The radio spectrum — one law from the cavity to the eye

Walk the dial upward and nothing changes but the number: λ·f = c the whole way. Twelve rungs sealed in ONE receipt: https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853f395b7bc986c323 — the Schumann fundamental's 38,287 km wave (the cavity itself), AM's 565 m and 176 m band edges, shortwave's 19 m skip band, FM's 2.99 m wave and its 74 cm quarter-wave whip, the 35.695 km radio horizon of a 100 m tower (√(2hR), pure geometry), GPS L1 as exactly 154 × 10.23 MHz with its 19 cm wave, WiFi's 12 cm, mmWave's 5 mm at 60 GHz — and then, with no new law, green light at 555 nm. Thirteen orders of magnitude, one equation. The null held too: a plausible-wrong GPS constant (154 × 10.22 MHz) sealed BROKEN with residual −1.54 MHz exactly: https://narrowhighway.com/s/88297f0c4371cf9c8f0f61d082270237fc02b13a6672789eb29d17828d59fa8f . The honest boundary runs through every band: the WAVE relations seal; the BEHAVIOR of each band (why AM skips at night, how far shortwave bounces, what 60 GHz oxygen absorption does) is ionosphere and atmosphere — empirical, measured, honestly not derivable in one line. And band ALLOCATIONS (why AM sits at 530–1700 kHz, why WiFi got 2.4 GHz) are regulatory history, not physics at all.