Frequency Images from Nonadapted Hermitian Structures

Definitions and mathematical statement

The supplied record concerns the frequency map of angular momenta of relative equilibria, denoted by $F$, and a source-specific set denoted by $A_{P_0}$. It does not define this map, the parameter $P_0$, the set $A_{P_0}$, or the class of Hermitian structures under consideration.

For the purpose of stating the requested equality, write $D$ and $Y$ for the unspecified domain and codomain of $F$. Thus \[ \operatorname{Im}F=\{y\in Y:\text{there exists }x\in D\text{ with }F(x)=y\}. \] The proposed assertion is \[ \operatorname{Im}F=A_{P_0}. \] The source describes this as asking whether non-adapted Hermitian structures contribute nothing to the image of the frequency map. If $D_{\mathrm{ad}}\subseteq D$ denotes the inputs corresponding to adapted Hermitian structures, this verbal description suggests the assertion \[ F(D)=F(D_{\mathrm{ad}}). \] However, the supplied record neither defines adaptedness nor supplies the identification $F(D_{\mathrm{ad}})=A_{P_0}$; consequently, the claimed equivalence cannot be established from this record alone. The notation $D$, $Y$, and $D_{\mathrm{ad}}$ introduces placeholders, not additional hypotheses about the intended mathematical setting.

The supplied assessment says that the conjecture is proved for $p=2$ in the extracted source and that the general assertion remains unresolved. The meaning and admissible range of $p$, the hypotheses on the relative equilibria, and the quantification over $P_0$ are not supplied. These omissions prevent a fully specified mathematical formulation.

Short English statement

Does allowing non-adapted Hermitian structures leave the image of the angular-momentum frequency map unchanged, with that image equal to $A_{P_0}$? The supplied record labels the general question open and reports a proof for $p=2$, but omits definitions and hypotheses needed for a complete statement.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $30001830$, source problem code catalogue entry, title "Frequency Images from Nonadapted Hermitian Structures." The supplied collection is "Oberwolfach Reports Open Problems." No individual proposer is supplied; the recorded proposed year is 2011.
• Supplied report citation: Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970. https://doi.org/10.4171/owr/2011/34. The background describes these reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source, labelled "original Oberwolfach report": https://doi.org/10.4171/owr/2011/34. The literature assessment dated exactly 2026-08-21 labels the problem open, reports a proof only for $p=2$ in the extracted source, and describes the general assertion about non-adapted Hermitian structures as unresolved. This is supplied dated curation, not independently verified here; its status and cited claims require independent checking.
• The supplied statement-status field is corrected_verified; its accompanying verification note says that the official report was checked and the statement repaired to match the source passage. This records a supplied verification claim, not an independent verification by this draft.