Higher-Dimensional Generalization of a Strassen-Type Result

Definitions and mathematical statement

Recorded target and unresolved formulation. The supplied record, titled "Higher-Dimensional Generalization of a Strassen-Type Result," describes a workshop question asking for an extension to higher dimensions of a recent one-dimensional generalization of Strassen's theorem. According to the supplied statement-verification note, the report does not identify that one-dimensional result precisely enough to yield a self-contained mathematical statement.

The source does not specify the underlying spaces, mathematical objects, hypotheses, order or comparison relation, conclusion, or quantifiers of the intended result. Consequently, no definitions or quantified extension problem can be supplied faithfully. In particular, choosing a particular version of Strassen's theorem or a particular higher-dimensional formulation would introduce information absent from the record.

The supplied statement and original-statement fields contain only a contextual remark that the question was posted to workshop participants and that the report passage was retained for context. The clean-statement field is empty, and the supplied statement status is unrecoverable. The intended extension remains an unresolved formulation in this statement-only draft; its mathematical content requires recovery of the precise one-dimensional result and the intended extension.

Short English statement

The recorded question asks whether an unspecified recent one-dimensional generalization of Strassen's theorem extends to higher dimensions. The supplied evidence does not identify the starting theorem or the intended extension, so a precise standalone problem cannot be reconstructed. The record's "open" label is supplied curation, not an independently verified mathematical assessment.

Sources

• Local UnsolvedMath registry, permanent ID $30005864$, source code catalogue entry, title "Higher-Dimensional Generalization of a Strassen-Type Result." The supplied record belongs to the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed year is 2024. Registry locations: data/unsolvedmath/problems.json and the supplementary catalog/problems.json.
• Supplied report citation: Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, pp. 1339--1386, DOI 10.4171/owr/2024/24. Source URL and literature-source label "original OWR report": https://doi.org/10.4171/owr/2024/24. The collection describes these reports as documenting mathematical workshops and their open-problem discussions. This authoritative report citation is supplied, but no precise passage location or identification of the relevant one-dimensional theorem is supplied.
• Supplied literature-source label "Frongillo minimax duality": https://arxiv.org/abs/2512.21026.
• Supplied literature-source label "Beiglböck--Pammer--Riess--Schrott weak optimal transport": https://arxiv.org/abs/2501.16316.
• Literature assessment dated exactly 2026-08-22: the supplied curation says the workshop report described the higher-dimensional extension as open, that later work obtained extensions in different formulations, and that no result establishing the specific higher-dimensional question in this record was identified. This is supplied dated literature triage derived from the OWR curation, not an independently verified assessment. The time-sensitive status and the claims about the cited works require independent verification.