Slavin Mirror Arithmetic and the Prime Mirror Spectrum Theorem

Slavin Mirror Arithmetic studies centered modular structures through reflection and inverse symmetry. Let p be an odd prime. For each nonzero multiplier r modulo p, this paper forms all shifted correlations of the centered least-residue sequence and then removes the shift labels, retaining only the resulting multiset. The Slavin Prime Mirror Spectrum Theorem proves that two such unlabeled spectra are equal if and only if their multipliers are equal or multiplicative inverses. The proof uses reflection symmetry to recover the zero-shift correlation as the unique value of odd multiplicity, followed by a Dedekind-sum congruence that recovers the multiplier up to inversion. The archive includes the formal paper, editable source, exact verification code, and recorded tests covering every odd prime through 101 with zero failures. The arithmetic ingredients are classical; the exact unlabeled-spectrum reconstruction statement and parity-anchor proof were not located in the literature reviewed.