Rayz, you ask “So how come he admits that his calculations are...

Rayz, you ask “So how come he admits that his calculations are not right even wrote a publication on why it's not completely right.”
The paper that you refer to deals with a different situation from that which was the focus of Gy’s first papers, and different from the situation of sampling material containing gold nuggets.
The paper you refer to deals with the situation where a sample that is of inhomogeneous composition on a significant scale (in relation to the assay sub-sample size) can be homogenised by fine grinding. But you can’t fine grind nuggets, Simple.
Gy’s initial work dealt with the nugget effect and the size of the initial sample that must be taken in order to obtain a reasonably representative sample. If a sample isn’t representative, then any subsequent testing is invalid. The paper you refer to deals with a situation where an inhomogeneous original sample can be treated by reducing the size of the “nuggets” (which are large particles, but not gold nuggets) by grinding or similar (comminution) so that the inhomogeneity (related to the particle size) is reduced to the extent that the assay sample meet Gy’s original criteria.
In other words, Gy’s original criteria relate to the size of the primary sample. The paper you have referred to applies where the “nuggets” in the primary sample can be reduced in size so that assay sub-sample will contain a statistically adequate number of smaller “nuggets” of inhomogeneous material (but not gold nuggets because these can not be ground up by any practical method).