whatA sun, a Jupiter on a circular orbit, and a belt of massless asteroids integrated by a symplectic leapfrog -- with a live histogram of their semi-major axes below. This Jupiter is eight times overweight, to compress a hundred million years of celestial mechanics into minutes; everything else is honest gravity, and nothing removes an asteroid by fiat.

whyThe claim: the gaps carve themselves. Wherever an asteroid's period is a neat ratio of Jupiter's -- 3:1, 5:2, 7:3, 2:1 -- the same nudge arrives at the same phase, orbit after orbit, pumping eccentricity until the orbit crosses something: a brush with Jupiter, a Mars-crossing perihelion. The histogram empties at exactly the marked ratios, the gaps Daniel Kirkwood found in the real belt in 1866. Pour new asteroids into a gap with a click; the resonance rejects them again.

howKick-drift-kick leapfrog in heliocentric coordinates with the indirect term; removals only for close encounters (inside 0.07 of Jupiter), sun-grazers (perihelion under 0.18), and escapers. Gap depth is measured as band density over flank density around each resonance. One integer seeds the belt; the HUD reports every gap's depth live.