A question about random linear combination

[wj404]

Gate identity and wiring identity get two independent sum check , the assumptions are((0, [f]]); f) and ((0, [[g]]); g), gate identity is μ variables, and wiring identity is μ + 1 + logl_w variables. In Remark 4.2, it is mentioned that a random linear combination is used by a random number k to obtain a sum check ((0 + k·0, [[f]], + k·[[g]]); f + k·g). Is this linear combination correct? For the merged sum check, why is the number of field elements sent by the prover is μ, should it not be equal to the number of univariate quiries?