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Entertainment / iPhone
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Columbus Labs
Built in the lab.
Shipped to the world.
Independent Software and Research Company
01 / On the App Store
02 apps
Apps you can download today.
QuotaKit
Productivity / iPhone + Mac
Costs at a glance
02 / Research
02 completed
Original mathematics, formally verified.
Enumerative combinatorics
Generalized stack permutations
Algebraic enumeration of the permutations a generalized (r,s)-stack can produce, with the headline theorem formalized in Lean.
Completed October 2026 · 4 papers · Verified in Lean
Dynamical algebraic combinatorics
Sharp exceptional density for interval-closed rowmotion
The exact leading rate at which rowmotion on interval-closed sets misses its generic period, proved for every fixed width and verified in Lean.
Completed October 2026 · 1 paper · Verified in Lean
03 / Coming soon
In development
In the lab now.
American Ambition
Simulation / Desktop Game
Hegemon
Strategy / iOS Game
Coming soon
Studio Head
Simulation / iOS Game
Coming soon
PlainSky
Weather / iPhone
Coming soonTap anything in development and we’ll email you when it launches.
04 / About
An independent research and software company.
Columbus Labs builds and runs its own apps and games, and publishes original research in mathematics with papers, code, and formal proofs anyone can check.