The Wiedemann-Franz law fixes the ratio of thermal to electrical conductivity in metals. Electrons carry both charge and heat; the same scattering limits both. The ratio — the Lorenz number — is a universal constant. Violations go downward: phonon drag, non-Fermi-liquid behavior, or selective scattering suppress thermal transport relative to electrical, reducing the Lorenz number below the Sommerfeld value.
In CoSi, the violation goes up. The electronic Lorenz number rises 40% above Sommerfeld. The mechanism is topological: CoSi is a chiral topological semimetal with electron-hole compensation. Both carrier types contribute to thermal transport cooperatively — they carry heat in the same direction even though they carry charge in opposite directions. The thermal conductivity is enhanced while the electrical conductivity, limited by carrier cancellation, is not.
Simultaneously, phonons — typically negligible in metallic thermal transport — dominate the lattice contribution below room temperature. The standard picture of a metal (electrons carry the heat, phonons are background) fails in both directions: the electrons carry more heat than expected per unit of electrical conductivity, and the phonons carry more heat than expected for a metal.
The structural point: the Wiedemann-Franz law fails upward when topological band structure decouples charge transport from heat transport in the electronic channel. Downward violations indicate that heat is harder to carry than charge. Upward violations indicate the opposite — and the mechanism is the topological structure of the Fermi surface, not exotic scattering. The direction of the violation diagnoses the cause.