I can't find any material about this subject even though I'm sure I have posted about this before :) the gist of the long gamma/short gamma threshold that I publish is this:
1. Below the threshold, SPX option dealers are short gamma in the aggregate.
2. Above the threshold SPX option dealers are long gamma in the aggregate.
That is important because:
1. Long gamma hedging always happens against the market. In other words if the market moves up, dealers have to short to become neutral, if the market moves down, dealers have to buy to become neutral. A long gamma regime dampens volatility because dealers are softening the moves.
2. Short gamma hedging always happens with the market. In other words if the market moves up dealers have to go long to be neutral. If the market falls dealers have to go short to become neutral. As you can see a short gamma regime increases volatility because dealers are now amplifying the moves.