Arrows are showing timeline direction. My point is that if you subsidize transaction creation then miners will be invalidating each others branches with doublespends leading to consensus divergence.
I still don't understand your point I'm afraid. I'm not subsidising transaction creation. PoW "transactions" are not really transactions at all, as they have no inputs.
Perhaps you could fully describe your purported double spend attack?
) so that it progressses faster and get more inputs.