Calibrations for Unoriented Minimum Matching

Definitions and mathematical statement

The supplied record asks:

How much of the calibration and filling-minimization procedure survives for the unoriented minimum-matching problem after discarding the linear duality between currents and differential forms?

The record does not define the unoriented minimum-matching problem, the calibration procedure, or the filling-minimization procedure. It does not specify an ambient space, input configurations, admissible matchings, an objective functional, a class of fillings, boundary conditions, or coefficients for currents. Nor does it identify which conclusions of the original procedure should survive, or what mathematical structure is retained after discarding the stated duality. Consequently, the supplied question cannot be converted into a uniquely determined quantified mathematical assertion without additional source context. No particular domain, coefficient system, replacement notion of calibration, or equivalence between matching and filling minimization is assumed in this draft.

Short English statement

The question asks which aspects of a calibration and filling-minimization procedure remain available for unoriented minimum matching when the linear duality between currents and differential forms is discarded. The underlying objects, procedure, and desired conclusions are unspecified, so a precise mathematical formulation requires further source context.

Sources

• Local UnsolvedMath registry, permanent ID $30002622$, title Calibrations for Unoriented Minimum Matching, source problem code catalogue entry, collection Oberwolfach Reports Open Problems. The supplied proposed year is 2014; no proposer is named.
• Supplied source citation: Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860. Source URL and supplied literature-source link, labeled "original Oberwolfach report": https://doi.org/10.4171/owr/2014/33. The record describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The cited report has not been independently consulted for this draft.
• Supplied literature assessment, checked on 2026-08-21: the extracted record is a vague fragment about how much of a matching procedure survives after discarding structure, and no uniquely identifiable proposition or resolution can be verified. The supplied status is open. This is supplied dated curation derived from the OWR record, not an independently verified assessment of mathematical status; time-sensitive status and cited claims require independent verification.
• The supplied statement status is exact, and its verification field describes the statement as clear, self-contained, publication-ready, and retained byte-for-byte. These are supplied editorial claims; they do not resolve the missing mathematical specifications identified above.