This is an utterly brilliant hack for dimensionality reduction leading to pattern recognition. That it even beats SVMs (albeit with a single carefully chosen example ;-) is icing on the cake.

One thing I don't understand is the addition of the constant 3 to the row index (in the paper just after formula 6). Intuitively this should be only 2, because the last row vector of the local topology lags the last state captured in the distance matrix by one row, and then we want to move ahead one more row to start forecasting.

What am I missing?

Isn’t it because m = n - 2 (above equation 4) and you want to get to n + 1?