Classification of Symbolic Systems with Specification

Definitions and mathematical statement

The supplied candidate problem is: "Classify symbolic dynamical systems with the specification property." This does not determine a precise mathematical classification problem. The record does not specify the alphabet, the acting group or semigroup, whether the systems are one-sided or two-sided, the definition of the specification property, or the equivalence relation and intended form of classification. No choices for these data are imposed in this draft.

The supplied original passage reads: "list of open problems, which is now maintained on the webpage [32]. The report passage is retained verbatim as the relevant context for this extracted problem." This fragment states no mathematical claim and supplies no definitions connecting it to the candidate problem. Consequently, neither the intended class of systems nor its defining assumptions and quantifiers can be recovered from the supplied passage. A precise mathematical statement remains unresolved pending identification of the actual problem and its definitions.

The registry labels the statement corrected_verified and says that it was reconstructed and checked against the official report. These are supplied verification claims; the evidence included here does not establish the connection. Likewise, the supplied open status is a registry classification, not an independently verified mathematical conclusion.

Short English statement

The record requests a classification of symbolic dynamical systems with specification, but its quoted source only mentions an unidentified online problem list. The intended systems, specification condition, and classification criterion remain unspecified, so a precise problem cannot be recovered from the supplied evidence.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30006174$, exact source problem code catalogue entry, title "Classification of Symbolic Systems with Specification." The record belongs to the Oberwolfach Reports Open Problems collection and the Set Theory category. It records proposed year 2025 and supplies no proposer attribution.
• Supplied report citation: Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140. https://doi.org/10.4171/owr/2025/2. This is the supplied report provenance; the included extract does not substantiate the candidate classification problem.
• Supplied literature source: "Oberwolfach Report 2/2025." https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf.
• Literature assessment checked at 2026-08-22: supplied dated curation, not independently verified. The supplied status is open. The accompanying assessment says that the extract merely mentions a maintained open-problem list without identifying a mathematical claim, and therefore cannot support a solved or refuted classification. The supplied background requests independent verification of time-sensitive status and cited claims.
• The original fragment refers to a webpage as reference [32], but its bibliographic entry and URL are absent. No authoritative citation establishing the specific classification statement is supplied beyond the unsubstantiated report attribution and registry verification claim.