Moroder, Binder and Goold proposed in 2026 a way to make a thermodynamic matrix-inversion device settle faster. A device like this relaxes towards the inverse, and the slowest modes of the matrix take the longest to arrive. So a digital processor finds those slowest modes first, with the Lanczos algorithm, and starts the device already holding them. The device then only has the fast modes left to settle, and the speed-up is real. The paper describes the digital step as negligible compared with the settling time. That comparison is between floating-point operations and seconds on a physical device, which share no unit, so it cannot be checked. It can be replaced by one that can: price the digital step in the unit the answer itself costs. Computing the whole inverse digitally by Cholesky costs about the cube of the dimension in operations. Counting Lanczos the same way, at the paper's own size of 500, finding ten slow modes costs one and a half times the entire inverse on the paper's first family of matrices and five times on its second. The start those modes produce already holds ninety-four percent of the answer's squared size. The digital processor has paid for the whole answer before the device begins, so the device cannot make the protocol cheaper than not using it, at any speed. On the first family the digital step falls below the inverse's cost only above a thousand, to a little over half at two thousand, and only there does the device's speed become the question. Operations are not joules either: the digital inverse runs as dense blocks of arithmetic, the work processors do fastest, so counted in seconds it wins by more than the operations say. The rule travels: when a hybrid protocol calls its digital half cheap, price that half in the unit of the answer.