The Riemann hypothesis is false. The follwoing doesn't prove that it is false but gives a gist of the proof to show that the Euler product has non-trivial zeros of the critical line.

Consider a number $z_0\in\mathbb{C}$ such that
$$z_0=-(\aleph_\mathcal{X}+b)+iy~~,\quad\text{where}\qquad b,y\in\mathbb{R}_0~~.$$
Observe that the Euler product form of $\zeta$ takes $z_0$ as
$$<br /> \zeta(z_0)=\prod_{p}\cfrac{1}{1-p^{(\aleph_\mathcal{X}+b)-iy}}\nonumber\\<br /> = \left(\cfrac{1}{1-P^{(\mathcal{X}\aleph_1+b)-iy}} \right) \prod_{p\neq P}\cfrac{1}{1-p^{(\aleph_\mathcal{X}+b)-iy}} \nonumber\\<br /> =\left(\cfrac{1}{1-\cfrac{\vphantom{\hat1}1}{P^b}\big(P^{\mathcal{X}}\big)^{\!\widehat\infty}\left[ \cos(y\ln P)-i\sin(y\ln P)\right]} \right) \prod_{p\neq P}\cfrac{1}{1-p^{(\aleph_\mathcal{X}+b)-iy}} \nonumber~~.$$
Let $y\ln P=2n\pi$ for some prime $P$ and $n\in\mathbb{N}$ or $n=0$. Then
$$\zeta(z_0)=\cfrac{1}{\infty} \prod_{p\neq P}\cfrac{1}{1-p^{(\aleph_\mathcal{X}+b)-iy}}=0~~.$$

SHORT
Quick Disproof of the Riemann Hypothesis
https://vixra.org/abs/1912.0030

MEDIUM
Zeros of the Riemann Zeta Function Within the Critical Strip and Off the Critical Line
https://vixra.org/abs/1912.0030

LONG
Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://vixra.org/abs/1906.0237

OLD
On The Riemann Zeta Function
https://vixra.org/abs/1703.0073