This is great! I have some comments.
B.1. As you may recall, the approval production bonus is multiplicative, not additive. I believe for influence it is additive as you indicate in your formula (see C)
B.2. Here is a screenshot of my highest influence planet (turn 619). Note that my *current influence* is 1384.3, and my *influence bonuses* bring it up to 2491.7. I think you are right that there is no limit. Or rather, I haven't found it yet, it seems.
C. In my graphic above you can see 3 culture rings each adding a 10% *influence bonus*. I actually have 4 in the area, but only 3 cover my planet. So the initial "Culture Ring" starbase has that immediate effect.
The 3 starbases have been upgraded to Interstellar Embassies, each granting 100% *influence growth*. My planet has +10 gb (colony capital + 3 outreach centers). I have 100% approval (another 50%) and adjacency bonus gets me another 30% *influence growth*. So
10 gb * (1 + 3.00 + 0.5 + 0.3) = 48.0 *influence growth*
This is reflected in the map view:
Also you can see in the above screenshot the growth for the planet I'm hoping to flip. Since my growth per turn is over 7x the enemy's, assuming 4x is needed to flip and assuming starbases only affect *my* planet's influence, and assuming no decay penalty (lots of assumptions, some probably not sound), I would eventually flip this planet.
Culture Ring says it has "Influence Growth +1" in addition to the 10% planet bonus.
I also want to point out that while I have owned Embor II for a while, I only added the consulates within the last 100 to 200 turns. Embor III, however, has probably been colonized for around 500 turns, so it has built up a rather large bank of influence that I need to overcome.
F. The GC2 conjecture about planet flipping, I may be wrong but I believe the mechanics were once you hit 4x and maintained at least 4x for 10 turns, after that there is an independent non-zero probability of flipping on each subsequent turn.
Now here are some of my conclusions based upon your work and my experience:
* With the current available starbase modules it is neigh-impossible to culture flip using just starbases if I do not hold a nearby planet. I say that because starbases have, at best, very low base points, thus little for the starbase module *influence growth* bonuses to multiply. I could stack several around the nearest (but still far) planet, but because of decay I get diminishing returns.
* Even if starbase modules did give base points, it would have to be A LOT to culture flip in a reasonable amount of time.
* The larger the map, the less viable culture-flipping becomes, because the more distant planets will have built up influence for a long time.
* Based upon all this, I believe the "clock" idea is a bad one. At the very least the numbers are widely out of balance. The longer a game goes before you are able to start your culture bomb in a given area, the more time it takes to flip. This could make for some VERY long and boring games, which is out of balance with the other victory conditions.