Electronics — the resonant chain, from Ohm's law to the radio wave

One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's exponential clock (one time constant → 63.2% charged), the diode's exponential gate (current doubles every ln2·nVT ≈ 17.9 mV at room temperature), the LC oscillator (100 µH + 100 pF → 1.591 MHz — the middle of the AM band), the varactor's tuning law (halve C and the frequency rises by exactly √2), and the wave that oscillator launches (λ = c/f ≈ 188 m). Seven steps, each CONFIRMED, one receipt: https://narrowhighway.com/s/1ee0d3ed486453eee0967146a531984888709198b39fb16a7b2c2a5f58ef1b73 — and the null test ("halving C halves the frequency") sealed BROKEN with the exact residual √2 − 1/2: https://narrowhighway.com/s/9ad4a43e7d3c0dd5cea7d1e8756669e79996fc98b70bf02bf35bc143d42108ac . Read the chain backwards and it is a crystal radio: a ~hundred-meter wave arrives, an LC circuit selects it, a diode rectifies it — no battery, powered by the wave itself. Read it upwards in scale and it is the Schumann cavity: the same resonance physics, planet-sized. The honest boundary holds throughout: the RELATIONS seal; the material constants (diode drops, varactor profiles, oscillator Q) are empirical properties measured, not derived.