Crystallization under Elastic Interaction Potentials

Definitions and mathematical statement

Research question as supplied. Can the crystallization and limiting results for the particle system be extended to more general interaction potentials that allow elastic deformations?

The supplied context describes an extension from rigid interaction models to more general potentials permitting elastic deformations. It does not identify the particle system, its configuration space, its interaction energy, the rigid reference model, or the crystallization and limiting results to be extended. Neither "crystallization" nor "elastic deformations" is given a mathematical definition in this record. No class of admissible potentials, boundary conditions, limiting parameter, convergence notion, or quantifiers over systems and potentials is specified.

Consequently, the statement above preserves the supplied research target, but a precise theorem or conjecture cannot be formulated from this record alone. Such a formulation requires identifying the reference model and results, specifying the enlarged class of potentials and the meaning of elastic deformation, and stating the hypotheses and conclusions of the proposed extensions. These qualifications remain unresolved; no particular model or interpretation is selected here.

Short English statement

The question asks whether crystallization and limiting results for rigid particle interaction models extend to more general potentials allowing elastic deformation. The supplied record does not specify the models or results sufficiently to state a precise conjecture.

Sources

• Local UnsolvedMath registry: supplied source record with permanent ID $30003986$, title Crystallization under Elastic Interaction Potentials, source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed year is recorded as 2018.
• Supplied report citation: Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, pp. 2915--2967, DOI 10.4171/owr/2018/49. https://doi.org/10.4171/owr/2018/49. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source: Oberwolfach Report 49/2018, https://doi.org/10.4171/owr/2018/49. The literature assessment dated 2026-08-21 labels the problem open and states that extensions from rigid interaction models to general potentials and elastic deformations are not established in the record or cited primary literature, with only special cases available. This is supplied dated curation, not independently verified; the background expressly requests independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and reports a manual semantic, typographic, and LaTeX review asserting self-containment and preservation of the mathematical target. This supplied review label does not resolve the missing mathematical specifications identified above.