New video. I recorded the presentation I gave at Foundations 2026.
Infrastructure. I optimized the github action build to only rebuild the latex of the documents that have changed. Well, Claude helped a lot… Thanks Claude!
Minor contributions. I integrated a couple of pull requests with minor fixes. It’s been a while since I last did that, and I have to say the github desktop integration works a lot better than I remembered. Thanks Saja, Tobias and Demitri!
More on quantum observables. I have been working on a way to fully derive self-adjoint operators from just having affine (i.e. linear) quantities of ensembles. Interestingly, it’s fairly easy to get to an operator O : V \to V’, where V’ is the dual (continuous dual if one assumes the affine functional to be continuous) through sesquilinear forms… but I have no physical intuition for forcing it to be O : V \to V. The condition is equivalent to assuming O is associated with a vector field on the space (no necessarily corresponding to a one-parameter group… just the infinitesimal version), but that’s about it for now. Also, I need to address how to define density operators on a generic vector space V… which I also don’t know how to do yet. I think I’ll pause the investigation on operators for now and checkpoint what I have.
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