Etched priors: what freezing inference arithmetic into silicon does to the social and linguistic biases of a language model

Inference silicon commits irreversibly to an arithmetic: what is fused, how transcendentals are approximated, and in which format weights are stored.Does that commitment bake in prejudice? We model a chip as a triple χ = (A ,π,Q) of arithmetic, schedule and weight datapath, prove four results boundingwhat each can do to a decision, and test them on fourteen bit-exact emulated chips (one 1.7 B model, 782 probes). The compute path is inert: fusion is provablythe identity (KL= 0) and approximate ALUs move log-probabilities by ∼10−7 nats. Drift enters only through Q, and only where the reference margin is belowthe perturbation spread, a bound obeyed by all 4,448 observed flips. At four bits the scaling scheme, not the width, decides who absorbs the error: NVFP4concentrates drift on Hindi, Bengali, Swahili and Yorùbá (tail ratio 1.69, 95% CI [1.19,2.44]), MXFP4 on English, French and Chinese (0.44, [0.33,0.60]), andNF4 moves the ambiguous-context stereotype score from +0.11 to +0.23 (Δ = +0.12, [−0.01,0.26]). Number-format selection is a fairness decision fixed attape-out.