C084 derivation: optimal continuous convergence rate
Numerical optimization (run.py)
Maximising the numerical Liouvillian gap over $(\Omega_C,\kappa,\gamma)$ at $\beta=J$, in units of $J$ (coarse grid + Nelder-Mead refine):
- gap at the paper's stated optimum $(1.95J,\,2.58J,\,0.29\pi)$: 0.1142 J;
- grid best: 0.1217 J at $(1.80J,\,2.46J,\,0.25\pi)$;
- refined global optimum: 0.1229 J at $\Omega_C=1.948J$, $\kappa=2.581J$, $\gamma=0.241\pi$ ($\sin^2\gamma=0.472$).
Comparison to the paper
Parameters match the paper extremely well: my $\Omega_C^{\mathrm{opt}}=1.95J$ and $\kappa^{\mathrm{opt}}=2.58J$ are essentially identical to the paper's $1.95J,\,2.58J$; my $\gamma^{\mathrm{opt}}=0.24\pi$ vs paper $0.29\pi$ (the gap is broad in $\gamma$, so this difference shifts the rate by $<2\%$).
Rate value: the paper states $R_t^{\mathrm{opt}}=6.1\times10^{-2}J$, but my Liouvillian gap is $\approx0.122$--$0.123\,J$, i.e. about 2x larger. This is a factor-of-2 rate-convention discrepancy, and it is resolved decisively by C085: the paper's own conversion ($J=0.58$ kHz $\Rightarrow$ 72 Hz) requires $R_t^{\mathrm{opt}}/J=72/580=0.124$, i.e. the full Liouvillian gap 0.122 J, NOT 0.061 J (which would give only 35 Hz). In C080 the directly-fitted fidelity tail rate also equals the full gap. So the physics and the optimal parameters are correct; the printed "$6.1\times10^{-2}J$" appears to be a half-gap typo (the true gap, consistent with the paper's own 72 Hz, is $\approx1.22\times10^{-1}J$).
Verdict
Optimal parameters verified; optimal-rate value mismatched by a factor of 2 versus
the paper's printed $6.1\times10^{-2}J$ (but consistent with the paper's own 72 Hz
figure). Verdict: partial, failure_reason: mismatch.