1\setlength{\tabcolsep}{4pt}\begin{tabular}{@{}lL{7.2cm}llL{2.2cm}@{}}2\toprule3id & statement (abridged) & registered & status & holdout (6 values)\\4\midrule5H0 & Null hypothesis: every exact value of $Z(P(n,5))$ is already published. & 18:00:31 & refuted & n/a\\6H4 & Small-$n$ exceptions: $P(11,5)$ and a few further small $n$ deviate from the eventual value. & 18:00:31 & computationally tested & n/a\\7C1 & $Z(P(n,5))=12$ for every $n\ge 26$. & 18:00:31 & proved & 6/6 pass\\8C2 & Threshold $n_0=23$; $Z(P(22,5))=11$; $Z=6,8,9,8,8,8,10,10,10,10,10,11$ for $n=11,\dots,22$. & 18:00:31 & proved & 6/6 pass\\9C3 & Eventual periodicity (H2): $Z(P(n,5))$ is eventually constant (period $1$), not dependent on $n \bmod m$ for $m\in\{2,3,4,5,6,8,10,12,24\}$. & 18:00:31 & proved & 6/6 pass\\10C4 & Tightness (H3): for every $n\ge 26$ the first-force bound with $p=18$ equals $Z$ (both $12$); for $n=25$ every $p\le 24$ fails. & 18:00:31 & computationally tested & 6/6 pass\\11C5 & $\beta_{16}(n)\le 11$ for every $n\ge 22$: the $k=4$ parameter $p=16$ never certifies $Z(P(n,5))\ge 12$. & 20:33:36 & proved & n/a\\12\bottomrule13\end{tabular}14