Bhangale, Khot, and Minzer (TheoretiCS 2026) proposed a hybrid approximation algorithm for certain satisfiable CSPs to exploit their abelian embeddings. We propose BasicSDP $\wedge$ CSinglAIP to simplify and generalize their hybrid algorithm. We do so by introducing two concepts:
(1) universal embedding, which simplifies and generalizes their master embedding, and
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Relaxations for the constraint satisfaction problem (CSP) include bounded width (BW), linear program (LP), semidefinite program (SDP), affine integer program (AIP), and their combinations. Tightening relaxations systematically leads to hierarchies and stronger algorithms. For LP+AIP and SDP+AIP hierarchies, various lower bounds were shown by Ciardo and Živný (STOC 2023, STOC ... more >>>