On the parameter space of fibered hyperbolic polynomials

The paper defines the quadratic QPF family Q_λ, the hyperbolic locus M_0(T^1), the submanifold H^*_0(T^1), and the fibered multiplier map κ̂(λ)=exp∫_{T^1}log λ(θ)dθ, then proves Theorem B: κ̂: H^*_0(T^1)→D^* is a holomorphic submersion and yields a codimension‑one holomorphic foliation. The proof shows weak holomorphy via an integral/Morera argument and obtains a local holomorphic section using parameter‑dependent MRMT and QC surgery, invoking the Banach‑manifold submersion criterion (Theorem 2.10) . The candidate solution instead gives an explicit local logarithmic chart around λ_0 (using wind(λ_0,0)=0), splits C(T^1)=ℂ⊕C_0(T^1), and shows that (κ̂, P∘log) is a local biholomorphism with inverse (κ,h)↦exp(log κ + h), so κ̂ is the projection in product coordinates, hence a holomorphic submersion. Aside from a minor omission (explicitly intersecting the chart with the ‘negative Lyapunov’ condition to remain inside H^*_0), the model’s proof is correct. The two arguments are logically independent: the paper uses surgery/sections; the model uses explicit Banach charts.