Finite-Group-Theory Contents Fragment

Definitions and mathematical statement

Statement unavailable. The supplied record for permanent UnsolvedMath ID $30006235$, source code catalogue entry, is titled "Finite-Group-Theory Contents Fragment." Its statement status is supplied as unrecoverable, and no clean statement is supplied. The extract contains table-of-contents entries, without an identifiable mathematical assertion, definitions, hypotheses, domains, boundary conditions, or quantifiers. Consequently, no precise conjecture can be stated from this evidence.

The retained context begins with an unidentified entry "Conjecture" followed by page 711, then lists:

• Justin Lynd (joint with Philip Hackney), "Partial groups and higher Segal conditions," p. 713.
• Lucia Morotti (joint with Alexander Kleshchev and Pham Huu Tiep), "Irreducible restrictions of spin representations of symmetric and alternating groups," p. 716.
• Bob Oliver (joint with Carles Broto, Jesper Møller, and Albert Ruiz), "Realizability and tameness of fusion systems," p. 718.
• Kevin I. Piterman (joint with Stephen D. Smith), "On Quillen's conjecture," p. 721.
• Cheryl E. Praeger (joint with Martin Liebeck, and also Cai Heng Li and Shu Jiao Song), "Maps, Simple Groups, and Arc-Transitive Graphs," p. 724.
• Colva M. Roney-Dougal (joint with Gareth Tracey), "Counting subgroups of the symmetric group," p. 726.
• Edoardo Salati, "Fusion systems of characteristic $p$-type---an approach via localities," p. 727.

These are contextual titles and contribution attributions; none identifies the intended conjecture or its proposer. In particular, the occurrence of Quillen's conjecture in a neighboring title does not identify it as the target. The record supplies the year 2025 but no proposer. Its supplied open label is a curation label, not verification that a recoverable mathematical conjecture is open.

Short English statement

This record preserves an incomplete table of contents from a 2025 Oberwolfach report. It supplies no identifiable conjecture to formalize. The intended statement, assumptions, and attribution require recovery and human review; the supplied open label does not establish a mathematical status.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $30006235$, exact source code catalogue entry, title "Finite-Group-Theory Contents Fragment," in the supplied collection "Oberwolfach Reports Open Problems." This draft uses the supplied complete registry record.
• Supplied report citation: Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, pp. 689--752, DOI 10.4171/owr/2025/16. Supplied source URL and literature-source link, labeled "original OWR report": https://doi.org/10.4171/owr/2025/16.
• Supplied literature assessment, checked 2026-08-22: status open. The assessment describes the extraction as a truncated table-of-contents fragment ending in "Conjecture," with no identifiable mathematical claim and no basis for a stronger classification. This is supplied dated curation, not an independently verified literature assessment; the background explicitly requests independent verification of time-sensitive status and cited claims.
• Supplied statement-verification note: the official report is said to confirm that the extraction is a table-of-contents fragment rather than a mathematical conjecture. The record states that no separate clean statement is promoted and that the original remains publicly visible for provenance. This verification claim is reproduced as supplied and has not been independently checked here.