The physical origin of quasi-periodic oscillations (QPOs) in blazars remains a question of debate; geometric and plasma-driven scenarios are the main competing interpretations. Discriminating between them requires probing variability beyond flux periodicity. We studied the spectral evolution of the BL Lac object PG 1553+113 over its ∼2.2-year gamma-ray QPO cycle to constrain the mechanism driving the oscillation. In particular, we tested whether the variability is chromatic (coupled to spectral changes) or achromatic (independent of spectral shape), thus allowing us to distinguish between plasma-driven and geometric scenarios. We analyzed 17 years of -LAT data (2008--2025) with 30-day binning. To mitigate red-noise effects, we applied singular spectrum analysis (SSA) to remove slow baseline trends and used a block bootstrap approach to quantify correlations between photon flux and photon index, while preserving temporal dependence. Fermi We find a robust softer-when-brighter chromatic trend---atypical for high-synchrotron-peaked blazars such as PG 1553+113 and which, based on our analysis, physically corresponds to softer-when-flaring episodes---that persists after detrending and accounting for temporal autocorrelation. In contrast, no significant correlation is detected between the photon index and the QPO phase, indicating that the periodic modulation is effectively achromatic. The coexistence of plasma-driven chromatic flares and an achromatic QPO disfavors scenarios in which the periodicity arises from intrinsic jet processes. Instead, the results support a geometric origin for the QPO modulation, such as jet precession, where Doppler-factor variations modulate the flux without altering the intrinsic particle energy distribution.
Madero et al. (Fri,) studied this question.