Abstract
This essay examines the structural properties of Stratified Linear Higher-Order Datalog with negation, as presented in recent work by Charalambidis, Kostopoulos, and Rondogiannis, and assesses its potential to inform the study of the Riemann Hypothesis through the lens of random matrix statistics and moment hierarchies.
Download Full Article
This article is available as a downloadable PDF with complete code listings and syntax highlighting.
Overview
This paper assesses whether the hierarchy of space complexity classes captured by Stratified Linear Higher-Order Datalog$^\neg$ (arXiv:2606.02394v1) offers any structural insight into the moments and zero statistics of the Riemann zeta function. The source paper establishes that restricting higher-order programs to linear recursion shifts their expressive power from time (EXPTIME) to space (EXPSPACE), enabling memory-efficient evaluation via state-overwriting.
The speculative angle explored here is whether this "time-to-space" shift parallels the transition from temporal dynamics to spatial statistics in zeta function theory, and whether the syntactic "linearity" constraint mirrors the linear statistics studied in random matrix theory. The analogy is rated as weakly suggestive metaphor only; no formal dictionary can be constructed without violating the distinct nature of the objects involved (discrete syntax versus analytic probability).
The essay is a negative result: it argues precisely where the correspondence breaks down—specifically, the mismatch between syntactic recursion constraints and analytic test functions, and between finite configuration graphs and infinite determinantal point processes. It concludes by identifying the type of source material (e.g., on Coulomb gases or critical multiplicative chaos) that could potentially sustain a rigorous analogy to the Riemann Hypothesis.
This essay was produced by an automated research pipeline and has not been peer reviewed; conjectures herein are unproven.