Signatures consistent with multi-frequency tipping in the Atlantic meridional overturning circulation

The paper demonstrates, via a conceptual delay model and comparisons to climate models, qualitative signatures consistent with multi‑frequency tipping: a folded resonance tongue (2:7) with a Chenciner bubble containing heteroclinic transitions, a small drop in the amplitude observable just before the heteroclinic line under noise, a larger drop near a subcritical torus bifurcation, and a tristability window with intermittency when the forcing is reversed. However, these are presented as numerical/phenomenological findings without a rigorous theorem; indeed, even the heteroclinic and homoclinic transitions are reported as tangles represented by single curves for clarity, acknowledging non‑rigor in that depiction . The candidate solution lays out a plausible rigorous route (center‑manifold reduction around an HSN point for the stroboscopic map, Chenciner‑bubble unfolding, adiabatic tracking, and large deviations), but it assumes crucial hypotheses—existence of the organizing HSN point for the specific RFDE, subcriticality of the Neimark–Sacker curve, and persistence of a distal low‑amplitude attractor—without verification for Eq. (1). Hence, the paper is qualitatively correct but non‑rigorous, and the model’s proof is conditional and incomplete for the specific system. Key paper evidence underpinning this verdict includes: the model Eq. (1) and parameter choices κ=11, τn=0.953, definition of the amplitude observable, and use of the 2:7 tongue ; the described Chenciner bubble with fold/torus/heteroclinic curves and subcritical torus bifurcation of the periodic orbit in the time series ; the noise‑anticipated small drop and big drop near the torus bifurcation in the hysteresis loop of amp[h(t)] ; and the observed tristability and intermittency near the heteroclinic transition .