Minimal subdynamics and minimal flows without characteristic measures

The paper proves exactly what the model declared likely open: for every countably infinite group G there exists a compact metrizable space X carrying a free (G×F2)-action whose restriction to G is minimal and which admits no F2-invariant Borel probability measure; hence X, viewed as a G-flow, has no Aut(X,G)-invariant (characteristic) measure. This is Theorem 1 of the paper; the abstract and statement spell out the stronger formulation with a commuting F2-action. The proof builds a new “B-irreducible” framework (Definition 11) and a paradoxical F2-subshift X_pdox with no F2-invariant measure (Proposition 15), then lifts to G×F2 and shows the G-minimal members are dense Gδ in the relevant class (Proposition 17), while freeness is generic for Cantor alphabets (Proposition 12). These components are all present in the text. The model’s assessment that the problem was open as of 2022-03-09 is contradicted by this March 2022 paper that gives a constructive affirmative answer.