The proof had to be con- tinually modified and aided by intri- cate analysis and geometry.
After years of effort, the referees gave up. Mean- while, Hales and the world were waiting for the ref- erees' conclusions. Annals finally decided on an un- precedented course of action: to publish the work with a disclaimer that the referees had been unable to verify the proof.
--- end quote ---
Well at least some good news by math journal publishers, is that sometimes they do act responsibly, only in the case above, not responsibly enough.
Publishers had been burned by the publication of the Hsiang fakery Kepler Packing. So to have been real responsible editors, they should not have published Hales offering at all, even with a disclaimer.
What the editors should have done was ask Hales to detail why he does not use a definition of density as kissing point density and to detail why that density does not work, because as we see from real mathematicians on Kepler Packing of recent:
--- quoting from --- Nature 460, 876-879 (13 August 2009) Dense packings of the Platonic and Archimedean solids S. Torquato & Y. Jiao (snip) Platonic solids (the tetrahedron, octahedron, dodecahedron and icosahedron) in three-dimensional Euclidean space. The densities are 0.782..., 0.947..., 0.904... and 0.836..., respectively. (snip) Combining our simulation results with derived rigorous upper bounds and theoretical arguments leads us to the conjecture that the densest packings of the Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This is the analogue of Kepler's sphere conjecture for these solids. --- end quote ---
What S. Torquato & Y. Jiao reveal in their data is that we must use KISSING POINT density as the definition, not Container Density.
So let Hales write a paper detailing all his objections to defining density as kissing point density.
Because in Container Density, Hales never tell us a precision definition of where finite ends and infinity starts in order to use a Container Density definition.
As I said earlier today, Hales is a case study fanatic, but Hales never understood that a proof in mathematics is never a collection of case studies. A proof in mathematics can be assisted by knowing some cases of the statement to be proved, but the proof is not a summation of cases. Because a statement to be proven in math, never comes screaming to you-- I have 27,003 cases and I am proven. But try telling that to Hales.
So mathematics is learning the hard way for it gave into the fakery of Appel & Haken on 4 Color Mapping and the fakery of Wiles on FLT and the fakery of Hsiang on Kepler Packing, but it left a disclaimer on Hales's fakery of Kepler Packing.
They should have done the right thing and tossed it out, because too many people in and out of science, once they hear something is in print published, no matter if true or a fakery, they believe it is true. To people are not scientists or weak in science, their mantra is not truth, but publication.