Boundary-Layer Sensitivity of Initial Conditions 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)(\alpha,\omega_0,\beta,Z_{\rm in})(α,ω0,β,Zin), the paper analyzes the observable triplet (uIV,E,Δθ)(u_{\rm IV},E,\Delta\theta)(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. Version 2 (v2)This version clarifies the geometric meaning of the boundary-layer structure. The gray region is now identified as an observable-inaccessibility band, where the reduced observables are undefined, rather than as a numerical low-response mask. The role of the minimal-response direction is reformulated as an operational proxy for compressed observable directions, and the competition ratio is interpreted as a weak-transmission diagnostic. Numerical checks are also strengthened, showing that the boundary-layer enhancement is driven by suppression of the history-shape sector rather than by growth of the initial-state response.