Constraining FRB Microstructure with Polarised Shot Noise

We present FIRES, a polarised shot-noise (PSN) framework that models fast radio burst (FRB) dynamic spectra as the incoherent superposition of Gaussian microshots with varying polarisation angles (PAs). Applied to the CRAFT bursts FRB 20191001A and FRB 20240318A, FIRES can reproduce key spectro-polarimetric behaviours seen in these data: scattering suppresses PA variability on the trailing edge, while the leading edge preferentially retains intrinsic structure when sufficient signal-to-noise is present. We quantify this behaviour using the PA variance ratio $\mathcal{R}_\psi$ and explore the joint plane of measured linear polarisation fraction $\Pi_L$ versus PA variance to identify allowed regions of microshot number $N$, intrinsic PA dispersion $\sigma_\psi$, and intrinsic linear fraction $\Pi_{L,0}$ at fixed signal-to-noise. This restricts these combinations permitted within the adopted shot-noise framework. For FRB 20191001A, the data are consistent with an extended parameter space, reflecting degeneracies between intrinsic PA structure, microshot superposition, scattering, finite sampling, noise, and the assumed microshot-property distributions. FRB~20240318A occupies a more restricted region, favouring fewer microshots and larger intrinsic PA dispersion. By combining an emission-mechanism-independent forward-modeling framework with minimal assumptions and observational constraints, FIRES facilitates qualitative and quantitative exploration of how microshot superposition, scattering, finite sampling, and noise can shape observed FRB polarimetry under the PSN model.