diff d1913c1..f6bf760 euclidean_plane_not_five_colorable_v2.txt
diff --git a/euclidean_plane_not_five_colorable_v2.txt b/euclidean_plane_not_five_colorable_v2.txt index efb7bb7..ce16a8f 100644 --- a/euclidean_plane_not_five_colorable_v2.txt +++ b/euclidean_plane_not_five_colorable_v2.txt @@ -170,28 +170,4 @@ HOW TO SPOT A PAPER LIKE THIS None of these proves the paper wrong. But they justify treating its conclusion as a claim, not a fact. -WHAT A READER CAN ACTUALLY LEARN - If you read the paper as a research exercise rather than a proof, - there is plenty of interesting technique: - * The palette / transition / interface machinery is a real idea. - De Grey's 2018 lower bound uses variants of the same shape. - * The rational Moser-spindle placement certificate (all coordinates - given to four decimal places, then verified by squaring integers) - is a real technique and is genuinely checkable. - * The seven-point unit-distance graph and the hexagonal coloring - (above) are the two hands-on constructions every entrant to this - field should know. - -BOTTOM LINE - Actual state of the art: 5 <= chi(R^2) <= 7, open. - Any document claiming chi(R^2) >= 6 is claiming-but-unverified. - The one in euclidean_plane_not_five_colorable_original.txt is such a - document. It should NOT be given to a student as if it were correct. - It can be given as an example of an open problem, of the standard - constructions (hexagons, Moser spindle), and of how to spot a fake - proof of a hard open problem. - - For real math: read the hexagon coloring and the Moser spindle. Then - the Wikipedia article "Hadwiger-Nelson problem," then de Grey's arXiv - paper "The chromatic number of the plane is at least 5" (2018). - Those are honest. +