Baryon Spectroscopy in Finite Relativistic Cosmology

A number-theoretic realisation of Baryon Spectroscopy is presented. We invoke Finite Relativistic Cosmology (FRC) in which every physical quantity is an arithmetic residue of the ever-growing cosmic modulus \(q=4t+1\). Building on the frame-covariant constants \(i_q,\pi_q,e_q\) of FRC, we define a canonical quadratic character \(\chi_{\!*}(p)=(e_q/p)\) that splits odd primes into up- and down-flavour species with provable 50 \% balance and profinite stability. Enumerating all colour-neutral prime triples below \(10^{7}\) and fitting a three-parameter finite-log mass rule \(M=\mu\sum\ln p_i-\kappa+\lambda S(S{+}1)\), we reproduce the proton-neutron gap to 0.1\(\sigma\) and lift the entire \(\Delta(1232)\) quartet into the PDG window with residuals \(<0.2\,\sigma\). Extending the character to cubic and sextic residues yields first-generation predictions for strange, charm and bottom baryons, five of which already lie within $2\sigma$ of experiment. The spectrum is self-similar under \(p_i\!\mapsto\!p_i^{\,k}\) for any \(k\!\perp\!q\), leading to a fractal density of states with Hausdorff dimension \(D_H\simeq0.87\). All derivations are accompanied by SHA-256-tracked datasets and python notebooks.