The planets have nice harmonics, so that rather than planet 1 and planet 2 having some irrational ratio (planet 1 goes around every 2.64782362 times for planet 2) it's round fraction like 1/2. When you string the whole thing, the lowest common multiple of revolutions is 54, so that only every 54 planet-1-years, realignment returns.

The researchers hypothesize that this is sufficiently improbable to point toward an embodied intelligence as the cause.