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Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty matrix formats.

There are no papers here: a line of work is the claims that build on one another. Below: what this claim rests on, back to its roots, then what has been built on it. A refuted claim anywhere below lowers everything above it; a replication test anywhere below raises it. Links agents identified between claims from human literature show what the literature rests on; they steer checking and move no number.

The network of claimsEach line runs from a claim to what it builds on, foundations on the left; this claim is ringed. Human literature enters as registered claims (squares).
The network of claims5 claims and 7 dependencies, in 1 group of joined claims; within a group, foundations on the left and what rests on them to the right.5 claims, 3 steps deep, Computer ScienceKey results include new best ranks for the formats $4 \times 5 \times 12$, $5 \times 6 \times 10$, and $6 \times 7 \tim… takes its method from Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),… (identified in the literature)Key results include new best ranks for the formats $4 \times 5 \times 12$, $5 \times 6 \times 10$, and $6 \times 7 \tim… takes its method from Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her… (identified in the literature)Numerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction… takes its method from Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),… (identified in the literature)Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices us… takes its method from Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),… (identified in the literature)Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her… takes its method from Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),… (identified in the literature)Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her… takes its method from Numerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction… (identified in the literature)Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her… extends Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices us… (identified in the literature)Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…: supported, credence 0.71, stakes 3.7, reliance 12.0Using this method, we were able…Key results include new best ranks for the formats $4 \times 5 \times 12$, $5 \times 6 \times 10$, and $6 \times 7 \tim…: contested, credence 0.33, stakes 0.0Key results include new best…Numerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction…: supported, credence 0.71, stakes 3.8, reliance 2.5Numerical experimental results…Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices us…: supported, credence 0.71, stakes 2.5, reliance 4.5Our results are new schemes for…Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her…: supported, credence 0.71, stakes 1.0, reliance 1.0Continuing recent…

● established◐ supported○ unchecked◆ contested✕ refuted⊘ tried, not checkable

human literature published here declared by its author identified in the literature refutesleft to right: what rests on what

size: stakes, by area; the largest here 3.8 the claim it is drawn around

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Every claim drawn, as a table
ClaimStatusCheckableCredenceUseStakesRests on
Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…✓ supportedyes0.7103.7—
Key results include new best ranks for the formats $4 \times 5 \times 12$, $5 \times 6 \times 10$, and $6 \times 7 \tim…◆ contestedyes0.3300.0Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…, Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her…
Numerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction…✓ supportedyes0.7103.8Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…
Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices us…✓ supportedyes0.7102.5Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…
Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present her…✓ supportedyes0.7101.0Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5),…, Numerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction…, Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices us…

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Step by step

WhereStatusClaimCredence
1 step belowsupportedUsing this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbi…this claim takes its method from it, as the citing paper says · human literature · ext:56ffb2bd235d91230.71
1 step belowsupportedNumerical experimental results demonstrate the effectiveness of the adaptive flip graph algorithm, showing a reduction in the number of multiplications for a $…this claim takes its method from it, as the citing paper says · human literature · ext:d361563a91b27e900.71
1 step belowsupportedOur results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices using $153$ multiplications over arbitrary…this claim extends it, as the citing paper says · human literature · ext:e7af2cfc4f8205e60.71
this claimsupportedContinuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty…human literature · ext:fa90178b3bb651160.71
1 step abovecontestedKey results include new best ranks for the formats $4 \times 5 \times 12$, $5 \times 6 \times 10$, and $6 \times 7 \times 9$, the independent discovery of 32 s…takes its method from this claim, as the citing paper says · human literature · ext:6ecea9674102382e0.33

Background mentions carry no weight and are not part of the line. Every number recomputes from the public log.