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In 2022 the BL Lac object S4 0954+65 underwent a major variability phase, reaching its historical maximum brightness in the optical and γ-ray bands. We present optical photometric and polarimetric data acquired by the Whole Earth Blazar Telescope (WEBT) Collaboration from 2022 April 6 to July 6. Many episodes of unprecedented fast variability were detected, implying an upper limit to the size of the emitting region as low as |$10^{-4}$| parsec. The WEBT data show rapid variability in both the degree and angle of polarization. We analyse different models to explain the polarization behaviour in the framework of a twisting jet model, which assumes that the long-term trend of the flux is produced by variations in the emitting region viewing angle. All the models can reproduce the average trend of the polarization degree, and can account for its general anticorrelation with the flux, but the dispersion of the data requires the presence of intrinsic mechanisms, such as turbulence, shocks, or magnetic reconnection. The WEBT optical data are compared to γ-ray data from the Fermi satellite. These are analysed with both fixed and adaptive binning procedures. We show that the strong correlation between optical and γ-ray data without measurable delay assumes different slopes in faint and high brightness states, and this is compatible with a scenario where in faint states we mainly see the imprint of the geometrical effects, while in bright states the synchrotron self-Compton process dominates. [ABSTRACT FROM AUTHOR]

In 2021 BL Lacertae underwent an extraordinary activity phase, which was intensively followed by the Whole Earth Blazar Telescope (WEBT) Collaboration. We present the WEBT optical data in the BVRI bands acquired at 36 observatories around the world. In mid-2021 the source showed its historical maximum, with R  = 11.14. The light curves display many episodes of intraday variability, whose amplitude increases with source brightness, in agreement with a geometrical interpretation of the long-term flux behaviour. This is also supported by the long-term spectral variability, with an almost achromatic trend with brightness. In contrast, short-term variations are found to be strongly chromatic and are ascribed to energetic processes in the jet. We also analyse the optical polarimetric behaviour, finding evidence of a strong correlation between the intrinsic fast variations in flux density and those in polarization degree, with a time delay of about 13 h. This suggests a common physical origin. The overall behaviour of the source can be interpreted as the result of two mechanisms: variability on time-scales greater than several days is likely produced by orientation effects, while either shock waves propagating in the jet, or magnetic reconnection, possibly induced by kink instabilities in the jet, can explain variability on shorter time-scales. The latter scenario could also account for the appearance of quasi-periodic oscillations, with periods from a few days to a few hours, during outbursts, when the jet is more closely aligned with our line of sight and the time-scales are shortened by relativistic effects. [ABSTRACT FROM AUTHOR]