Geometric Characterization and Removal of Stickiness

Definitions and mathematical statement

The supplied record concerns stickiness in the setting of asymptotic statistics on stratified spaces. It does not define stickiness, full stickiness, the set $Q_0$, or a degree of full stickiness. Nor does it specify the class of spaces, the statistical objects exhibiting stickiness, the admissible changes of geometry, or the convention for tangent cones. These terms therefore remain unresolved source terminology; no particular definition is imposed here.

Subject to resolving these definitions and domains, the source asks for the following geometric characterization problems:

1. Find descriptors for the degree of full stickiness.
2. Determine whether stickiness can always be removed by changing the geometry. If this universal removability assertion fails, characterize the classes for which stickiness cannot be removed by the admissible changes of geometry.
3. Determine whether every sticky subset must be contained in $Q_0$. Here $Q_0$ is retained exactly as supplied, without an inferred definition; the intended meaning of a sticky subset also requires clarification.
4. Characterize when stickiness is possible, for example by conditions involving the tangent cone.

The word "always" in the second question requires quantification over an unspecified class of initial geometries and sticky configurations, followed by existence of a permitted replacement geometry. The source does not specify these domains, the data preserved by replacement, or whether removal is required for a particular configuration or uniformly for a class. Likewise, the fourth question does not specify the point at which a tangent cone is taken or the meaning of possibility. Consequently, these are source-faithful research questions, not a fully determined conjecture with fixed hypotheses and quantifiers.

Short English statement

Describe the strength of full stickiness, determine when changing geometry can eliminate it, decide whether sticky subsets must lie in $Q_0$, and characterize the geometric conditions allowing stickiness, possibly through tangent cones. The supplied record leaves the central definitions and quantifier domains unspecified, so a precise formal conjecture requires source clarification.

Sources

• Supplied local UnsolvedMath registry record: permanent ID $30002683$, source problem code catalogue entry, title "Geometric Characterization and Removal of Stickiness," in the collection "Oberwolfach Reports Open Problems." The recorded proposed year is 2014; no individual proposer is supplied.
• Supplied report citation: Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, pp. 2481--2527, DOI 10.4171/owr/2014/44. https://doi.org/10.4171/owr/2014/44. The background also identifies this as Oberwolfach Report 44/2014. The supplied 2015 title date and 2014 report identification are retained without resolving their relationship.
• Supplied literature source: Sticky Flavors. https://doi.org/10.48550/arXiv.2311.08846.
• Supplied literature source: Types of Stickiness in BHV Treespaces. https://doi.org/10.48550/arXiv.2304.05025.
• Supplied dated literature curation, checked 2026-08-21: the record labels the problem partially solved and reports that later work provides topological definitions, degree measures, and sticky limit theorems for several model stratified spaces, while no general characterization of the listed degree, removability, sticky-subset, or tangent-cone questions is known. This is the supplied dated assessment, not an independently verified literature conclusion. The background explicitly calls for independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and states that mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. This supplied editorial qualification does not resolve the definitions missing from the present record and is not independent mathematical verification.