additive transition function, new smooth time stepping mode (fail)

Concerning the search for the generic smooth time stepping mode, I came up with an intriguing idea today which nonetheless failed, as of yet. Remember that like in the original GoL for SmoothLife with discrete time stepping we consider snm the new function value for each time step. So for snm to be an additive value one has to consider the analog in the original GoL first! That was my idea today. I haven't tried it explicitly, but it is straightforward. Just imagine instead of setting cells to 0 or 1, subtracting or adding 1 appropriately. These would be the rules of additive GoL:

• if a cell is 0 then add 1 if it has 3 neighbors
• if a cell is 1 then subtract 1 if it has less than 2 or more than 3 neighbors

(leave it as it is in all other cases)

Unlike in all previous attempts, this is directly translatable into a smooth, continuous snm!
We take our discrete snm and lower the death-end by 1, i.e. subtract 1 there. So if the value is outside the d1,d2 interval, 1 is subtracted. If it is inside, nothing is added or subtracted, it stays the same, namely 1. Likewise at the birth-end, if it is outside the birth interval it stays 0, if it is inside, 1 is added. Of course there has to be a smooth interpolation in between, but we already have many ways to do that. We can use our smooth step functions for this.

To make a long story short: I tried it, but sadly it lead to unsatisfactory results. Nothing spectacular. Maybe I did something wrong, maybe I'll try again one day. But for now I consider this path as leading to nothing.