diff --git a/src/affine.jl b/src/affine.jl
index 95b50cb..33b2558 100644
--- a/src/affine.jl
+++ b/src/affine.jl
@@ -143,6 +143,16 @@ function affine_transform_tensors(
         b = @. b >> 1
     end
 
+    # If the carry set is empty, no valid integer mappings exist for this
+    # transformation. Return zero tensors forming a valid (zero) MPO.
+    if isempty(carry)
+        @warn "Affine transformation has no valid integer mappings; returning zero MPO."
+        for r in 1:R
+            tensors[r] = zeros(Bool, 1, 1, 1 << M, 1 << N)
+        end
+        return tensors, carry
+    end
+
     if boundary == OpenBoundaryConditions() && maximum(b) > 0
         # Extend the tensors to the left until we have no more nonzero bits in b
         # This is equivalent to a larger domain.
@@ -154,6 +164,15 @@ function affine_transform_tensors(
 
             carry = new_carry
             b = @. b >> 1
+            isempty(carry) && break
+        end
+
+        if isempty(carry)
+            @warn "Affine transformation has no valid integer mappings; returning zero MPO."
+            for r in 1:R
+                tensors[r] = zeros(Bool, 1, 1, 1 << M, 1 << N)
+            end
+            return tensors, carry
         end
 
         weights = map(c -> carry_weight(c, boundary), carry)
diff --git a/test/affine_tests.jl b/test/affine_tests.jl
index 7e49df4..3fdac94 100644
--- a/test/affine_tests.jl
+++ b/test/affine_tests.jl
@@ -158,4 +158,28 @@
             end
         end
     end
+
+    @testset "degenerate_rational (issue #46)" begin
+        # This transformation has no valid integer mappings because
+        # A_int has all even entries while b_int[3] is odd, so
+        # A_int*x + b_int can never be divisible by the even denominator s=42.
+        A = [1 0 0; -1//7 6//7 6//7; -10//21 6//7 -1//7]
+        b = [0, 27 // 7, 61 // 14]
+        R = 3
+
+        M, N = size(A)
+        bc = Quantics.OpenBoundaryConditions()
+
+        # The full matrix should be all zeros (no valid mappings)
+        T = Quantics.affine_transform_matrix(R, A, b, bc)
+        @test nnz(T) == 0
+
+        # The MPO construction should not crash (was DivideError before fix)
+        # and should emit a warning about no valid mappings.
+        mpo = @test_warn "no valid integer mappings" Quantics.affine_transform_mpo(
+            outsite[1:R, 1:M], insite[1:R, 1:N], A, b, bc)
+        Trec = Quantics.affine_mpo_to_matrix(
+            outsite[1:R, 1:M], insite[1:R, 1:N], mpo)
+        @test T == Trec
+    end
 end