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 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. 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://arxiv.org/abs/2603.15716

 

Abstract Prime Systems. https://zenodo.org/records/22239664