a week ago i chatted with @AchimWar about favourite problems and the caratheodory conjecture came up. i literally wanted to just read about it but i did see the complicated literature situation and so in hopes i could help asked him if it was ok to look at with a model. me, John-Paul Smith, and of course claude checked and (i hope im being a better citizen, hadamard led to a lot of flaming) i sent over a pdf writeup, and for the past week it’s circulated round. i did wanna have it recorded somewhere public though so i’ll try to again give a form certifiable by models
C^\infty caratheodory and loewner are false, let f(x + iy) := -\cos(2x) / 4 + 3\cos(2y) / 10 - \cos(4y) / 32 + \sin(x)\sin(y), and, for k\in \Z^+, g_k(z) := |z|^2 e^{-|z|^{-1/4} e^{-|z|^2}} f((100 / \bar{z})^{k/2}) / (1 + |z|^2) + 10^{10}. then g_k has an index 1 + k/2 umbilic point at 0, and g_2, regarded as C^\infty on S^2 = \P^1(\C) thanks to the e^{-|z|^2}, is the support function of a convex body with exactly one umbilic point.
- a week ago i chatted with @AchimWar about favourite problems and the caratheodory conjecture came up. i literally wanted to just read about it but i did see the complicated literature situation and so in hopes i could help asked him if it was ok to look at with a model. me, John-Paul Smith, and of course claude checked and (i hope im being a better citizen, hadamard led to a lot of flaming) i sent over a pdf writeup, and for the past week it’s circulated round. i did wanna have it recorded somewhere public though so i’ll try to again give a form certifiable by models C^\infty caratheodory and loewner are false, let f(x + iy) := -\cos(2x) / 4 + 3\cos(2y) / 10 - \cos(4y) / 32 + \sin(x)\sin(y), and, for k\in \Z^+, g_k(z) := |z|^2 e^{-|z|^{-1/4} e^{-|z|^2}} f((100 / \bar{z})^{k/2}) / (1 + |z|^2) + 10^{10}. then g_k has an index 1 + k/2 umbilic point at 0, and g_2, regarded as C^\infty on S^2 = \P^1(\C) thanks to the e^{-|z|^2}, is the support function of a convex body with exactly one umbilic point.
Whats up with all the words? I miss the proper leventposts already
Are X links actually permanent? We would like to cite them in the future and put in the library of humanity. Congratulations and looking forward to the actual paper!
amazing! would be very cool if you can take a shot at this problem - mariokrenn.wordpress.com/graph-theory-q… it has a lot of implications to quantum resource theory. verification is also easy as we fully formalized it in leanI see a lot of vibe-mathing giga chads getting interested in graph theory conjectures. So here's a conjecture with a 3000 USD cash reward for y'all to have fun. The problem is also formalized in lean, so you dont have to worry about correctness once you want to claim a proof!
