On this page
Multi-marginal transport representation audit
Family 373: Nonattainment of the three-marginal Coulomb Monge problem. First source-informed review, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Optimal-transport research teams can flag exact-attainment claims that restrict three-particle Coulomb couplings to two deterministic measure-preserving maps.
Applicability and commercial boundary
The paper exhibits smooth compact densities where a Kantorovich optimum exists but the Monge representation does not attain it, even though the infima agree. The formal scope covers R3 Coulomb; broader Riesz extensions remain outside it. Approximating maps are not ruled out.
Initial business decision
Conditional research. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.
Next verification action
Extract a discretized counterexample with an explicit relaxation gap or nonattainment indicator and distinguish numerical approximation from exact continuum attainment.
Evidence scope
The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.