A unique class of local Higher Spin Gravities with propagating massless fields in 4d — Chiral Higher Spin Gravity — was first found in the light-cone gauge. We construct a covariant form of the corresponding field equations in all orders, thus completing the previous analysis of arXiv:2204.10285. This result is equivalent to taking the minimal model (in the sense of L∞-algebras) of the jet-space BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about counterterms, anomalies, etc.

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