Primordial black holes (PBHs) are compact objects hypothesized to form in the early universe from large primordial energy-density fluctuations. Interacting essentially only through gravity, and able to survive from the early universe to the present when heavier than roughly $5\times10^{14},\mathrm{g}$, they remain a viable candidate for dark matter. A PBH emits Hawking radiation, producing thermally every particle species whose rest mass lies below its Hawking temperature, and the resulting photon spectrum offers one of the most direct observational windows onto the PBH abundance and mass function.
Most existing analyses, however, proceed parametrically: a specific functional form is assumed for the mass distribution, the corresponding spectrum is computed over a grid of parameters, and the parameter space is then constrained against observations through exclusion limits or Bayesian inference. This ties the conclusions to the assumed family of mass functions.
We step outside this parametric paradigm. Using a neural operator, we construct an amortized inverse map that, given a photon spectrum attributed to PBH evaporation, directly reconstructs a plausible mass function without assuming any functional form. Going further, we characterize the full ensemble of mass functions that yield a statistically indistinguishable spectrum, thereby exposing the intrinsic degeneracy, the physical information ceiling, of the inverse problem. The result is a geometry-aware, calibrated uncertainty quantification that distinguishes what a photon spectrum can in principle reveal about a PBH's mass from what it fundamentally cannot.
