Skip to content

The 3D lattice laboratory

lab-3d/ accompanies the preprint "AB-Cloud: A Universal Lattice Operating System for the Riemann Zeros".

What it is

A three-dimensional non-Hermitian Hofstadter Hamiltonian with topological vortex lines (instead of point vortices):

  • 36³ lattices, Payerls phases e^(2πiαy), 5000 embedded ζ zeros;
  • Python implementation (with Julia bridge), requirements.txt included;
  • data/ — embedded zeros; outputs/ — complete generated reports (July 2026 runs: 3d_bridge, full_verification, 3d_advanced, deep_zeros); preprint/ — the preprint source and PDF.

Running

cd lab-3d
pip install -r requirements.txt
make run          # see lab-3d/Makefile for all targets

See lab-3d/README.md for the full description of the model and the verification tasks.