A rational chamber inside the 1:2:3 sphere frame.
Aim into the centered cube and read the selected point in four registers: raw rational address, reduced divisor band, metric sphere shell, and six-cardinal direction.
Controls
Direction presets
Manual ray direction
Classical presets
View
Rational cube + metric frame
Faint line is the exact aimed ray. Solid point is the snapped rational address.
SNAP
counter...
points...
bands...
snap_error...
Method and limitations
What is native here
- GCD shell identity q = n / gcd(n,kx,ky,kz).
- Jordan shell count J₃(q) and divisor-band conservation.
- The ideal cube's 1:2:3 squared-radius sphere frame.
- Ray target, snapped address, and snap error.
What stays separated
- Arithmetic bands are not metric shells.
- Rendered positions depend on boundary convention.
- The six-cardinal projection is a lossy direction summary.
- This v1 does not include density, perfect-number, or Picone overlays.
Coordinate note
- Coordinate origin is additive 0.
- J₃(1)=1 is the multiplicative empty-product floor.
- These are different operation rooms: where the point sits vs how many points a band contains.