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.
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