I'm not going to tear my hair out if I somehow get a point of not-Purity, but I really want focusing on one Affinity to be viable.
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Purity does research Robotics and Genetic Engineering, just not from an angle of becoming a robot or massively altering the human form with genetic engineering.
(Though they are okay with improving it from the angle of creating the "perfect" human, so long as the human form is preserved.)
The main themes of Purity are a wariness in changing humanity, terraforming, and remembering history.
I stress that last point as what separates Purity from the others beyond Terraforming and what it does not do - honoring and preserving the past's legacy is absolutely central to Purity.
(Whereas Harmony and Supremacy, in comparison, abandon it with their separate visions of what will be best.)
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Every Hybrid needs points that they agree on and disagree on with both Affinities, so it does not follow that none of the Hybrids would terraform.
Harmony / Purity could easily be envisioned as crafting a perfect environment to match their "perfect" race.
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I agree that Dome life seems more likely and thematically fitting for Purity / Supremacy, but there could still be distinctions.
I would have them create human-like AI's to serve them, perhaps eventually being seen as equals.
This would disagree with Purity in creating sentient AI's and with Supremacy's vision of a computerized humanity - Supremacy would likely also disapprove with limiting AI's to make them human-like.