Real monopoles and a spectral sequence from Khovanov homology

Given a based link $(K,p)$, we define a "tilde"-version HMR̃(K,p) of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler characteristic of HMR̃(K,p) is equal to Miyazawa's invariant $|deg(K)|$ arXiv:2312.02041 and examine some examples. Further, we construct a spectral sequence over F₂ abutting to HMR̃(K,p), whose E₂ page is the reduced Khovanov homology Khr(K̄) of the mirror link K̄.