  The four-color conjecture has puzzled mathematicians for over 170 years and
has yet to be proven by purely mathematical methods. This series of articles
provides a purely mathematical proof of the four-color conjecture, consisting
of two parts: the transformation step and the decycle step. The transformation
step uses two innovative tools, contracting and extending operations and
unchanged bichromatic cycles, to transform the proof of the four-color
conjecture into the decycle problem of 4-base modules. Moreover, the decycle
step solves the decycle problem of 4-base modules using two other innovative
tools: the color-connected potential and the pocket operations. This article
presents the proof of the transformation step.
