refactor(Core/Probability): mathlib-register Gumbel, rewrite GumbelLuce - #1716
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From the GumbelLuce audit, targeting "what would actually go in mathlib": mathlib has no Gumbel (or any extreme-value) distribution, so the universal half becomes a genuine upstream candidate and the RUM half becomes thin glue.
Core/Probability/Gumbel.leanin theMathlib/Probability/Distributionsregister (density →withDensitymeasure → CDF as a theorem → max-stability → the max-probability integral), location-scale, replacing the old bare-ℝgumbelCDF/gumbelPDFpair that was stipulated in the wrong order (CDF primitive, never connected to its density) and the 150-line private FTC block.GumbelLuce.leanrewritten: shared n-ary RUM carrierrumMaxProblands inRandomUtility.lean(parallel to the probit side);mcfaddenIntegral— an unevaluated proof intermediate consumers were quantifying over — is gone, withFlemming2021/GaussianChoice/SignalDetectionrestated overrumMaxProb/softmax/sigmoid(Flemming's MaxEnt=RUM theorem now states the claim its docstring made);fromGumbelRUMis defined throughfromSoftmax.yellott-1977/marschak-1960/luce-suppes-1965added; staleCore.Agent.*doc paths swept.