The Mathematical City Mini AI Labs
THE MATHEMATICAL CITY · MINI AI LABS
Six questions. One cycle.
Interactive laboratories by Nicholas Kouns exploring mathematical structure, invariance, dynamics, memory, measurement, and prediction.
OPEN THE UNIFIED LAUNCHER · EXPLORE THE MATHEMATICAL CITY
🔬 01 · SPECTRA — STRUCTURE
What structure is there?
Explore spectra, invariant kernels, projectors, and contraction. Follow the E47 construction from a 125-dimensional carrier to its selected 47-dimensional subspace.
Launch SPECTRA → · Methods & City page
🧬 02 · FOLD — INVARIANCE
What survives transformation?
Watch a modeled state ensemble contract toward a constrained structure. Explore the relationship between folding-inspired geometry, spectral selection, and invariance.
Launch Fold → · Methods & City page
🐦 03 · MURMURATION — DYNAMICS
How does structure move and reorganize?
Explore a moving swarm through its changing connections and topology. Follow how collective geometry produces loops, harmonic structure, and transitions over time.
Launch Murmuration → · Methods & City page
🧠 04 · MNEMOSYNE — MEMORY
What did we know, and when did we know it?
Create and verify a cryptographic seal for a forecast. Explore the accompanying record of predictions, reveals, and corrections.
Open Mnemosyne Seal Utility → · Forecast program & City page
🌀 05 · DENSITY — MEASUREMENT
What can we reconstruct from incomplete observation?
Reconstruct simulated fields from limited angular views. Compare the reference target, iterative reconstruction, filtering, error maps, and interactive 3D slices.
Launch Density → · Methods & City page
🛰️ 06 · HORIZON — PREDICTION
What invariant comes next?
Bring the laboratory roles together. Forecast when a topological feature will appear or disappear in a synthetic trajectory, commit the prediction, and compare it with the revealed outcome.
Launch Horizon → · Methods & City page
STRUCTURE → INVARIANCE → DYNAMICS → MEMORY → MEASUREMENT → PREDICTION → STRUCTURE
Each City page connects its laboratory to methods, source material, validation records, and current research scope.
