  The classification of the ground-state phases of complex one-dimensional
electronic systems is considered in the context of a fixed-point strategy.
Examples are multichain Hubbard models, the Kondo-Heisenberg model, and the
one-dimensional electron gas in an active environment. It is shown that, in
order to characterize the low-energy physics, it is necessary to analyze the
perturbative stability of the possible fixed points, to identify all discrete
broken symmetries, and to specify the quantum numbers and elementary wave
vectors of the gapless excitations. Many previously-proposed exotic phases of
multichain Hubbard models are shown to be unstable because of the ``spin-gap
proximity effect.'' A useful tool in this analysis is a new generalization of
Luttinger's theorem, which shows that there is a gapless even-charge mode in
any incommensurate N-component system.
