= Solution
For an experimental-noise interpretation of Nyquist's theorem, a <resistor> $R$ in thermal equilibrium at <temperature> $T$ has one-sided open-circuit voltage-noise <spectral density>
$$
\boxed{S_V(f)=4k_BTR},\qquad
\boxed{\langle v_n^2\rangle=4k_BTR\,\Delta f}
$$
in the classical range $hf\ll k_BT$, over an approximately rectangular <bandwidth> $\Delta f$. Across a matched load, half the open-circuit voltage appears, giving available noise <power> $k_BT\Delta f$. This is thermal agitation, present without a mean current, and is distinct from <shot noise>. A real readout weights the spectrum with its <transfer function>: $\langle v_{\rm out}^2\rangle=\int_0^\infty S_V(f)|H(f)|^2df$. Cooling, reduced <bandwidth> and suitable impedance/noise matching reduce measured noise; the <resistor>'s noise does not simply disappear in an ideal amplifier model.<Thermal Agitation of Electric Charge in Conductors by Harry Nyquist>[Printed p. 113, equations 4–8, thermal emf and bandwidth]{ref}
The bare name also has a sampling interpretation. The <Nyquist–Shannon sampling theorem> permits exact reconstruction of a bandlimited signal from sufficiently fast uniform samples. The practical condition is \b[$f_s>2f_{\max}$], with an <anti-aliasing filter> before sampling; otherwise distinct continuous <frequencies> produce identical samples. Ideal reconstruction uses shifted <sinc functions>. Critical-rate equality needs an appropriate signal class and can fail for unrestricted edge-frequency sinusoids with unknown <phase>. Sampling fast enough prevents <aliasing>, but does not remove <thermal noise>. This distinction covers the source's unspecified use of “Nyquist's theorem”.<What the Nyquist Criterion Means to Your Sampled Data System Design by Walt Kester>[MT-002, sampled spectra and anti-aliasing discussion]{ref}
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