Incomplete Lorentzian-Geometry Result Fragment

Definitions and mathematical statement

The supplied record is an incomplete Lorentzian-geometry result fragment, not a recoverable standalone conjecture. Its opening reference, "Conjecture 3.4]", does not identify a complete claim. No precise open problem can therefore be stated from this evidence alone.

The surviving text mentions quantities $(h_\epsilon)_{\mu\nu}$, metrics denoted by $g_\epsilon$ and $g$, a space denoted by $M$, a set $U$, and a point $p$. Their definitions and governing hypotheses are absent. In particular, no relation between $h_\epsilon$ and $g_\epsilon$ is specified in the supplied fragment.

One surviving condition is \[ (h_\epsilon)_{\mu\nu}\longrightarrow 0 \qquad\text{as }\epsilon\longrightarrow 0, \] together with convergence of all derivatives along $\partial_t$ and a spatial differentiation operator whose printed coefficient is corrupted. The extraction places the tokens $1$, $(\epsilon^2+|x|^2)$, and $2$ before $\partial_x$, without reliably preserving their mathematical arrangement. Thus the spatial operator cannot be specified. The parameter domain, index ranges, coordinates, domain of convergence, and topology or uniformity of convergence are also unspecified.

A further surviving clause, labelled (iii), says that in "setting (II)" one can moreover ensure $g_\epsilon=g$ outside the domain of influence of $\overline U$. Setting (II), the meaning of domain of influence, and the construction or existence statement to which this clause belongs are missing.

The fragment additionally says that "this also holds" when $(M,g)$ is a neighborhood of the domain of outer communications (DOC) of a subextremal $\mathrm{Kerr(dS)}$ spacetime, with $U$ connected and containing both $p$ and a point in the black hole interior. The antecedent of "this", the allowed spacetime parameters, and the convention intended by $\mathrm{Kerr(dS)}$ are not supplied. These clauses are retained as incomplete source qualifications; they do not define a quantified mathematical assertion.

Short English statement

The record preserves fragments of convergence, localization, and a subextremal $\mathrm{Kerr(dS)}$ extension, but omits the underlying result and essential hypotheses. Its supplied "open" label does not identify a complete open conjecture. A statement requires recovery and human mathematical review of the surrounding source.

Sources

• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $30006041$, source problem code catalogue entry; supplied title: "Incomplete Lorentzian-Geometry Result Fragment". The supplied record belongs to the Oberwolfach Reports Open Problems collection. No proposer is identified; the recorded proposed year is 2024.
• Supplied source citation: Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112. Supplied source URL: https://doi.org/10.4171/owr/2024/36. The supplied literature-source label for the same link is "Oberwolfach Report 36 (2024)". The differing year descriptions are retained without resolution.
• Literature assessment dated exactly 2026-08-22: supplied dated curation, not independently verified here. It labels the record open while explaining that the extraction is an incomplete reference to Conjecture 3.4, does not identify a complete claim, and has had its unresolved status normalized to open. The background requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification field reports that the official report confirms a damaged fragment of a result and surrounding technical hypotheses, rather than a standalone open problem. It assigns statement status "unrecoverable", promotes no clean statement, and retains the original record for provenance. This verification report is supplied metadata, not an independent source check performed here.