When an empire has researched a technology, within 15 days every other empire will be compared:

• First, the triggering empire must have at least 5% less tech than the one we're looking at, otherwise nothing will happen (this comparison uses the game "tech ratio").
  The idea is to prevent tech-behind empires to just get better techs than their tech-ahead neighbors. The mod is there to prevent them to get completly dropped behind, to give a chance to catch up, nothing else!
  
  
• We start with the value "1".
  
  
• If empires have a commercial pact, a factor of 0.15 will be added. If it's a migration treaty or a research agreement, respectively 0.22 and 0.33 instead (does not add up!). Otherwise 0. Also, non aggression pacts & defensive pacts were added in a later version, for values of 0.075 & 0.22.
  
  
• If both empires are in the galactic community, add the following bonuses: 0.075, 0.05 or 0.025, if you have respectively excellent, positive or just non-hostile/non-rival relations.
  
  
• Finally, if empires are neighbors with open borders, multiply the number by 2. Divide by 4 if they are instead neighbors with closed borders / hostile relations. Neighbors rivals gets nothing again.
  
  
• Now, if total score is >= 1, substract the initializing 1 value. If it's now equivalent to 0, nothing else to do: no multiplier to apply, no bonus.

If we do have something to apply, we just add the tech ratio and we have the final multiplier! (ie: if you have 10% less tech, you have 0.10 more added to the total number. If you have less than half the techs, like 40% of what they have ("pathetic" ingame), then 0.60 etc.).

The triggering empire will get, as research bonus point, half the difference research points between the two empires, multiplied by the number we just got.

I later added a few "hardcoded limits" to prevent crazy situations, like obtaining +3k points in research while you only have +100. Indeed, per checked empire, you can obtain only twice your own production (if it's a neighbor, half of that otherwise) and you can only obtain up to 6 times your own production as total bonus.


The difference research points between the two empires is halved so you can never get more research than this specific empire, and so investing in research infrastructures will only reduce the bonus received by 0.5 for each new point you get.
So developping your own research is still encouraged - and recommended, you never know what will happen to that specific tech-neighbor or your good relations! Also with the later additions, enhancing your own research means higher hardcoded limits!

Here's a real world example: if you are behind in tech with +100 in physics and a neighbor has +200, you will gain a multiplier off 50 points - for example with only a migration treaty it's 0.22, so you get +16 if you are 10% behind in tech ((0.22+0.1) * 50), or +21 if you are 20% behind. A 20% bonus of your own production if you are 20% behind is quite good right?
Keep in mind you can obtain these bonuses from each empire in the game with the same tech gap & treaty.

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You may have noted that, since one part of the multiplier is determined by diplomacy, which is quite "fixed" (let's call it the "diplomacy multiplier") and the second part is linear depending on the tech ratio, that means you'll earn statistically more if you are closer to them in tech than far behind.
That was completly sought here: the more you are behind, the harder it gets to understand the wonders they have! You do not get less points the further you are, but you get less percentage increase. This is even more true with the latter additions and the "relative hard caps".

• The biggest achievable "diplomatic multiplier" is 1.81: a neighbor with open borders, excellent relations, inside galactic community and with a research treaty. That means it is hard to get more than the research point difference but it is possible through the tech ratio: you have to be 20% behind in tech in this example, which is already a big gap by mid-game!
  Let's take this example the other way: say you are 50% behind (they are nearly "overwhelming" you), you then need a diplomatic ratio of 1.5 => this is not achievable without an open-border neighbor, again. The diffusion is intended to happen mostly through borders indeed!
  
  
• The maximum you can get from a non-neighbor is 0.33 + 0.075, ie: 40.5% (of half the difference research points). So yeah, I kinda lied when I said previously that opening borders is equal to double bonuses. It's actually 1 + double bonus.
  
  
• The lowest multiplier (besides 0) while neighboring is 0.25, when they have closed border but aren't rival or hostile, without any treaty and one of the empire isn't part of galactic community.
  
  
• The absolute lowest non-neighbor without enigmatic engineering is 0.025 from a non-rival non-bordering fellow galactic member without treaties.
  Yes that means every non-hostile member in the galactic community "gives" 2.5% wether they closed or opened their borders with you. That number could seem high (especially on big galaxies with 30-40 AIs) but rest assured it's only >2% of half the tech points difference< IF you are behind, that's not much. A (not that hard to get) research treaty with one of the "big players" will earn you much more!
  
  
• If you do not want empires to get bonuses from you, close your borders with your neighbors or use enigmatic engineering. Thus you'll divide by 4 what diplomatic bonuses they can get. That means 0.625% for the case we saw just above, 1.875% for each galactic member with excellent relations and no treaties, and 45% for the biggest achievable outcome with a neighboring ally!

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Note you may see that the galactic technological progression will be a bit faster than vanilla, not that researching will happen quicker but empires which were far behind won't be anymore, so the >average< will be better. If crises becomes too easy that could be the culprint, so you may want to set 1.25x tech costs or mid-game/late game dates a bit closer (or harder crises).

With the addition of technology ascendant I play with 1.5 costs.