  We study the properties of roots of a polynomial system of equations which
define a set of identical point particles located on a Unique Worldline (UW),
in the spirit of the old Wheeler-Feynman's conception. As a consequence of the
Vieta's formulas, a great number of conservation laws is fulfilled for
collective algebraic dynamics on the UW. These, besides the canonical ones,
include the laws with higher derivatives and those containing multi-particle
correlation terms as well. On the other hand, such a ``super-conservative''
dynamics turns to be manifestly Lorentz invariant and quite nontrivial. At
great values of ``cosmic time'' $t$ roots-particles demonstrate universal
recession (resembling that in the Milne's cosmology and simulating
``expansion'' of the Universe) for which the Hubble's law does hold true, with
Hubble parameter being inversely proportional to $t$.
