Prime Lattice Lab

Hex-Depth Number System (HDNS) on the Allen Orbital Lattice. Click cells to place pistons; explore ζ readouts, presets (Euler, Gauss, primes, von Mangoldt, Möbius), and the Atom Lab (O + H → H₂O).

Hex-Depth Pistons + ζ Readouts

Click: +step · Alt+Click: −step · Shift+Click: clear cell
Basel (axis 0): 0.000000 π²/6≈1.644934
ζ(σ+iτ) avg (6 axes): 0.000000
Non-zero pistons: 0

Advanced Controls

τ max: step

ζ Spectrum Sparkline (|ζ(σ+iτ)| vs τ)

Atom Lab — place O and H, then Join → H₂O

Oxygen amplitude: (center + 6 neighbors)
q: r:
Hydrogen amplitude: (single cell)
q: r:
q: r:
Valuta L¹: 0.000 Valuta L²: 0.000
“Join” adds atom motifs into the lattice state. Clearing overlays doesn’t undo a join—use “Clear” on the main widget to reset the state.