can anyone (or SD) explain the six TechInflation entries in Galciv3GlobalDefs?

<TechInflationExponent_All>1.2</TechInflationExponent_All>
<TechInflationMultiplier_All>0.12</TechInflationMultiplier_All>
<TechInflationExponent_Tree>1.1</TechInflationExponent_Tree>
<TechInflationMultiplier_Tree>0.12</TechInflationMultiplier_Tree>
<TechInflationExponent_Specialization>1.1</TechInflationExponent_Specialization>
<TechInflationMultiplier_Specialization>0.10</TechInflationMultiplier_Specialization>

End of quote

It's pretty clear what  they do & altering them definitely makes a difference in research speeds, but there are too many variables nrtween the six to figure out how they interact with the ResearchCost  beyond "makes it bigger".  doing some more extensive tests going deep into the tech tree to figure out the formula would take a really long time :(

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I do not know, but my guess is that the formula looks like this:

TechCost = BaseCost * (1 + TechInfMult_all * Ntechs_all^TechInfExp_all + TechInfMult_tree * Ntechs_tree^TechInfExp_tree + TechInfMult_spec * Ntechs_spec^TechInfExp_spec)

where BaseCost is the cost defined in the tech tree, TechInfMult_all and similar are what you should think they are based upon the XML section you posted, Ntechs_all is the total number of techs you've researched, Ntechs_tree is the total number of techs researched in this tree, and Ntechs_spec is the number of specialization techs you've researched. I would further expect that the specialization section applies only if you're researching a specialization tech, though I don't know.

I haven't done any testing on this whatsoever. A potential alternative formula would be

TechCost = BaseCost * (1 + TechInfMult_all * Ntechs_all^TechInfExp_all) * (1 + TechInfMult_tree * Ntechs_tree^TechInfExp_tree) * (1 + TechInfMult_spec * Ntechs_spec^TechInfExp_spec)

but that grows quite quickly and I think the first formula is more likely, though again, I haven't done any tests to try to figure out how the tech costs grow. A quick test to see if the multipliers add together or multiply one another would be to set all of the multipliers to 1 and the exponents to 0; if the multipliers multiply one another, then researching 1 tech should double the cost of the out-of-tree techs and quadruple the cost of the in-tree techs, while if the multipliers multiple one another then researching 1 tech should double the cost of the out-of-tree techs and triple the cost of the in-tree techs.