Foliations and Diffeomorphism Groups — Question 54

Definitions and mathematical statement

The supplied excerpt introduces the term non-spreading for an element satisfying the conclusion of a preceding proposition, and then asks: "Is the converse true?" The referenced proposition is absent from the supplied record. In particular, the ambient class of elements, the hypotheses and conclusion of that proposition, and any relevant assumptions, quantifiers, or boundary conditions are unspecified. Thus neither a mathematical definition of non-spreading nor a precise statement of the requested converse can be recovered from this record. The question must remain unresolved at the level of formulation pending the missing proposition and its context.

Short English statement

The source asks whether an unspecified proposition has a converse, after naming elements satisfying its conclusion non-spreading. The missing proposition is necessary to state the question precisely. The registry labels the problem open; this is supplied status information, not an independently verified assessment.

Sources

• Supplied local UnsolvedMath registry record: permanent ID $800113$, exact source problem code catalogue entry, title "Foliations and Diffeomorphism Groups --- Question 54." The registry attributes the problem to Nariman and Yazdi, with proposed year 2025.
• Nariman and Yazdi, Problem List on Foliations and Diffeomorphism Groups (2025), Question 54. Supplied source URL: https://arxiv.org/abs/2503.18274. The record reports access on 2026-10-16 and extraction by arxiv_latex; these are supplied provenance details, not evidence of independent source consultation here.
• Supplied upstream revision: d371ee917ac9647fbb06cd6fc529deec6f3dda82. The cited source is identified, but the preceding proposition needed to formulate this question is not included in the supplied excerpt.