Unbounded Sizes of Sensitive Triangulations

Definitions and mathematical statement

The supplied source asks: "Are the sizes of sensitive triangulations unbounded?" It supplies no definition of a sensitive triangulation, no definition of its size, and no specification of the underlying spaces or admissible triangulations. Consequently, a complete mathematical formulation cannot be recovered from this record alone.

Conditionally, if $\mathcal{S}$ denotes the intended class of sensitive triangulations and $s\colon\mathcal{S}\to{\mathbb{R}}_{\geq 0}$ denotes the intended numerical size, the unboundedness question takes the schematic form \[ \text{Is it true that }\quad \forall M\in{\mathbb{R}}_{\geq 0}\;\exists T\in\mathcal{S}\quad s(T)>M\,? \] This schema does not supply the missing definitions or assert that the intended size has this codomain. In particular, the record does not specify whether dimension is fixed or allowed to vary, what geometric or combinatorial restrictions define $\mathcal{S}$, what boundary conditions apply, or which quantity $s(T)$ measures. These qualifications must be resolved before this can serve as a precise statement of the original problem.

Short English statement

The question asks whether sensitive triangulations can have arbitrarily large size. The supplied record does not define sensitivity, size, or the admissible triangulations, so the displayed quantifiers express only a conditional formulation. The intended dimension restrictions also remain unresolved.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30002860$, title "Unbounded Sizes of Sensitive Triangulations," source problem code catalogue entry, in the collection "Oberwolfach Reports Open Problems." The original, clean, and displayed source statements all ask the same unboundedness question. No individual proposer is identified; the proposed year is recorded as 2015.
• Supplied report citation: Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, pp. 1139--1200, DOI 10.4171/owr/2015/21. Supplied source URL and literature-source link, labeled "Oberwolfach Report 21": https://doi.org/10.4171/owr/2015/21. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The report contents were not supplied or independently consulted.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem open, describes it as a long-standing open problem, and reports that no theorem establishing a uniform bound or unboundedness for all dimensions was found. The listed checked source is Oberwolfach Report 21 at the URL above. This is supplied dated curation, not an independently verified literature assessment; the record itself requests independent verification of time-sensitive status and cited claims.
• The registry supplies status open and statement status corrected_verified. Its verification note says that notation and publication prose were repaired without changing the mathematical question. These are supplied registry labels and editorial assertions, not independent mathematical verification.