Exact source-bound arithmetic is a measurable cost
Both shortened profiles completed. Source-body bounding takes 29% of profiled propagation time. Its general affine-radius calculation takes about 12–13%, and the additional derivative-based radius takes another 12%. These times overlap their parent functions and must not be added to the parent totals.
Both operations repeatedly construct exact fractions from binary floating-point inputs. Binary inputs have power-of-two denominators. Integer arithmetic can represent their differences, products and sums exactly without reducing a new general fraction at every step. The next implementation will test that change against the existing exact-rational reference, including arbitrary centers, all 27 columns, tiny values and nonbinary fallback inputs.
This is a proposed arithmetic optimization, not evidence that the timeout problem is solved. Require identical outputs in component and native checks, then measure a separate finite full-history screen. Preserve the completed 48-region comparison, its failures and the horizontal-width requirement.