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 the project is mainly a formal construction at this stage, I am using freely available AI platforms (with limited usage) as a day‑to‑day assistant. 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.

 

From Scalar Rigidity to System Solutions and Abstract Prime Systems. https://doi.org/10.5281/zenodo.21281074

 

Related works

(2026): (Root) Rigidity and Structural Asymmetry of Bounded Solutions. 

 

 

(2026): On a Rigidity Equality for Bounded Solutions: Request for Counterexamples.

 

 

(2026): Holomorphic Wronskian for abstract rigidity inequalities.

 

 

(2026): (Bridge) Asymmetry and the Riemann Hypothesis. 

 

 

           or: Scalar rigidity, abstract prime systems, and the Riemann zeta function.  

 

 

(2026): Rigidity and Spectral Asymmetry for Operators in Linear Dynamics. 

 

(2026) (Deduction of the Theory (PR)) Euler products from abstract prime systems and rigidity.