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We classify all Rota--Baxter operators of weights zero and one on the truncated polynomial algebra R=K[x_1,\\dots,x_n]/m^2. For weight zero, we prove that the Rota--Baxter operators are precisely the linear maps P satisfying P^2=0 and Image(P) \\subset m/m^2. For nonzero weight, a standard rescaling reduces the classification to weight one. In this case, the operators split into two disjoint families according to the value of P(1)\\in{0,-1}. 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We classify all Rota--Baxter operators of weights zero and one on the truncated polynomial algebra R=K[x_1,\\dots,x_n]/m^2. For weight zero, we prove that the Rota--Baxter operators are precisely the linear maps P satisfying P^2=0 and Image(P) \\subset m/m^2. For nonzero weight, a standard rescaling reduces the classification to weight one. In this case, the operators split into two disjoint families according to the value of P(1)\\in{0,-1}. On the maximal ideal m/m^2, such "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We classify all Rota--Baxter operators of weights zero and one on the truncated polynomial algebra R=K[x_1,…,x_n]/m^2. For weight zero, we prove that the Rota--Baxter operators are precisely the linear maps P satisfying P^2=0 and Image(P)⊂m/m^2. For nonzero weight, a standard rescaling reduces the classification to weight one. In this case, the operators split into two disjoint families according to the value of P(1)∈{0,−1}. On the maximal ideal m/m^2, such operators induce an endomorphism L satisfying L^2+L=0, equivalently, −L is idempotent. 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For weight zero, we prove that the Rota--Baxter operators are precisely the linear maps P satisfying P^2=0 and Image(P)⊂m/m^2. For nonzero weight, a standard rescaling reduces the classification to weight one. In this case, the operators split into two disjoint families according to the value of P(1)∈{0,−1}. On the maximal ideal m/m^2, such operators induce an endomorphism L satisfying L^2+L=0, equivalently, −L is idempotent. 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