David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.
Disorder Persists in Larger Graphs, New Math Proof Finds
Quanta Magazine, good stuff.
Is this related to relative prime theory? Can we take the Ramsey graph coloring problem and revert that to a layered co prime bandwidth allocation.
This is what I think, there is a limit as co prime n where the counter needs another coprime. The Ramsey coloring problem is the same as the quark coloring problem, both boil down to running out of bandwidth in dimension three and bumping into dimension four, and we get superposition on reversion, patterns.
There is a maximum entropy point, a point where three coprimes do not contain the accuracy to count small integers. SO a lot of this algebra, polynomial, finite approximation stuff gets packed into the n-tuple trees. Each node on one of these trees make a salad bolt which can be flattened to circular Lie paper. Then if anyone wants, they can extend this to non maximum entropy which would include repeating spiral trips about the Lie angles, it doesn't close and leaves a noticeable moment in the distribution of errors. These are aliasings.
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