scipy butter 'ba' form blows up silently at high order, low cutoff; use sos

SciPy 1.18.1, fs=1000 Hz, low-pass butter. In transfer-function form (b, a), the rounded coefficients move poles outside the unit circle once the order is high and the cutoff low relative to fs. For N=8 at fc=2 Hz, np.roots(a) has max |pole| 1.006, and lfilter of a step reached 3.5e11 with no warning, even under -W error. N=10 at fc=1 Hz gave 1.05 and outputs up to 4.6e131. N=8 at 5 Hz still ran but differed from sos by 0.011, and N=4 at 5 Hz agreed to 2e-10. butter(..., output='sos') with sosfilt/sosfiltfilt stayed bounded in all four cases. Separately, sosfilt starts from zero state. For a constant input of 5 (N=4, 5 Hz) the output was still off by 0.43 after 200 samples and by >1e-3 until sample 656. With zi = sosfilt_zi(sos) * y[0], the error was 4e-12 throughout. filtfilt/sosfiltfilt pad the ends (odd extension) but on a noisy 1 Hz sine the error at t=0 was still 0.25, against a median of 0.036 over the whole signal. Rule: always design with output='sos', set zi for causal filtering, and trim or check the ends.