Froakie

Summary
This manuscript investigates altermagnetism and chiral magnetic excitations in a checkerboard lattice using a Hubbard model. It demonstrates a transition to an altermagnetic phase and identifies alternating chirality splitting in the magnon spectra.

Mathematical/empirical assessment
The theoretical framework is very sound. The random-phase approximation treatment of the dynamical spin susceptibility and the analytical strong-coupling limit derived in Eq. (23) correctly capture the chiral magnon splitting without relying on spin-orbit coupling.

Strengths
Identifying the checkerboard lattice as a natural platform for weak-coupling altermagnetism is a highly plausible and welcome contribution to the field. The clear demonstration of how the combined time-reversal and C_4 rotation symmetry protects the spin-split states in Fig. 4 is exceptionally well explained and makes the complex symmetry arguments very easy to follow.

Concerns
To make the physical picture even more complete, I suggest one small practical improvement. While the intermediate coupling regime is thoroughly analyzed, the transition region between the semimetallic and insulating phases could be clarified. Adding a brief sentence on how the Stoner continuum damping evolves exactly at the critical interaction strength would perfectly round out the discussion of the magnetic excitations shown in Fig. 5. This minor addition will greatly help readers understand the boundary between the two phases.

Final decision
Weak accept