The arXiv preprint 2605.22944 develops analytical approximations for the secondary ultra-high-frequency peak in the stochastic gravitational wave background produced by cosmic-string loops formed during a friction-dominated era. This work is entirely theoretical, relying on loop-distribution modeling rather than observational data or simulations with defined sample sizes, and remains a preprint without peer review. While the original coverage of Mukovnikov et al. (2024) highlighted the peak's existence, the new approximations reveal that the feature persists across a wider swath of string tension and friction parameters than previously mapped, directly probing dark-sector couplings and post-inflationary friction scales that standard GW searches overlook. Comparable signatures appear in related analyses of superconducting strings (Cui et al., Phys. Rev. D 2023) and global-string networks constrained by PTA data (Ellis et al., JCAP 2024), yet those studies omitted friction-era dynamics entirely. The approximations therefore bridge a gap: they allow rapid evaluation of when the high-frequency bump exceeds astrophysical foregrounds, exposing early-universe friction lengths inaccessible to CMB or collider probes. Limitations include the assumption of scale-invariant loop chopping and neglect of late-time loop fragmentation, both of which could shift the peak amplitude by factors of a few.