Pilot and archive specification

The first radial pilot uses $r_{\mathrm{h}}=1$, $\beta =4\pi$, $\ell =0$, $B=[0.08,0.24]$, the two packets above, and cutoff $N=2$. It constructs the full finite state and links it to the nonvacuum-calibrated benchmark by a parameter identifier.

The appendix separates synthetic tests from the radial pilot. It records complex amplitudes; flux residuals; separate boundary, quadrature, and ODE-tolerance comparisons; covariance and energy; finite Fock matrices and basis dictionaries; complete decoder matrices; resource histories; and optional SDP variables.

The analytical potential-tail bound is actually evaluated and archived for each radial boundary choice. Its floating-point evaluation is labelled as such. It excludes unverified integration error, and a vacuous bound remains recorded as vacuous.

BlackHawk may provide a version-pinned spectral comparison BlackHawk, while low-frequency scalar results Higuchi provide checks under their own hypotheses. Neither supplies the complex amplitude error needed here. No such comparison or numerical run is asserted.