Detuning, Readout, and Audit

Detuning Window Accepts a Nearby Mode

A detuning window test accepts a candidate mode when its frequency square falls within a fixed tolerance of the target. The candidate frequency square 1/4 is a distance 3/4 from the target 1, which is within tolerance 1, so the accepted bit is 1 exactly for the stated ideal frequency-square model; real devices have calibration drift, linewidth, noise, fabrication spread, loss, thermal photons, crosstalk, and readout uncertainty.

A detuning decision is an exact window test over checked mode squares. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A nearby candidate stays inside the window

The target frequency square is 1 and the candidate is 1/4 per square second.

∣1−14∣=34\left|1-\tfrac{1}{4}\right|=\tfrac{3}{4}
Nearby detuningThe candidate cites its own checked mode source.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2inductance=2 Hcapacitance=2 FlcProduct=4 s^2omegaSquared=1/4 1/s^2targetOmegaSquared=1 1/s^2candidateOmegaSquared=1/4 1/s^2tolerance=1 1/s^2distance=3/4 1/s^2acceptedBit=1 bit

Inside the tolerance gives accepted bit one

The distance is 3/4, which is within tolerance 1, so the accepted bit is 1.

34≤1⇒accepted=1\tfrac{3}{4}\le 1\Rightarrow accepted=1
Accepted detuningEquality would also accept by the declared rule.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2inductance=2 Hcapacitance=2 FlcProduct=4 s^2omegaSquared=1/4 1/s^2targetOmegaSquared=1 1/s^2candidateOmegaSquared=1/4 1/s^2tolerance=1 1/s^2distance=3/4 1/s^2acceptedBit=1 bit