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

We revisit the 95 GeV excesses in the $\gamma \gamma$ and $\tau \tau$ 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 $H\to \gamma \gamma$, while the fermionic rescaling controls $H\to \tau \tau$, yielding combined signal strengths compatible at the $2\sigma$ level. The scenario predicts characteristic patterns in the singlet mixing and triplet vacuum expectation values and is highly testable at the HL-LHC and future lepton colliders via precision ${\kappa }_V$ measurements and direct exotic searches.