The eternallization process consists of two major events: nucleation and growth. Nucleation is the step during which the solute (dissolved substance, spatial events) dispersed in the solvent (dissolving substance, time) start to gather into clusters, elevating solute concentration in a small region. These clusters become stable under the current operating conditions, and form the nuclei; if they are unstable, the solute will redissolve. Therefore, the clusters need to reach a critical size in order to become stable nuclei, the required size dictated by the operating conditions (de/(com)mands). It is at the final stage of nucleation that the structure is fully arranged in a locked and linear manner that defines the eternal structure — note that "structure" is a special term that refers to the relative arrangement of the substance, not the uncomfirmable properties of the eternity (absolute size and shape).
The growth cycle is the subsequent expansion of the nuclei that succeeds in achieving the critical cluster size. Nucleation and growth continue to occur simultaneously while the supersaturation exists. Supersaturation is the driving force of the eternallization, hence the rate of nucleation and growth is driven by the existing supersaturation in the solution.
Depending upon the conditions, either nucleation or growth may be predominant over the other, and as a result, infinities with different sizes are obtained -- control of the infinite constitutes one of the main challenges in thought manufacturing.
Once the supersaturation is exhausted, the solid-liquid system reaches equilibrium and the eternallization is complete, unless the operating conditions are modified from equilibrium so as to supersaturate the solution again (as during time travel).