Abstract

The paper proves the property-τ\tau input that completes the uniform congruence spectral-gap argument for arithmetic lattices.

Role in dependence graphs

Proof-critical source

Bounded trajectories of quasi-rays

This paper is included only for the following marked statement:

  • Theorem 3.1 · Theorem 3.1; structural proof §§1.1 and 3.2Completes the congruence spectral-gap/property-τ\tau input used in the general lattice argument.

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