  To address unsolved fundamental problems of the intermediate state (IS), the
equilibrium magnetic flux structure and the critical field in a high purity
type-I superconductor (indium film) are investigated using magneto-optical
imaging with a 3D vector magnet and electrical transport measurements. The
least expected observation is that the critical field in the IS can be as small
as nearly 40% of the thermodynamic critical field $H_c$. This indicates that
the flux density in the \textit{bulk} of normal domains can be
\textit{considerably} less than $H_c$, in apparent contradiction with the long
established paradigm, stating that the normal phase is unstable below $H_c$.
Here we present a novel theoretical model consistently describing this and
\textit{all} other properties of the IS. Moreover, our model, based the
rigorous thermodynamic treatment of observed laminar flux structure in a tilted
field, allows for a \textit{quantitative} determination of the domain-wall
parameter and the coherence length, and provides new insight into the
properties of all superconductors.
