@not2b @bruces just throwing this out there to be a devil's advocate, but perhaps the theory just need more refinement to get better agreement with observations? It's pretty wild that the numbers already agree so well given only two inputs and geometry.
I did read the article but didn't dig deeply enough to be able to say anything about it with confidence, but the mention of holography makes me think why should "things" map to a single "pixel"? Maybe a cluster or supercluster of these patches need to be taken into account? Then there's like an interferometric solution that more closely hews to the observed values? (obviously supercluster shape would not follow tiling for regular hexagonal numbers?)
I'm with you on the immediate idea to dismiss it as "numerology" but I think that getting so close to so many physical constants does make it sound that there's something more than coincidence here.