Among the most satisfying for me interactions on social media such as Bluesky could be described as codependent. We argue incessantly without convincing each other. One such climate denier was fooled by anti-doomists into believing the keeling curve is exponential when it is obviously parabolic. The climate denier prefers for it to be exponential because anti-doomists falsely believe worse is less motivating than less than worse. Anyway, after trouncing the climate denier with the rolling average of the derivative of the keeling curve, I suggested taking me down with a counter example to my proof of the constructibility of linear spaces, and the climate denier took me up on the challenge. By then, I was arguing with copy pasted images of professionally formatted text from AI. After some undefined insistence from the AI, I got a reference out of it, and it turns out there is a counter example buried in the literature that I never could have found on my own. One thing that nagged me about my proof was that it did not depend on my definition of linear. Now I believe my proof is still good, and contains a better definition of linear. I just need to state precisely what that is.
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