The Boundary‑Regime: A Geometric Reading of CMS UPC Data

This work introduces a geometric reading of the CMS D⁰ photoproduction data in ultra‑peripheral collisions, focusing on the low‑pT suppression region where boundary‑regime behavior becomes visible. The analysis applies the χ diagnostic from the Foundry and ODIM frameworks to identify the onset of projection‑capacity limits and manifold tightening in the observed distribution. The χ peak remains stable under broad variations of modeling parameters, with its location and width showing lower drift than the spread of standard nPDF expectations. This stability suggests that χ functions as a low‑variance marker for boundary‑regime transitions in this dataset. The paper outlines the geometric interpretation, the diagnostic behavior, and the implications for observer‑dependent structure in high‑energy photoproduction.