What does this research mean for the field?

Optimal transport theory and Kantorovich-Rubinstein duality provide a geometric metric on probability spaces that bridges measure theory and computational limits. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Characterize the mathematical links between optimal transport theory, Kantorovich-Rubinstein duality, and computational limits across geometric probability spaces.

August 30, 2026Open Access

Wasserstein Distance: Bridging Measure Theory and Computational Limits via Kantorovich-Rubinstein Duality — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Theoretical analysis demonstrates optimal transport bounds via Kantorovich-Rubinstein duality and spectral gaps in probability spaces, highlighting connections to geometric dimension reduction.

Key Points

Characterize the mathematical links between optimal transport theory, Kantorovich-Rubinstein duality, and computational limits across geometric probability spaces.
Formulated Wasserstein-1 distances using coupling measures and dual supremum representations over Lipschitz-1 continuous functions.
Derived convergence decay bounds using the spectral gap of a continuous-time Markov generator.
Analyzed the geometric curvature and low-dimensional embedding properties of Wasserstein spaces relative to optimal quantization on root system lattices.
Identified that the spectral gap λ1 of a Markov generator explicitly bounds the decay of the Wasserstein-1 distance by the exponential factor e^(-λ1 t).
Demonstrated that Wasserstein spaces exhibit geodesic metric structures that map intrinsic dimension reduction to optimal quantization on An and Dn root system lattices.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a93f1266c1a8fb52e79ded1 https://doi.org/10.5281/zenodo.22154681

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Implication

Theoretical analysis demonstrates optimal transport bounds via Kantorovich-Rubinstein duality and spectral gaps in probability spaces, highlighting connections to geometric dimension reduction.

Wasserstein Distance: Bridging Measure Theory and Computational Limits via Kantorovich-Rubinstein Duality — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Wasserstein Distance: Bridging Measure Theory and Computational Limits via Kantorovich-Rubinstein Duality — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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