Boundary-Layer Sensitivity from Initial-State Degrees of Freedom in Reduced Reheating Geometry

This work studies how an explicit initial-state degree of freedom deforms reduced reheating geometry. Extending the reduced parameter space to (α,ω0,β,Zin)(α,ω_0,β,Zᵢₙ)(α,ω0,β,Zin), the paper analyzes the observable triplet (uIV,E,Δθ)(uIV,E,Δθ)(uIV,E,Δθ) through the reduced Jacobian and the associated competition structure. The analysis shows that the initial-state degree of freedom does not create a new dominant bulk sensitivity sector. Instead, a Jacobian-degenerate band appears where the reduced observables collapse and ratio-based diagnostics become ill-defined. The relevant enhancement of initial-state competition is found only in the immediate exterior of this degenerate band, within a surrounding weak branch-sensitive region where the reduced map remains well-defined but weakly transmitting. This identifies the boundary-layer structure not with the degenerate band itself, but with its well-resolved exterior.