The Pi Exclusion Complement: Exact Local Statistics, Autocorrelation, and Spectral Extinction

The Pi Exclusion Complement is the increasing sequence of positive integers rejected by the Pi Exclusion Sieve. This companion preprint gives the complement an autonomous same-shell selection rule, an exact logarithmic-depth counting recursion, and closed gap and maximal-run statistics. Through the parent compact-group coding it derives an exact all-lag autocorrelation recursion, a closed formula for every Fourier coefficient, extinction of the nonzero first-coordinate Bragg family, and a geometric law for spectral mass by support level. The enumerator has the classical complementary Beatty slope (π/(π-1)) but is not the Beatty sequence OEIS A054386. The negative extremal discrepancy direction remains open.