Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Develops an optimized Ekedahl sieve for the discriminant polynomial singular locus that bypasses inductive steps and yields stronger tail estimates incorporating modular conditions.
Any order in a number field decomposes uniquely as an intersection of irreducible orders, with the index distributing multiplicatively and the conductor factoring into pairwise coprime ideals.
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Uniformly Positive Mean Dimension
Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.