Precision Audits for Compiled Transformers with Source-Level Ground Truth

Compiled transformers provide source-level ground truth for a numerical/compiler audit: does reduced-precision execution still compute the intended program? In CRAFT, an LU-triangular-solve compiler, a certified-exact lookup oracle reveals that low precision can preserve finite outputs and hard attention while fetching the wrong source value. Across 142 executing programs and 359,202 emitted rows, no row fails above 17 tested arithmetic bits. Full bf16 breaks 105/142 programs; protecting the address path at every tested width of 18 bits or above restores selector correctness while leaving value error. The arithmetic-only sufficient rule is approximately $2{\log }_{2}P+4.4$ bits; storage rounding adds a separate term. A microbenchmark reaches $P=131,071$ and shows two additional bits per address doubling. Binary codes and direct gather delimit this representation-specific effect. Native Apple-GPU fp32-address/bf16-value runs also restore selectors on three frontier programs. In a public Tracr case, official ACDC recovers the full known graph despite int8 errors on 232/256 inputs; additional ACDC and trained controls remain correct. These results support source-level numerical auditing of compiled artifacts, without establishing universal fragility, compression benefits, or generalization to trained transformers.