Lamination Realization of Higher Tropical Friezes

Definitions and mathematical statement

The supplied question is: "Can every higher tropical frieze pattern be realized by an A-lamination?" The record does not define either a higher tropical frieze pattern or an A-lamination, or specify the realization construction.

A formal statement of the intended realization question can therefore be given only conditionally. Let $\mathcal{F}$ denote the intended class of higher tropical frieze patterns, let $\mathcal{L}_{A}$ denote the intended class of A-laminations with compatible underlying data, and let \[ \Phi\colon\mathcal{L}_{A}\longrightarrow\mathcal{F} \] be the construction referred to by the supplied background, which asserts that higher-dimensional A-laminations produce higher tropical frieze patterns. The question asks whether this construction is surjective: \[ \forall f\in\mathcal{F}\;\exists\lambda\in\mathcal{L}_{A} \quad\Phi(\lambda)=f. \] These symbols are placeholders for definitions absent from the supplied record. In particular, the dimension or rank, underlying geometric or combinatorial data, value and weight domains, defining frieze relations, boundary conditions, and any equivalence or normalization involved in realization are unspecified. The displayed formula is a logical restatement of the question, not a fully specified mathematical conjecture. It must be interpreted only after the intended classes and construction have been identified from reliable source material.

Short English statement

Does every higher tropical frieze pattern arise from an A-lamination under the intended construction? The supplied record labels this question open, but does not provide the definitions and compatibility conditions needed for a precise realization conjecture.

Sources

• Local UnsolvedMath registry, supplied record with permanent ID $30002969$, title "Lamination Realization of Higher Tropical Friezes," source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the recorded proposed year is $2015$.
• Supplied report citation: Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894. https://doi.org/10.4171/owr/2015/48. The record describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The citation's year $2016$ differs from the proposed year and the year component in the DOI; this discrepancy is unresolved.
• Supplied literature reference: Oppermann--Thomas, Higher-Dimensional Cluster Combinatorics. https://ems.press/content/serial-article-files/46598.
• Supplied literature reference: Le, Higher Laminations and Affine Buildings. https://arxiv.org/abs/1209.0812.
• Supplied literature reference: Friezes Workshop Problem Statement. https://ems.press/content/serial-article-files/46598. This is the same URL supplied for the Oppermann--Thomas reference; the bibliographic relationship has not been verified.
• Literature assessment dated 2026-08-21: the supplied curation labels the problem open and states that higher-dimensional A-laminations produce higher tropical frieze patterns, while a converse realization theorem for all such patterns has not been proved. This is supplied dated curation derived from the OWR material, not an independently verified assessment. Its status and cited claims require independent verification.