This manuscript presents the absolute mathematical closure of the scientific publication and peer-review system, rigorously modeling it as a positive admissibility operator within a spectral zeta framework. Moving beyond heuristic critiques of editorial judgment, the paper translates the entire publication pipeline—manuscript evaluation, reviewer aggregation, identity-sensitive masking, and editorial thresholding—into exact operator-theoretic mechanics. The framework establishes that editorial ambiguity manifests strictly as low-spectrum density, bias acts as channel-sensitive kernel deformation, and decision stability emerges as spectral-gap separation. The paper derives exact heat kernel asymptotics for both finite empirical matrices and continuum pseudodifferential manifolds. This explicitly links geometric curvature and reviewer disagreement to the poles of the publication zeta function, while establishing an odd-zeta hierarchy as a direct measure of ambiguity-tail concentration. To preempt heuristic defenses of neutral human judgment, the manuscript deploys three terminal mathematical constraints: The von Neumann/Holevo Information Bound: Proving that empirical reviewer variance forces a strictly positive conditional entropy, making perfect recovery of objective manuscript merit mathematically impossible. The Fredholm Topological Obstruction: Proving that institutional prestige networks introduce a non-zero Fredholm index to the editorial decision map, rendering pure neutrality topologically prohibited. Doob Submartingale Drift: Proving that identity-sensitive prestige biases act as a strict submartingale drift on the admissibility operator, mathematically enforcing the Matthew Effect (oligarchic divergence). Furthermore, the publication system is lifted into noncommutative geometry via a Connes Spectral Triple, upgrading heuristic "manuscript similarity" into exact geometric spectral distance. Finally, the artifact bridges pure theory and practical application by providing an executable empirical data pipeline. It includes a formal schema for structuring real-world review datasets and a synthesized figure suite demonstrating empirical spectrum extraction, heat-trace decay, Weyl-law fitting, and odd-zeta ambiguity diagnostics.
Andrew Kim (Sun,) studied this question.