GeezerVison

Thanks for the quick fix. I ran it against a dozen discrete-time loops, from first order up to order ~1,350 (moving averages, EWMAs and blockchain difficulty-retarget rules), comparing with a dense frequency scan. With this branch every gain margin matches under poly, best and frd; on main, 9 of the 12 return inf. Phase margins are unchanged on all but one.

That one is an interaction with #1266, through _z_filter being shared with the gain-crossover search. For an even-length moving average, the |L| = 1 polynomial has a reciprocal pair of real negative roots, e.g. -1.040 and -0.962 at N = 144. #1266's tolerance (0.88 there) lets them through, and their argument is exactly π, so this branch now keeps them as a gain crossover at w = π, where |L(-1)| = 0. poly then reports pm = 0.000:

import warnings
import numpy as np
import control as ct

warnings.simplefilter("ignore")
for N in (16, 30, 72, 144):
    num = np.r_[0.0, np.full(N, 1.0 / N)]
    L = ct.tf(num, np.polysub(np.r_[1.0, np.zeros(N)], num), dt=1)
    gm, pm, sm, wpc, wgc, wms = ct.stability_margins(L, method="poly")
    print(N, round(pm, 3), round(wgc, 4), abs(complex(L(-1))))

Both are wrong, so this isn't a regression in kind, but 0° reads as a marginally stable loop. Two ways to keep this PR's fix without it: keep z = -1 only in the phase-crossover filter (_poly_z_real_crossing), or accept a gain crossover at π only if |L(-1)| is close to 1 (the check #1266 suggests for every candidate).

Thanks for catching this. I reproduced the false zero-degree phase margins for N = 16, 30, 72 and 144.

The follow-up commit restores _z_filter and the gain-crossover search to their upstream behavior. The Nyquist endpoint is now evaluated directly only for phase crossovers, so it no longer admits those off-circle roots as gain crossovers.

The four moving-average phase margins now match main exactly (12.122, 6.309, 2.569 and 1.270 degrees). Those values are still inaccurate because of #1266; this change does not attempt to fix that separate tolerance problem. The gain margins from #1267 remain 2, 1 and 2 under all three methods.

Added a moving-average regression for the false Nyquist gain crossover. Margin tests: 74 passed, 2 skipped. Margin, FRD, transfer-function and LTI tests together: 428 passed, 129 skipped.

@RoboX2020 Please add AI tool disclosures, ensuring consistency with https://numpy.org/doc/stable/dev/ai_policy.html ? (Given how long and verbose your responses are and how quickly you are committing, I assume you used a chat bot for most or all of this...)

Disclosure for my comment above: it was written with an AI agent, Claude Code (Anthropic's Claude Opus 5.5 model).

• How it was used: the agent applied this PR's diff to a clone of main (not installed from the branch), ran the margins on a dozen loops, wrote the comment and its code, and posted it through the GitHub CLI.
• What's AI-generated: the text and code. The numbers are program output, and the code block was rerun on both branches before posting.
• My part: I read and approved the comment before it was posted.

Thanks @gimballock I guess @RoboX2020 is a bot who simply closed the PR in response to request...

If you want, @gimballock , feel free to review this or open a PR that re-uses the code for this PR. I assume @RoboX2020 did not author any of it, so you can just claim authorship.