Why it is a question
THEORY-548 holds the linear result for generalised Lotka–Volterra dynamics with every interaction delayed: stability is lost at τ_c = min_j arctan(|Re j|/|Im j|)/|j| over the community eigenvalues j, where a pair of roots crosses the imaginary axis transversally. It also holds the variability pattern in Saeedian et al.’s one setting (strong self-regulation, d_B = 10, σ_B = 0.1, C = 1), which the promotion review found matches a null of independently oscillating species. Three things the source reports or implies are not settled. Saeedian et al. show τ_c falling with diversity at strong self-regulation only. They see sustained oscillation past τ_c, but supercriticality is not derived. Past a second threshold τ_c^C their Euler runs diverge, and refining the step did not remove it. Until 2026-10-20 the first and third were THEORY-548’s promote_when.
What would answer it
- The same analysis with weak self-regulation, where interactions rather than growth rates set the leading eigenvalue, showing whether τ_c still falls with S.
- A centre-manifold or normal-form computation of the first Lyapunov coefficient at τ_c, or numerical continuation of the cycle.
- A stiff delay-equation solver run past τ_c^C, showing bounded or unbounded trajectories.
What would not answer it: more Euler runs at the one strongly self-regulated setting.