One Beat, Many Scales: A First-Principles Derivation of the φ^9 Macro-Clock in Recognition Science

Recognition Science (RS) asserts that all physical change is tallied by a universal recognition cost and an eight-tick ledger-neutral cycle whose base tick is tau_0 = h/E_coh = 7.33 × 10^-15 s. We show that without adding parameters these axioms force a hierarchy of larger "heartbeats" whose periods scale by phi^9 ≈ 34. The resulting macro-clock predicts a ladder of concrete rhythms—0.7 s, 90 min, 11 yr, 92 yr, ~3 k yr, . . . —each an integer multiple of the eight-tick packet. We tabulate these periods, derive the linear cost reset that makes the factor unique, and show that well-known peaks in solar, geomagnetic, and human physiological data coincide with four rungs of the ladder. These empirical hints do not yet prove universal synchrony, but they justify targeted coherence tests now feasible with public datasets. The derivation is falsifiable: if any rung is absent (p > 0.01) in a mature dataset or if adjacent rungs fail to obey the ratio, the macro-clock must be rejected while RS's micro-engine survives.