Stability Problems in Symbolic Integration

The paper proves the exact characterization for stability of t = f·exp(g) (Theorem 3.14) and its proof is coherent, relying on Liouville’s theorem, a reduction lemma, and a degree-descent/valuation argument . The model’s solution reaches the same conclusion but its necessity proof contains a false step: it claims that a rational function with a nonzero finite limit at infinity must be constant, which is incorrect (e.g., (x+1)/(x+2) → 1). This gap leaves the exclusion of non-affine g unproven in the model’s argument, whereas the paper correctly establishes δ(g) is constant and f is a polynomial.