscript studies constructions for Erdős problems 96 and 97, with a companion Lean 4 formalization.
With Jensen Kohlmeyer & Liam Price
PAPER / 02Additive number theory
Non-unique sums, parts I and II
When integers are written as sums of two elements of a set, how often is the representation unique? This draft studies a quantitative bound addressing both parts of the problem.
With Jensen Kohlmeyer
PAPER / 03Discrete geometry
Unit distances in convex position
A separate draft exploring convex point sets with many pairs exactly one unit apart, and a proposed construction challenging a linear upper bound.
With Jensen Kohlmeyer
PAPER / 04Graph theory
Counterexample via arc graphs
An arc-graph construction explores the tension between high chromatic number and restricted subgraphs. The draft proposes a counterexample using triangle-free graphs.
With Jensen Kohlmeyer
PAPER / 05Combinatorics
Permutations avoiding four-term progressions
Can all natural numbers be reordered without creating an increasing or decreasing four-term arithmetic progression? This draft develops a proposed permutation through finite extensions.
With Jensen Kohlmeyer
PAPER / 06Extremal set theory
Arithmetic-intersection families
How large can a family of sets be if every pair intersects in an arithmetic progression? A counting argument investigates the strong variant and its linear error term.
With Jensen Kohlmeyer
PAPER / 07Additive number theory
Two floor-doubling sequences, part I
A study of sums of distinct terms from two floor-doubling sequences. The draft uses binary carries and symbolic systems to investigate the multiplier-two case.
With Jensen Kohlmeyer
PAPER / 08Graph theory
Critical graphs
Graphs that need every vertex, yet resist the removal of edges. A proposed four-color construction studies how vertex-criticality and edge-deletion resilience can coexist.
With Jensen Kohlmeyer
PAPER / 09Additive combinatorics
Lipschitz graphs and progressions
A draft construction of a Lipschitz integer-valued function whose graph avoids nontrivial three-term arithmetic progressions, together with a computational certificate and Lean source.
With Jensen Kohlmeyer
PAPER / 10Coding theory
Binary linear covering codes
How efficiently can binary linear codes cover all nearby vectors? This manuscript investigates covering radius two and a proposed sequence of codes with density approaching one.
With Jensen Kohlmeyer
PAPER / 11Number theory
Quadratic-containment counterexample
A proposed counterexample built from prime squares tests exact containment in a quadratic image. The draft specifically treats exact containment, rather than versions allowing finitely many exceptions.
With Jensen Kohlmeyer
PAPER / 12Additive combinatorics
Binary sumsets at density one half
What structure appears when a set occupies nearly half of a binary vector space? This draft investigates subspaces inside its sumset and quantitative bounds on their codimension.
With Jensen Kohlmeyer
No manuscripts match this search.
From the working notebook. Draft labels reflect the original records; these manuscripts have not been independently peer reviewed. Original PDFs, credits, and available Lean sources are preserved.
A LITTLE EXPERIMENT
Try the
3n + 1 problem.
Pick a positive integer. If it’s even, halve it. If it’s odd, multiply by three and add one. Keep going.
Does every starting number reach 1?
That’s still an open question.
TRY
THE JOURNEY TO 1n₀ = 27
111STEPS TO 1
9,232HIGHEST VALUE
1FINAL VALUE
Logarithmic vertical scale · An interactive illustration, not a proof.
03 / NOTES FROM THE WORKBENCH
THE MESSY, INTERESTING MIDDLEUnder
the hood.
The decisions behind Sundrift: how a world is built, how a car feels, and what changes between iterations.
Design. Build. Refine.
From a model to a working idea.
CSWACertified SOLIDWORKS Associate ↗CSWPCertified SOLIDWORKS Professional ↗Dassault Systèmes · May 2026
Read the build notes here, or download a copy to keep.
04 / ON YOUTUBE
Visit my channel ↗A different
lens.
Cars, physics, and the stories behind the machines.
A few things I’ve put on camera.
05 / A LITTLE ABOUT ME
Always
in progress.
I’m Liam. I work across code, mathematics, and creative projects — from making a mathematical argument precise to designing a world you can play in.
I’m interested in how things behave, how they’re made, and how to make them better. This is a collection of the work and the thinking behind it.
Also studying engineering at Purdue University.
More on LinkedIn ↗GOOD IDEAS START WITH A CONVERSATION