= Solution
In weak-coupling <BCS theory>, a useful scale is
$$
\boxed{k_BT_c\simeq1.14\hbar\omega_D\exp\left[-\frac1{N(0)V_{\rm eff}}\right].}
$$
Here the <phonon> spectrum sets the attractive-interaction cutoff, $N(0)$ is the consistently defined Fermi-level <density of states> and $V_{\rm eff}$ the effective pairing attraction after repulsion is accounted for. Light hydrogen supports high vibrational frequencies; strong <electron>–<phonon> coupling and favourable metallic <density of states> can raise $T_c$. Pressure changes bonding, phase stability, electronic structure and <phonon> frequencies. It is not simply an independent multiplier in this expression. In a real strongly coupled hydride, <Eliashberg theory> uses the full <spectral function> and a screened Coulomb pseudopotential; the elementary exponential is a mechanism guide rather than a controlled quantitative fit to $203\,\mathrm K$.
Measure a four-terminal resistance that falls below the instrumental bound, and test that a <magnetic field> suppresses the transition. Independently detect diamagnetic screening and, where feasible, field-cooled flux expulsion or an AC susceptibility signal with controlled cell background. A resistance drop alone can reflect contact changes or a filamentary path; a consistent magnetic response is important evidence for <superconductivity>. A reproducible isotope shift upon replacing hydrogen by deuterium tests the involvement of <phonon>[lattice motion], although it is not by itself proof of <superconductivity>.
Extreme-pressure samples are microscopic and enclosed in a diamond-anvil cell. Reliable separate electrical contacts, homogeneous pressure, pressure <calibration> during cooling, chemical stability and the tiny magnetic signal relative to the anvils and gasket are practical difficulties. Structural identification matters because a sulfur-rich hydrogen compound formed under pressure need not retain the starting stoichiometry.
\b[Historical correction:] the original primary report associates the $203\,\mathrm K$ transition with pressures near $155\,\mathrm{GPa}$, while roughly $90\,\mathrm{GPa}$ is the metallization scale, not that same transition point. The printed pairing of $203\,\mathrm K$ with $90\,\mathrm{GPa}$ should not be treated as an established measured pair. The statement about the highest conventional transition <temperature> is also a historical statement in this 2018 examination.<Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system by A. P. Drozdov and others>[Primary 2015 report: metallization near 90 GPa, high-temperature transition near 155 GPa, transport, magnetic and isotope evidence]{ref}
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