\begin{table}[t]\centering\footnotesize
\caption{Pre-registered hypotheses of the first two rounds (H1--H5, H6--H10), the estimate with its 95\% interval and
the verdict. (a) marks amendments made before the results; (p) marks readings or tests chosen after the results.
Contrasts are candidate minus comparator. Contrasts across batches are raw; seed-adjusted values are in Table~\ref{tab:batches}.}\label{tab:hyp}
\setlength{\tabcolsep}{3pt}
\begin{tabular}{>{\raggedright\arraybackslash}p{0.30\linewidth}>{\raggedright\arraybackslash}p{0.47\linewidth}>{\raggedright\arraybackslash}p{0.16\linewidth}}\toprule
hypothesis (as registered) & estimate & verdict \\ \midrule
H1 placebo loops show a positive selection gain of predictable size & first-round best scores inside leave-one-out
predictive intervals; six loops $\vhPlaceboMin$--$\vhPlaceboMax\%$ vs $\vhPlaceboPred\%$ predicted & supported \\
H2 DGM loops' selection gain exceeds their fresh gain; fresh gain positive & per-loop excess (tasks resampled)
$\vhtwoMinInfl$ to $\vhtwoMaxInfl$ points, every interval includes 0; six loops (hierarchical) $\vhtwoMean$
[$\vhtwoLo$, $\vhtwoHi$]; fresh gains all positive & not supported \\
H3 best log-free edit reaches $\geq 0.8\times$ the loops' fresh gain & (a) on $F_1$: ratio $\vhThreeRatio$ & not
supported \\
H4 from the engineered seed, fresh gains of all arms within $\pm 3$ points, selection gains $> 0$ & DGM loops:
\nhFourCI{} on $F$ (p: 90\% two one-sided tests) and $+\ngainStrongB$ [$\ngainStrongBlo$, $\ngainStrongBhi$] on $F_1$;
single-edit arms ($F_1$): $\nladSCone$ [$\nladSConelo$, $\nladSConehi$] and $\nladSCtwo$ [$\nladSCtwolo$,
$\nladSCtwohi$]; selection gains of the loops $+\nSgainStrongA$ and $+\nSgainStrongB$ & not supported (equivalence not
shown) \\
H5 evolved-agent gains shrink or vanish under Haiku~4.5 and Sonnet~4.6 & (a) on $F_1$, loops 1 and 3 (loop 2's agent
not run); change of gain, loop 3's agent: $\vhfiveKThree$ [$\vhfiveKThreelo$, $\vhfiveKThreehi$], $\vhfiveSThree$
[$\vhfiveSThreelo$, $\vhfiveSThreehi$]; loop 1's: $\vhfiveKOne$ [$\vhfiveKOnelo$, $\vhfiveKOnehi$], $\vhfiveSOne$
[$\vhfiveSOnelo$, $\vhfiveSOnehi$] & supported only for loop 3 under Sonnet~4.6 \\ \midrule
H6 best textbook combination $\geq$ best first-round loop agent $-3$ (and cheaper) & (a) chosen on $F_1$
(\vHsixWinner), on $F_2$: $\vHsixFtwo$ [$\vHsixFtwolo$, $\vHsixFtwohi$]; literal, best on all of $F$ (\vhsixLitBest; chosen and scored on the same problems):
$\vhsixLit$ [$\vhsixLitlo$, $\vhsixLithi$], seed-adjusted $\vhsixLitAdj$ [$\vhsixLitAdjlo$, $\vhsixLitAdjhi$]; (a)
pre-specified single candidates on all of $F$: all four moves $\vpsEBLPRaw$ [$\vpsEBLPRawlo$, $\vpsEBLPRawhi$], L
$\vpsLRaw$ [$\vpsLRawlo$, $\vpsLRawhi$]; all cheaper & not supported; literal reading supported on raw scores, not
after seed adjustment \\
H7 random-diagnosis loops $\geq$ first-round DGM loops $-3$ (mean fresh gain) & $\vhRandomMinusDgm$ [$\vhRandomMinusDgmlo$,
$\vhRandomMinusDgmhi$]; (p) vs six DGM loops $\vhRandomMinusDgmAll$ [$\vhRandomMinusDgmAlllo$, $\vhRandomMinusDgmAllhi$]
& not supported \\
H8 best of five one-shot redesigns $\geq$ best loop agent $-3$; mean redesign $\geq$ mean loop best $-3$ & (a) best on
$F_2$: $\vHeightOpusbest$ [$\vHeightOpusbestlo$, $\vHeightOpusbesthi$]; literal, best on all of $F$:
$\vheightLitOpusRaw$ [$\vheightLitOpusRawlo$, $\vheightLitOpusRawhi$]; mean: $\vHeightOpusmean$ [$\vHeightOpusmeanlo$,
$\vHeightOpusmeanhi$] & best: not supported; mean: supported \\
H9 two edits carry $\geq 80\%$ of a loop's fresh gain & loop 1 has exactly two edits; for loop 2 half and for loop 3
all but one of the leave-one-out variants do not apply & not testable (loops 2, 3) \\
H10 seed $+$ textbook moves ($+$ retry) $\geq$ published best $-3$ on fresh tasks & (a; pilot results known) DGM
SWE-bench with Sonnet~4.5, moves: $\vsweMovesMinusBest$ [$\vsweMovesMinusBestlo$, $\vsweMovesMinusBesthi$] as run,
$\vsensMovesMinusBest$ [$\vsensMovesMinusBestlo$, $\vsensMovesMinusBesthi$] with early-ended patches kept; moves and
retries: $\vsweRetryMinusBest$ [$\vsweRetryMinusBestlo$, $\vsweRetryMinusBesthi$] and $\vsensRetryMinusBest$
[$\vsensRetryMinusBestlo$, $\vsensRetryMinusBesthi$]; ADAS (CoT-SC vs agent): holds on MGSM, DROP, MMLU, fails on
GPQA; HGM and DGM Polyglot not run & (a) supported for DGM SWE-bench; 3 of 4 for ADAS \\ \bottomrule
\end{tabular}\end{table}