Incomplete Nonlinear Eisenstein-Conjecture Continuation

Definitions and mathematical statement

The supplied record does not contain a recoverable mathematical conjecture. Its entire extracted statement is:

conjecture is (at least a priori) much stronger than the $p$-curvature conjecture. Anabelian Geometry and Representations of Fundamental Groups 2633

The final words and number appear as a report heading and page reference in the supplied extraction. The antecedent of "conjecture" is missing.

According to the supplied statement-verification note, this is a dangling continuation of a preceding conjecture about nonlinear differential equations, and no independently recoverable statement is available in this record. The supplied literature assessment associates the fragment with the Lam--Litt algebraicity and integrality conjecture; the record title calls it an incomplete nonlinear Eisenstein-conjecture continuation. Neither description supplies the missing formulation.

Consequently, no precise conjecture can be stated from the supplied evidence: the mathematical objects, base domains, differential equations, hypotheses, integrality conditions, algebraicity conclusion, and quantifiers are absent. Even the comparison with the $p$-curvature conjecture is qualified by "at least a priori" and cannot be formulated as an implication without the missing antecedent. This draft records the unresolved formulation rather than supplying an invented mathematical statement.

Short English statement

This entry preserves an incomplete sentence comparing an unspecified conjecture with the $p$-curvature conjecture. The supplied curation associates it with Lam--Litt algebraicity and integrality, but the actual hypotheses and conclusion are missing. A precise statement requires recovery and mathematical review of the preceding source text.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $30006072$, source problem code catalogue entry; title: "Incomplete Nonlinear Eisenstein-Conjecture Continuation." The supplied record labels the statement unrecoverable and its status open. No proposer is supplied.
• Supplied source citation: Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670; the fragment contains page number 2633. https://doi.org/10.4171/owr/2024/45. The supplied literature list labels this "Oberwolfach Report 45/2024," and the registry gives proposed year 2024; these supplied year designations are retained without reconciliation.
• Lam--Litt, Algebraicity and integrality, as identified by the supplied literature list: https://arxiv.org/abs/2501.13175.
• Lam--Litt, p-Curvature and non-Abelian cohomology, as identified by the supplied literature list: https://arxiv.org/abs/2601.07933.
• Supplied literature assessment, checked 2026-08-22: the fragment is associated with the Lam--Litt algebraicity and integrality conjecture, described as strengthening the classical $p$-curvature conjecture; the assessment reports special cases and a non-abelian analogue, but no proof of the general conjecture. This is supplied dated curation, not an independently verified literature assessment. The supplied background expressly requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification note reports that the official report confirms a dangling continuation of a preceding nonlinear differential-equation conjecture, with no separate clean statement promoted. This verification claim is reproduced as source metadata and has not been independently checked here.