A Width-Range Boundary Atlas for Fixed-Point Quantum LDPC Min-Sum Decoding

<title>Abstract</title> <p>Fixed-point quantum low-density parity-check decoders are often described by word width, although width does not determine dynamic range. We report a preregistered descriptive study of 19 width--range formats across 48 cells covering four codes, both Calderbank--Shor--Steane sectors, three physical error rates and two normalisation recipes. No tested format was jointly resource-qualified and non-inferior in every cell; eight-bit behaviour changed with clip level and normalisation. Reproducible finite-precision reports must therefore include width, the normalisation recipe and the clip level. Evidence is limited to the tested code-capacity bank, with many unresolved cells and no held-out confirmation.</p>