  The existence of a fundamental length (or fundamental time) has been
conjecture in many contexts. Here one discusses some consequences of a
fundamental constant of this type, which emerges as a consequence of
deformation-stability considerations leading to a non-commutative space-time
structure. This mathematically well defined structure is sufficiently
constrained to allow for unambiguous experimental predictions. In particular
one discusses the phase-space volume modifications and their relevance for the
calculation of the GZK sphere. Corrections to the spectrum of the Coulomb
problemb are also computed.
