Walid OUKIL       

  Associate Professor
   Faculty of Mathematics, USTHB

About the Prime Rigidity Theory (PR)

 

I am currently developing (without funding) a long‑term research programme called the Prime Rigidity Theory (PR). This work builds on my arlier results concerning bounded solutions of complex differential equations and the rigidity inequalities that force structural asymmetry. The goal now is to generalise these ideas step by step to an operator‑theoretic framework, where the complex parameter is replaced by a bounded linear operator, and the classical Euler product is replaced by an system product over an abstract prime system. Because this project is currently in its formal construction stage, I utilize AI platforms (free and limited), for structural organisation, and language editing. These tools help me draft and organise the working papers, but every definition, theorem, and proof is guided by the scalar theory alread established. The current writings are deliberately kept as “working papers”: they aim to build a clean formal skeleton of the theory, rather than to provide finished computational results. All the details are recoverable by specialising the operator statements to the classical scalar case. The vision is that the abstract prime systems,  and the rigidity functionals together form a unified language that connects differential equations, functional calculus, and factorisation structures in a completely new way

 

Scalar Rigidity.   https://zenodo.org/records/21624894

 

Philosophical note:

One of the perspectives consists in interpreting classical set theory as a special case of a more general framework of generated systems satisfying a rigidity property. The rigidity property, introduced in the preprint "Euler products from abstract prime systems and rigidity", leads to considering Zermelo-Fraenkel sets as trivial realizations of this general theory.

Can this rigidity law serve us as a measure or index of the consistency of the thiorie?

French version:

L'une des perspectives consiste à interpréter la théorie classique des ensembles comme un cas particulier d'un cadre plus général de systèmes engendrés satisfaisant une propriété de rigidité. La propriété de rigidité, introduite dans le préprint "Euler products from abstract prime systems and rigidity" , conduit à considérer les ensembles de Zermelo-Fraenkel comme des réalisations triviales de cette théorie générale.

Cette loi de rigidité peut elle nous servir comme mesure ou indice de la consistance de la théorie?