On the Uniqueness of Embeddings of Causal Sets

Nathan Madsen

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arXiv · 2607.05840

On the Uniqueness of Embeddings of Causal Sets

Nathan Madsen

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Abstract

We introduce the notion of a well-conditioned embedding of a causal set into a Lorentzian manifold and prove that if a causal set admits well-conditioned embeddings into two manifolds, then their interiors are related by an $\varepsilon$-approximate isometry. To justify the definition, we show that in the high-density limit a Poisson sprinkling almost surely yields a causal set possessing a well-conditioned embedding. The error $\varepsilon$ is given explicitly and tends to zero in the high-density limit.

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Nathan Madsen. 2026-07-07. On the Uniqueness of Embeddings of Causal Sets. https://arxiv.org/abs/2607.05840

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