alignment

Every positive integer falls into one of three tiers. The mirror bound from the nines complement forces everything with rough part past 7 below the golden line. The classification is unconditional.

Past the digit-partitioning boundary, the alignment splits into lanes. Different smooth factors choose different lanes, and the limit may not exist as a single number. But no prime past 3 reaches the golden threshold.

In base 10, exactly three primes produce total digit separation: 3, 7, and 11. Three different mechanisms, one shared condition, one universal formula.

A cubic equation has a root in (0,1) for every prime. The golden ratio's minimal polynomial divides it at exactly one. The remainder names the prime 3.