\begin{table}[t]\centering\small
\caption{Reported best agents of all Haiku~5.5 loops, re-evaluated together with the seed in one batch (all 232 fresh
problems, two runs each). $S$: the selection score for which the loop reported the agent. Inflation: selection gain
over the seed's pooled selection score ($\nseedDgmSmean\%$ over $\nseedDgmSn$ evaluations) minus fresh gain. Cost in dollars per thousand tasks. The first-round DGM loops and the second-round
arms (more DGM loops, random diagnosis, HGM-style) are registered; the loops without hint prompts are exploratory. The
last rows are references measured in the same batch.}\label{tab:loops}
\begin{tabular}{llrrrr}\toprule
loop type & loop & $S$ & fresh gain [95\% CI] & inflation & cost \\ \midrule
\csname @@input\endcsname tab_loops.tex
\bottomrule\end{tabular}\end{table}
The random-diagnosis loops draw every request from the fixed list of \S\ref{sec:round2}; because one request targets
empty responses, they search over textbook requests rather than without any diagnosis. In the final batch they gain $\vhRandom$ points [$\vhRandomlo$, $\vhRandomhi$] on average,
whereas the first-round DGM loops gain $\vhDgmTwo$ [$\vhDgmTwolo$, $\vhDgmTwohi$]. The registered non-inferiority test
(H7) fails: the difference is $\vhRandomMinusDgm$ [$\vhRandomMinusDgmlo$, $\vhRandomMinusDgmhi$]. Against all six DGM
loops it is $\vhRandomMinusDgmAll$ [$\vhRandomMinusDgmAlllo$, $\vhRandomMinusDgmAllhi$]. HGM-style parent selection gains
$\vhHgm$ [$\vhHgmlo$, $\vhHgmhi$], which is $\vhHgmMinusDgmAllAbs$ [$\vhHgmMinusDgmAllAbslo$, $\vhHgmMinusDgmAllAbshi$]
points more than the six DGM loops (Table~\ref{tab:loops}). These intervals resample problems (\S\ref{sec:round2}). Compared at the
level of loops (three or six per arm), none of the arm differences is significant (Welch tests: HGM-style vs DGM
$p=\vllHgmP$, random vs first-round DGM $p=\vllRandomThreeP$, random vs all DGM $p=\vllRandomSixP$). Four of the 14 loops
reach the level of the single move L: loop 3, both loops without hint prompts and one HGM-style loop; one of the six DGM
loops does.

For each DGM loop the selection gain exceeds the fresh gain, by $\vhtwoMinInfl$ to $\vhtwoMaxInfl$ points. With each
loop's own sampling error (tasks resampled, as registered for H2) every interval includes zero, and over the six loops
the hierarchical estimate is $\vhtwoMean$ points [$\vhtwoLo$, $\vhtwoHi$]. The placebo loops' best selection scores
are given in \S\ref{sec:round1}.