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What is a rigidification?

What is a rigidification? Here are some definitions.

Noun
  1. (uncountable) The process of becoming rigid, stiff or inflexible; of rigidifying.
  2. (geometry) A form of isomorphism applied between line bundles.
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Examples
It is a property of networks to rigidity and of the critical reader to become the reluctant agent of rigidification.
Granted the resources of rigidification and the thinkability of any actual object, the scope of general thought seems to have no obvious limits.
It therefore involved a confirmation, crystallization, and rigidification of the preexisting implicit boundaries of a white national identity and belonging.

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