Character-Field Conjecture Introduction

Definitions and mathematical statement

The supplied record for UnsolvedMath ID $30005511$, source code catalogue entry, is titled "Character-Field Conjecture Introduction." Its entire supplied statement is: "We propose the following. The report passage is retained verbatim as the relevant context for this extracted problem." No subsequent conjecture or mathematical definitions are included.

The background identifies the intended context as a fields-of-values "Conjecture B," but does not state its hypotheses, domains, quantified objects, or either condition of the proposed equivalence. Consequently, a precise mathematical statement cannot be recovered from this record without additional source text. In particular, the reference to height-zero characters in quasisimple blocks in the supplied literature assessment does not specify the conjecture itself.

The source marks the statement as unrecoverable. Its supplied verification note says that the official report confirms this extraction is only an incomplete setup and that "the following record preserves the full conjecture"; that following record is not supplied here. No missing formulation is inferred.

Short English statement

This record contains an introduction to a character-field conjecture, but omits the conjecture itself. The supplied dated curation labels the intended problem partially solved; a precise statement requires the missing continuation or referenced following record.

Sources

• Local UnsolvedMath registry, permanent ID $30005511$, exact source code catalogue entry, title "Character-Field Conjecture Introduction." The record lists proposed year 2023 and supplies no named proposer.
• Supplied report citation: Representations of Finite Groups (2023), Oberwolfach Reports, pp. 1031--1084, DOI 10.4171/owr/2023/19. https://doi.org/10.4171/owr/2023/19. The registry attributes the extraction to workshop open-problem discussions documented in this report; the relevant conjecture text is absent from the supplied record.
• Supplied literature source: "Navarro--Ruhstorfer--Tiep--Vallejo, fields of values." https://arxiv.org/abs/2304.12869.
• Supplied literature source: "Oberwolfach Report 19/2023." https://doi.org/10.4171/owr/2023/19.
• Supplied literature source: "On a conjecture of Navarro and Tiep on character fields." https://doi.org/10.1080/00927872.2025.2584406.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the fields-of-values Conjecture B partially solved, states that the "if" implication is proved, and states that the "only-if" implication is reduced to height-zero characters in quasisimple blocks, with the full equivalence remaining open. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The supplied background explicitly requests independent verification of time-sensitive status and cited claims.