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Thermal noise is the predominant instability in the provision of ultrastable laser frequency by reference to a cavity. Reducing the thermal-noise limit of a cavity means either making it larger to spread thermal fluctuations, reducing the sensitivity of the cavity to temperature, or lowering the temperature. We report on a compact photonic resonator made of solid fused silica that we cool in a cryogenic environment. We explore a null in the resonator's frequency sensitivity due to the balance of thermal expansion and thermo-optic coefficients at a temperature of 9.5 K, enabling laser stabilization with a long-term frequency drift of 4 mHz/s on the 195 THz carrier. The robustness of fused silica to cryogenics, the capability for photonic design to mitigate thermal noise and drift, and operation at a modest 9.5 K temperature offer unique options for ultrastable laser systems.