The compositum of the two Mahler minimizers: exact measure, conjugate census, house, and minimal product recurrence, with the Bedford-Kim plastic family, Lehmer's polynomial, and the E_m Coxeter bridge
Kernel-checked certificates for the multiplicative compositum of the two registered Mahler minimizers — rho, the real root of x^3 = x + 1 (the plastic number: Smyth's nonreciprocal minimum, Siegel's smallest Pisot number) and Q, the real root > 1 of x^4 = x + 1 (the degree-4 entry of the minimal-measure tables) — together with the Bedford-Kim spectral family whose limit rho is, and (new in version 2) the identification of that family with the Coxeter-element spectra of the E_m star trees. Twenty-two compared theorems. The spectral half: (1) for n >= 7 the family chi_n(x) = x^(n+1)(x^3 - x -…
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