  The Garvey-Kelson (GK) relations are powerful algebraic expressions
connecting the masses of neighboring atomic nuclei and derived under reasonable
physical assumptions. In this contribution we show that these relations are
even more general than originally assumed as their validity is conditioned by
the smoothness of the underlying nuclear mass function and nothing else. Based
on the assumed smoothness of the underlying physical function, the main
conclusions from this study are: (1) the GK relations are model independent;
(2) any slowly-varying physical observable satisfies the GK relations; and (3)
the accuracy of the GK relations may be systematically improved. Examples from
nuclear physics (charge radii) and from particle physics (baryon masses) are
used to illustrate the flexibility of the approach.
