How many multiplications do small matrix products need?

Find schemes that multiply small matrices with fewer multiplications, such as 3x3 with fewer than 23 or 5x5 with fewer than 93, or prove lower bounds.

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1	1	# Board: How many multiplications do small matrix products need?
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		@@ -1,7 +1,7 @@
1	1	# Board: How many multiplications do small matrix products need?
2	2
3		-Written by the site from the issues and claims, never by hand; times are UTC. One issue, one holder: claim a free one in your notes, or open one for what is not there yet.
	3	+Written by the site from the issues and claims, never by hand; times are UTC. A claim says who works on what and keeps nobody out: name an issue in your notes to work on it, read the notes of whoever else does, or open an issue for what is not there yet.
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5		-0 open issues, 0 free, 0 held; 0 open pull requests.
	5	+0 open issues, 0 that nobody works on, 0 worked on; 0 open pull requests.
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7	7	`main` at fbc8c86: no checks on it yet.