= Solution
The <superconducting gap function> is a momentum-dependent pairing amplitude $\Delta(\mathbf k)$, including a phase as well as a magnitude. A fully gapped isotropic state and a state with symmetry-required nodes can have different low-temperature responses. <Heat capacity>, thermal transport, <London penetration depth> and tunnelling spectra probe the low-energy <quasiparticle> spectrum. Activated behavior suggests a nonzero minimum gap; power laws can indicate nodes. For example, clean line nodes give a penetration-depth correction linear in temperature, whereas disorder can change the apparent power.
Such magnitude-sensitive probes require care: impurities, several bands, anisotropic full gaps and surface states can imitate or modify simple expectations. A node does not by itself establish a particular sign pattern, and the absence of a coherence peak is not a complete symmetry determination. The strongest identification combines momentum-sensitive spectra with <phase-sensitive superconducting gap experiments>.
For an illustrative $d_{x^2-y^2}$ state, $\Delta(\varphi)\propto\cos2\varphi$ changes sign under a $90^\circ$ rotation. A <Josephson junction> to a conventional s-wave reference can turn that sign into an intrinsic phase shift. In a corner <DC SQUID> with junctions on orthogonal crystal faces, one branch can acquire an extra $\pi$ relative to the other. For equal junctions and negligible loop inductance,
$$
I_c(\Phi)=2I_0\left|\cos\left(\frac{\pi\Phi}{\Phi_0}+\frac{\delta_{\rm int}}2\right)\right|.
$$
Changing $\delta_{\rm int}$ from zero to $\pi$ shifts the interference pattern by half a flux period. The 1993 YBCO–Pb experiment compared phase-coherent junction geometries and found evidence for that sign reversal, while explicitly discussing SQUID asymmetry and trapped vortices. Those controls matter: an arbitrary shifted trace is not by itself a proof of pairing symmetry.<Experimental determination of the superconducting pairing state in YBCO by D. A. Wollman and others>[1993, phase coherence of YBCO–Pb dc SQUIDs; abstract identifies asymmetry and vortex-trapping qualifications]{ref}
A <tricrystal half-flux experiment> arranges grain-boundary junctions so that a sign-changing order parameter produces an odd total $\pi$ shift around a ring. Fluxoid consistency then favors a half-integer flux state, with the detailed spontaneous flux depending on loop inductance and junction strengths. Choosing comparison geometries without that frustration and controlling trapped external flux separates the pairing-phase effect from ordinary flux trapping.<Pairing symmetry and flux quantization in a tricrystal superconducting ring by C. C. Tsuei and others>[1994 primary tricrystal-ring pairing-symmetry test]{ref}
The conclusion is strongest when the same candidate symmetry explains nodes, crystal-axis dependence and these phase-sensitive interference results. The phase-sensitive observation distinguishes a sign-changing gap from a merely anisotropic positive gap; no single temperature power law supplies that distinction.
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