Is there a research program that attempts to reconstruct an underlying structure from the statistical properties of the Riemann zeros?

I am a curious outsider to mathematics and recently started reading about the Riemann Hypothesis.

I am aware that many outsiders mistakenly believe they have solved the Riemann Hypothesis. I am not making such a claim. I am only trying to understand whether this perspective already exists in the literature.

I am not claiming a proof or a solution. Rather, I am trying to understand whether a particular way of thinking about the problem already exists in the literature.

Many explanations of the Riemann Hypothesis focus on the locations of the non-trivial zeros of the zeta function.

My intuition, coming from a problem-solving and diagnostic perspective, is to ask a different question:

What if the zeros themselves are not the primary object of interest, but instead are a statistical fingerprint of some deeper mathematical structure?

More specifically, I am wondering whether there are research programs that focus on reconstructing an underlying object from the global statistical organization of the zeros, rather than primarily studying individual zeros or local properties of the zeta function.

The reason I ask is that the combination of symmetry, structure, and apparent irregularity in the zero distribution reminds me of inverse problems in other fields, where the observed signal is used to infer a hidden system.

I suspect this may overlap with topics such as:

• Random Matrix Theory
• Quantum Chaos
• Spectral Geometry
• Inverse Spectral Problems
• The Hilbert–Pólya Program

My question is:

Are there existing research directions that explicitly view the zero set as a statistical fingerprint of a deeper generating structure and attempt to reconstruct that structure from the observed properties of the zeros?

If so, what references would be a good starting point for understanding this perspective?

I am looking for references and existing mathematical frameworks rather than speculative discussion.