Unified interpretation of 95 GeV di-photon and di-tau Excesses in the Georgi-Machacek Model

We revisit the 95 GeV excesses in the $γγ$ and $ττ$ channels in the Georgi-Machacek model, where a single light $CP$-even custodial singlet H can account for both hints. Using one-loop renormalization group-improved effective potential and positive-definiteness conditions for vacuum stability, together with perturbative unitarity, electroweak precision tests, B-physics, and Higgs data, we identify a narrow but viable parameter region. In this region, charged and doubly charged scalars enhance H→γγ, while the fermionic rescaling controls H→ττ, yielding combined signal strengths compatible at the $2σ$ level. The scenario predicts characteristic patterns in the singlet mixing and triplet VEV and is highly testable at the HL-LHC and future lepton colliders via precision κV measurements and direct exotic searches.