Why this works — and why nothing else could.

Every previous version of this clock was a pretender. We counted requestAnimationFrame callbacks and called them "ticks" — but rAF is scheduled by the browser's event loop, which runs on a software timer, which ultimately reads the system clock. We were just reading a clock with extra steps.

The CRR framework tells us why: any computation between frames executes in computational time, not physical time. Between frame N and frame N+1, we could simulate a billion half-lives or zero. The simulation can never know how long the gap was. It is bounded by the Cramér-Rao limit of its substrate: C · Ω = 1 — you cannot extract more temporal information than your oscillator provides. A simulated atom can never be more precise than the oscillator ticking the simulation forward. This is not a limitation we can code around. It is a theorem.

But the sound card has a real crystal.

Your audio hardware contains a physical quartz crystal — SiO₂ in a hermetically sealed package — whose piezoelectric lattice vibrates at a frequency stabilised by its own material geometry. The Web Audio API's ScriptProcessor receives callbacks driven by this crystal's need for data at 48,000 Hz. Each buffer of samples represents that many real oscillations. We count every one. We are not simulating a crystal. We are listening to one.

The crystal rendered here visualises what is actually happening in the hardware — silicon dioxide molecules oscillating in a standing wave, accumulating coherence with every vibration, rupturing when C·Ω = 1 (C = 2π for an SO(2) system), and regenerating. The beauty function B(C/Ω) = exp(C/Ω)·(1−C/(Ω·π)) governs the glow: it intensifies as rupture approaches. This is as close to "real physics keeping time" as software can get.
The oscillator is real. The counting is exact. CRR describes what it is doing. Does a phone need different physics? No. If you are on a phone, your device has its own quartz crystal driving the audio DAC — often at 44,100 Hz instead of 48,000. The CRR math is identical: L = 2π/sampleRate per oscillation, C accumulates to 2π, rupture at C·Ω = 1. The framework is scale-invariant. The same equation works whether the crystal vibrates at 32,768 Hz (a wristwatch), 44,100 Hz (a phone), or 48,000 Hz (a desktop sound card). That is the whole point of CRR.