Rational Address Showpiece
two classical readings, one cube

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.