The gold sale cap is all the evidence you need.
In January it fell out at 0.25/million
Now it is 0.0296 per million
Gold was worth approx 8.4x as much in January as compared to the US dollar.
Since items and gold are exchangeable and items vs dollars are exchangable, hyperinflation of diablo gold has indeed happened.
Now at the same time, as time goes by, better and better items are found and the "top tier" of items gets a new standard every few months, so while items with a particular stat may go down in price, this doesn't mean that hyperinflation did not occur.
Compare a relatively constant wealth medium: Radiant Stars.
In january a radiant star emerald was around 2.60
Now they are 0.81
So while gold was worth 8.4x as much in January, gems were only worth 3.2x as much.
This tells us 2 things,
1) gold is not a viable currency (probably because it can be botted easily)
2) no matter how you look at the facts, you cannot deny inflation. Even conservatively 320% inflation when looking at gems.
See, but that's the thing. No one can deny that the exchange rate between external currencies (dollars, euros) is inflating. I'm sorry if I gave the impression that I did. But the internal economy, the exchange between items and gold, that's been incredibly stable. This is reflected in the changes in exchange rates. Your numbers were incorrect: these were the average exchange rates in January:
1 RS Emerald = $6.86 (RMAH)
1 RS Emerald = 28.5m gold (GAH)
28.5m gold = $7.38 (RMAH)
And this is right now:
1 RS Emerald = $0.64 (RMAH)
1 RS Emerald = 25m gold (GAH)
25m gold = $0.73 (RMAH)
One RS Emerald has cost between 23 and 28m gold for most of 2013. A significant part of that is fixed crafting costs, but removing those from the equation still gets us a range of 8m-13m, with short term fluctuations and long term stabilty. This in turn means that gold is in fact an excellent
currency for Diablo 3. If you had 1b gold in January, and 1b today, you would be able to get roughly the same kind of items.
The fact that the dollar value of that gold has dropped in that time is irrelevant if you're just interested in playing the game. This is not a financial market or an investment vehicle to make profit on. This is a game.
If you're really rich though, this does cause a legitimate problem, which I did not recognize when I made my previous post. For the ultra-high end market, gold is not the primary currency, because of the 2b trade limit. Prices are therefore measured in dollars, and since the dollar : gold exchange rate has been dropping for most of Diablo 3's history, I was totally wrong about high end inflation.
 Source: http://www.diablohub.com/price-tracker/
 Radiant Star Emeralds dropped to as low as 5m gold in October 2012. Whoever bought at those prices would've made a killing
come January. (This baffles me, by the way. If anyone has an explanation for this I'd be interested to hear it.)
 That said, look at the dollar value of gold since late May: significant fluctuations, sure, much more than for gems. But, again, no discernable trend. Maybe things are stabilizing?