A relationship between the uncertainty principle and spatial curvature

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TL;DR

Is there a relationship between the uncertainty principle and spatial curvature?

The uncertainty principle is a principle of quantum mechanics, while spatial curvature is a concept in general relativity. It is generally believed that the two are unrelated. However, a recent preprint published on the Zenodo platform suggests that they are closely related. Below is a screenshot from that paper.

The paper analyzes two cases:
First, a point-like particle appears first at point A and then at point O. The uncertainty (difference) in its momentum along the x-axis is Δpx′, and the uncertainty in the x coordinate direction is Δx′.
Second, a point-like particle appears first at point B and then at point O. The uncertainty (difference) in its momentum along the x‑axis is Δpx″, and the uncertainty in the x‑coordinate direction is Δx″.

Since the curvature at point A is smaller than that at point B, we have Δpx′<Δpx″, but Δx′ > Δx″. This is consistent with the uncertainty principle, suggesting that the uncertainty principle arises because the space around a point like particle is curved.

Everyone is welcome to discuss this analysis and share their opinions. The URL of the paper is:
https://zenodo.org/records/19504704