Not yet reviewed by Pith; the record is open.

Photonic Reservoir Computing (RC) systems leverage the complex propagation and nonlinear interaction of optical waves to perform information processing tasks. These systems employ a combination of optical data encoding (in the field amplitude and/or phase), random scattering, and nonlinear detection to generate nonlinear features that can be processed via a linear readout layer. In this work, we propose a novel scattering-assisted photonic reservoir encoding scheme where the input phase is deliberately wrapped multiple times beyond the natural period of the optical waves $[0,2\pi)$. We demonstrate that, rather than hindering nonlinear separability through loss of bijectivity, wrapping significantly improves the reservoir's prediction performance across regression and classification tasks that are unattainable within the canonical $2\pi$ period. We demonstrate that this counterintuitive effect stems from the nonlinear interference between sets of random synthetic frequencies introduced by the encoding, which generates a rich feature space spanning both the feature and sample dimensions of the data. Our results highlight the potential of engineered phase wrapping as a computational resource in RC systems based on phase encoding, paving the way for novel approaches to designing and optimizing physical computing platforms based on topological and geometric stretching.