And any idea how to decode WTF this is saying?

Yeah, it kinda makes sense after a couple of reads. f() is a boolean fn of n bits, and w is a vector of weights. If you can find weights and T, such that the dot product of (the boolean inputs X and the weights) >T exactly when f(x) is true, then it's a threshold function. The weights and T together define a plane in the truth table hypercube, and the truth table is all T on one side of the plane, and all F on the other side. An XOR of the inputs is an example that's NOT a threshold function.

It somehow reminds me of lattice geometry and lattice cryptography