Global parameter-explicit error theorem for the complete response

Establish a global parameter-explicit error theorem for the complete fluorescence peak-time response, with simultaneous control of the large-distance transport remainder, the lifetime-shifted peak window, and root nondegeneracy.

Background

The paper develops quadratic and cubic lifetime-unified approximations for the peak time of a fluorescence response in a homogeneous half-space diffusion model with a point fluorophore. Its rigorous error analysis is layered: one component arises from replacing the exact zero-lifetime transport response with the large-distance profile, and another arises from locally approximating that profile by quadratic or cubic logarithmic expansions before applying the fluorescence-lifetime convolution.

A conditional peak-location stability proposition transfers convolution residuals into peak-time errors when the relevant root is nondegenerate. However, the paper does not prove uniform control of the full incoming convolution tail, the large-distance approximation remainder, or a parameter-independent lower bound on the derivative at the peak-balance root. The authors therefore identify a global parameter-explicit error theorem for the complete response as unresolved.