Interacting Lattice Bosons on the Concrete Buchholz Algebra -- All-Temperature Equilibrium States from Functional-Integral Local-Number Bounds

Interacting Bose--Hubbard dynamics is formulated on the concrete Buchholz algebra in Fock space. Under repulsive finite-range interactions and a low-activity gap, a discrete functional integral gives volume-uniform exponential local-number bounds at all temperatures. These bounds remove the local-moment hypothesis and yield finite-volume approximation and KMS accumulation states in arXiv:2505.13170.