This 28-page paper by Le Gall lowers the best-known estimate for the asymptotic complexity of matrix multiplication from $O(n^{2.3728642})$ to $O(n^{2.3728639})$, a reduction by 0.00001%. However, it simplifies the previous method, so it does not really qualify as "notably long or difficult proof". Maybe this definition applies more to the previous improvement in a paper by Vassilevska-Williams, which brought down the exponent from $O(n^{2.374})$ to $O(n^{2.3728642})$

This 28-page paper by Le Gall lowers the best-known estimate for the asymptotic complexity of matrix multiplication from $O(n^{2.3728642})$ to $O(n^{2.3728639})$, a reduction by 0.00001%. However, it simplifies the previous method, so it does not really qualify as "notably long or difficult proof". Maybe this definition applies more to the previous improvement in a 73-page paper by Vassilevska-Williams, which brought down the exponent from $O(n^{2.374})$ to $O(n^{2.3728642})$

This 28-page paper by Le Gall lowers the best-known estimate for the asymptotic complexity bound of matrix multiplication from $O(n^{2.3728642})$ to $O(n^{2.3728639})$, a reduction by 0.00001%.

This 28-page paper by Le Gall lowers the best-known estimate for the asymptotic complexity of matrix multiplication from $O(n^{2.3728642})$ to $O(n^{2.3728639})$, a reduction by 0.00001%. However, it simplifies the previous method, so it does not really qualify as "notably long or difficult proof". Maybe this definition applies more to the previous improvement in a paper by Vassilevska-Williams, which brought down the exponent from $O(n^{2.374})$ to $O(n^{2.3728642})$