A BEAT FROM THE POST-DOUBLING LAW
Rule 30's edge has a spectrum: bit b repeats with period 2^p(b), and where p climbs by one the bit is a doubling bit. Strike on every doubling bit and you have a bar that, by the theorem, can never strike three times in a row.
Write p(b) for the exponent of bit b's period and δ(b) = [p(b) > p(b−1)] for a doubling. The post-doubling law (Lars Rocha, 2026-08-25): if b+1 is a doubling bit then δ(b+2) = s(b), the period-weight parity of column b; and a doubling column has even weight, so two doublings in a row force the third to be silent. The positions of the strikes are the sequence A094604; the theorem says it holds no three consecutive integers. The XOR driver's spectrum doubles only at powers of two, so its voice is the rim on 1, 2, 4, 8, 16, 32. The hat follows the rain bit of the tri_xor almanac, a clock with period 512.
Never Three · by Lars Rocha · the bar is SIClocks.rhythm from clocks.js; the theorem is in cards/clocks.md.