Next society will be decentralized
Traditional Marxist theory holds that the working class will defeat the capitalist class, creating its new centralized state power and nationalize production.
But the spiral theory of development shows that the society after capitalism will have a decentralized economy and decentralized government.

Working class not the revolutionary class
The spiral theory of development model conflicts with the orthodox Marxist theory that the working class will lead a revolution against capitalism.
For most of the time in previous societies (Slavery/Land-duty), the class struggle centered on the conflict between the owning class (slave owners/landowners) and the laboring class (slaves/peasants). But, when these class struggles had helped mature these societies, the class struggle centered on the conflict between the owning class and parts of the former middle classes. It was from the middle classes that the new revolutionary classes (landowners/capitalists) emerged.
Like all laboring classes, the working class is a dependant class that cannot exist without the owning class. The working class relies on the capitalist class to create jobs for it. Also, when the capitalist class was defeated by the working class to form Communist Party states, the managers of the nationalized industries transformed into capitalists. The working class cannot break free of capitalism.
So, following the historical pattern, the core of the class that will defeat capitalism will be from the middle classes and not the working class. The working class will then merge into this new core class.

A more detailed explanation of who will form the next revolutionary class is in the e-book "The revolutionary class".