  We offer a physicists' proof that center-vortex theory requires the area in
the Wilson-loop area law to involve an extremal area. Area-law dynamics is
determined by integrating over Wilson loops only, not over surface fluctuations
for a fixed loop. Fluctuations leading to to perimeter-law corrections come
from loop fluctuations as well as integration over finite -thickness
center-vortex collective coordinates. In d=3 (or d=2+1) we exploit a contour
form of the extremal area in isothermal which is similar to d=2 (or d=1+1) QCD
in many respects, except that there are both quartic and quadratic terms in the
action. One major result is that at large angular momentum \ell in d=3+1 the
center-vortex extremal-area picture yields a linear Regge trajectory with Regge
slope--string tension product \alpha'(0)K_F of 1/(2\pi), which is the canonical
Veneziano/string value. In a curious effect traceable to retardation, the quark
kinetic terms in the action vanish relative to area-law terms in the large-\ell
limit, in which light-quark masses \sim K_F^{1/2} are negligible. This
corresponds to string-theoretic expectations, even though we emphasize that the
extremal-area law is not a string theory quantum-mechanically. We show how some
quantum trajectory fluctuations as well as non-leading classical terms for
finite mass yield corrections scaling with \ell^{-1/2}. We compare to old
semiclassical calculations of relativistic q\bar{q} bound states at large \ell,
which also yield asymptotically-linear Regge trajectories, finding agreement
with a naive string picture (classically, not quantum-mechanically) and
disagreement with an effective-propagator model. We show that contour forms of
the area law can be expressed in terms of Abelian gauge potentials, and relate
this to old work of Comtet.
