{"id":"palomar/PALOMAR-2026-09-01-000005","url":"https://github.com/stalex444/mahler-minimizer-compositum/tree/84b364a5f98daefc1be387ae0aeb3d39866eca79","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-01-000005-v2.json","repo":"https://github.com/stalex444/mahler-minimizer-compositum","tags":["math.NT","math.DS","math.GR","math.RT","msc:11R06","msc:11R04","msc:11B37","msc:14E07","msc:37B40","msc:20F55"],"score":0,"title":"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","trust":"high","domain":"math.NT","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.NT","summary":"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 -…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"Dynamics of rational surface automorphisms: linear fractional recurrences","identifier":"Journal of Geometric Analysis 19 (2009), 553-583","relationship":"formalizes"},{"title":"Cyclotomic factors of Coxeter polynomials","identifier":"Journal of Number Theory 129 (2009), no. 5, 1034-1043","relationship":"formalizes"}]}