GeezerVison

Fixes #1267. This resubmits #1268 by @RoboX2020, which was closed before review; its two commits are unchanged.

What it does, for discrete-time systems:

• stability_margins checks z = −1 directly: if L(−1) is real and negative, there's a phase crossover at ω = π/dt with gain margin −1/L(−1).
  • In the poly path this is a check after the real-axis search, not a change to _z_filter. That filter is shared with the gain-crossover search, and widening it let stability_margins: 'poly' (and default 'best') returns spurious gain crossovers for discrete-time systems of moderate order; the root tolerance eps**(1/n) grows with degree #1266's off-circle roots through (see the discussion on Fix missing discrete-time Nyquist endpoint in stability margins #1268).
  • In the frd path, and best's fallback to it, L(−1) is taken before the conversion to FRD. User-supplied FRD data is unchanged.
• phase_crossover_frequencies also returns the real-axis intersection at π/dt.
• Tests: stability_margins misses a phase crossover at the Nyquist frequency (w = pi/dt) for discrete-time systems, so gm is inf when L(-1) < 0 #1267's three loops under all three methods, a positive endpoint that must not become a crossover, and a moving-average regression for the interaction.

How it was checked:

• The full test suite: 3,866 passed and 558 skipped, against 3,853 and 558 on main (bfe9380).
• Gain margins: 12 discrete-time loops up to order ~1,350 (moving averages, EWMAs and difficulty-retarget rules), plus stability_margins misses a phase crossover at the Nyquist frequency (w = pi/dt) for discrete-time systems, so gm is inf when L(-1) < 0 #1267's three, against a dense frequency scan. All 15 match under poly, best and frd; on main, 12 of the 15 return inf.
• Phase margins: on the 12 loops, identical to main. The moving averages' are still wrong on both, which is stability_margins: 'poly' (and default 'best') returns spurious gain crossovers for discrete-time systems of moderate order; the root tolerance eps**(1/n) grows with degree #1266, not addressed here.

Disclosure: written with an AI agent, Claude Code (Anthropic's Claude Opus 5.5 model). The code is #1268's, by @RoboX2020, unchanged; its author has said it was bot-written. The agent ran the checks above, reviewed the diff and wrote this description. Before posting, it walked me through the change and this description, with a short quiz on the key points: the bug, why the fix checks z = −1 directly, and what it leaves to #1266. I didn't write any of the code.