Warped-Cone Rigidity Without Property FSL

Definitions and mathematical statement

The supplied record asks: "Can the technical condition FSL be removed from the warped-cone rigidity theorem?" It does not define FSL, specify the warped-cone construction, or state the rigidity theorem and its remaining hypotheses and conclusion. Thus a self-contained mathematical formulation cannot be recovered from the supplied text alone.

The intended logical question can be expressed only schematically. If the referenced theorem has the form \[ \forall x\in\mathcal C,\qquad \left(H(x)\land\operatorname{FSL}(x)\right)\Longrightarrow R(x), \] where $\mathcal C$ is its class of admissible data, $H$ comprises all its other hypotheses, and $R$ is its rigidity conclusion, does one have \[ \forall x\in\mathcal C,\qquad H(x)\Longrightarrow R(x)? \] Here $\mathcal C$, $H$, $\operatorname{FSL}$, and $R$ are unresolved placeholders, not definitions extracted from the cited theorem. The precise domains, assumptions, boundary conditions, and rigidity conclusion must be recovered from the intended source before this schematic question becomes a precise mathematical statement. The registry labels the problem open; this is a supplied status, not an independently verified mathematical assessment.

Short English statement

Determine whether the intended warped-cone rigidity theorem remains valid after removing only its FSL assumption. The supplied record does not define FSL or identify the theorem precisely enough to state its hypotheses and conclusion; this draft therefore records the intended question schematically and requires human mathematical review.

Sources

• Local UnsolvedMath registry, supplied source record: permanent ID $30003782$, title "Warped-Cone Rigidity Without Property FSL," source problem code catalogue entry, collection "Oberwolfach Reports Open Problems." The record gives proposed year 2018 and supplies no named proposer.
• Supplied report citation: Mini-Workshop: Superexpanders and Their Coarse Geometry (2019), Oberwolfach Reports, pp. 1117--1160, DOI 10.4171/owr/2018/19. https://doi.org/10.4171/owr/2018/19. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source, labeled "workshop report": https://ems.press/content/serial-article-files/46739.
• Supplied literature source, labeled "rigidity theorem": https://www.sciencedirect.com/science/article/pii/S0001870819301069. No theorem number or theorem statement is supplied.
• Supplied literature source, labeled "warped-cone embeddings": https://arxiv.org/abs/1705.06725.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem open and reports that no general removal of FSL or replacement by a proved weaker hypothesis was found by that cutoff, and that available rigidity theorems retain substantial extra assumptions. This is supplied dated literature triage derived from the OWR curation, not an independently verified assessment. The record explicitly calls for independent verification of time-sensitive status and cited claims.