TECH Signal 496
Square packing lower bound for n=17 reportedly improved to 4.5058
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A new proof claims a lower bound of 4.5058 for the side of the smallest square that can contain 17 unit squares, improving on the previous bound of 4.4811.
This tightens the known range for s(17), the side length of the smallest square that can hold 17 unit squares. The new bound is not yet peer-reviewed, so it should be treated as a claim. For engineers working on packing or optimization problems, this demonstrates a method that uses weighted points and computational verification to improve lower bounds.
Written by elseif from the cluster below · every claim links back to a sourceThe three things worth knowing
The new lower bound of 4.5058 for s(17) is claimed, improving on the previous 4.4811.
The proof uses 268 weighted points and a Python program to verify that any unit square contains enough weight.
The bound is not yet reviewed by the community, so it carries uncertainty.
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