Classification of Laminations and Higher Tropical Frieze Patterns

Definitions and mathematical statement

Is there a useful description of all A-laminations, and an explicit description of all higher tropical frieze patterns?

The requested task is to describe exhaustively the objects called A-laminations and higher tropical frieze patterns in the intended workshop setting. The supplied record does not define either class. It specifies no underlying geometric or categorical data, allowed ranks or higher parameters, coefficient or value domains, equivalence relation on laminations, or defining relations and boundary conditions for the patterns. Consequently, the scope of "all" cannot be fixed from this record, and no precise classification statement can be given without additional source definitions. The terms "useful" and "explicit" also have no stated mathematical criterion.

There is a further unresolved scope qualification: the question asks about all A-laminations, whereas the supplied literature assessment discusses the lack of a complete description of all higher A-laminations. The record does not establish whether the first part of the question is intended to be restricted to higher A-laminations. These formulations are therefore preserved without identifying their scopes.

Short English statement

Describe all A-laminations and all higher tropical frieze patterns in the intended workshop setting. The supplied record leaves the objects, parameters, equivalences, and boundary conditions undefined, and its question and literature assessment differ on whether the laminations are restricted to the higher setting. A precise formulation requires human review of the cited source.

Sources

• Supplied local UnsolvedMath registry record, permanent ID 30002970, in the Oberwolfach Reports Open Problems collection; exact source problem code catalogue entry. No individual proposer is supplied; the recorded proposed year is 2015.
• Supplied source 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 2016 label and the record's 2015 proposed year are retained without reconciliation.
• Supplied literature source: Friezes Workshop Open Questions. https://ems.press/content/serial-article-files/46598.
• Supplied literature source: Jorgensen, Tropical Friezes and the Index. https://arxiv.org/abs/1806.02108.
• Supplied literature source: Le, Higher Laminations and Affine Buildings. https://arxiv.org/abs/1209.0812.
• Supplied dated literature curation, checked 2026-08-21: status open. Its assessment states that classical tropical friezes admit an A-lamination description and higher tropical friezes have categorical constructions, but that a complete description of all higher A-laminations or all higher tropical patterns remains unavailable. This is supplied dated curation derived from the OWR record, not independently verified here; its time-sensitive status and cited claims require independent verification.