Why does packing exactly 992 circles in a square behave exceptionally? It is not so surprising that the problem of Circle packing in a square is a chaotic and often-unpredictable problem. However, after looking over the data on hydra.nat.uni-magdeburg.de, we find quite the anomaly.
Here is a graph of the first ~1000 densities of the best known solutions.
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The graph is perhaps unsurprisingly chaotic, beit with some patterns, of course. However, Something incredibly unusual / significant seems to happen at number 992.
Below I've added its solution, compared to known neighboring solutions.

Noticeably, it's rather regular, especially compared to it's neighboring solutions. This is likely the cause for the sudden change in density. Of course, the exact densities are subject to change, as better solutions are found. But even if new solutions are found at and near 992, I seriously doubt this anomaly will go away, given its relatively huge gap in the sequence, and the already enormous computation done over the years that went into this data. So my wondering is,

What is so special about 992 and its local neighborhood of solutions, that allows for it to have such a regular (yet inefficient) solution, and drop in density? Is it as simple as the fact that we haven't found a better solution, up to par with the others? Or is it just special, given that it's of the form $n(n+1)$, or of some other "nice" property?


It appears that the table contains errors (or at least obviously inferior solutions).  The maximum radius should never increase, as it does from $n=990$ to $n=991$:
990 0.016463423221309863655952299335
991 0.016714637930021076293666393417

You can trivially improve the given $n=990$ solution by arbitrarily removing any circle from the $n=991$ solution, preserving the larger radius.
And again from $n=992$ to $n=998$:
992 0.015873015873015873015873015873
998 0.016670442622470923459332814794

You can trivially improve the given $n=992$ solution by arbitrarily removing $6$ circles from the $n=998$ solution, preserving the larger radius.
