  A sunspot emanates from a growing pore or protospot. In order to trigger the
formation of a penumbra, large inclinations at the outskirts of the protospot
are necessary. The penumbra develops and establishes by colonising both umbral
areas and granulation. Evidence for a unique stable boundary value for the
vertical component of the magnetic field strength, $B^{\rm stable}_{\rm ver}$,
was found along the umbra-penumbra boundary of developed sunspots. We use
broadband G-band images and spectropolarimetric GFPI/VTT data to study the
evolution of and the vertical component of the magnetic field on a forming
umbra-penumbra boundary. For comparison with stable sunspots, we also analyse
the two maps observed by Hinode/SP on the same spot after the penumbra formed.
The vertical component of the magnetic field, $B_{\rm ver}$, at the
umbra-penumbra boundary increases during penumbra formation owing to the
incursion of the penumbra into umbral areas. After 2.5 hours, the penumbra
reaches a stable state as shown by the GFPI data. At this stable stage, the
simultaneous Hinode/SP observations show a $B_{\rm ver}$ value comparable to
that of umbra-penumbra boundaries of fully fledged sunspots. We confirm that
the umbra-penumbra boundary, traditionally defined by an intensity threshold,
is also characterised by a distinct canonical magnetic property, namely by
$B^{\rm stable}_{\rm ver}$. During the penumbra formation process, the inner
penumbra extends into regions where the umbra previously prevailed. Hence, in
areas where $B_{\rm ver} < B^{\rm stable}_{\rm ver}$, the magneto-convection
mode operating in the umbra turns into a penumbral mode. Eventually, the inner
penumbra boundary settles at $B^{\rm stable}_{\rm ver}$, which hints toward the
role of $B_{\rm ver}^{\rm stable}$ as inhibitor of the penumbral mode of
magneto-convection.
