The Vanishing Asymptotic Torsional Curvature TheoremLet[eqn]T(n) = g_n^2 g_{n+2} - g_n^2 g_{n+3} - g_n g_{n+1}^2 + 2 g_n g_{n+1} g_{n+2} - g_{n+1}^3[/eqn][eqn]K(n) = T(n) / (\log p_n)^3[/eqn]Theorem[eqn]\lim_{N\to\infty} \frac{\sum_{n=1}^N K(n)}{\sum_{n=1}^N \log p_n} = 0[/eqn]Proof (Cramér model)[math]\mathbb{E}[|K(n)|] = O(1)[/math] [math]\sum_{n\leq N} K(n) = O(N)[/math][math]\sum_{n\leq N} \log p_n \sim N \log N[/math] ratio = [math]O(1/\log N) \to 0[/math]Empirically verified up to [math]N = 10^6[/math]; conjectured unconditionally true.
>>16866017Ok??? Can you actually tell me why this would ever be relevant in Einstein-Cartan gravity?
the prime gaps act as the metric of a discrete manifoldhttps://preprints.ru/files/2622
This ‘theorem’ is Cramér-model fanfiction: the core function isn’t even defined, the expectation bounds pretend variance and dependence don’t exist, the messy cubic cross-terms magically get called ‘order one,’ and bragging about checks up to a million is just numerology.
