Triple

T20404904
Position Surface form Disambiguated ID Type / Status
Subject Fuchsian singularity E500440 entity
Predicate usedIn P98 FINISHED
Object Riemann–Hilbert correspondence NE NERFINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Riemann–Hilbert correspondence | Statement: [Fuchsian singularity, usedIn, Riemann–Hilbert correspondence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann–Hilbert correspondence
Context triple: [Fuchsian singularity, usedIn, Riemann–Hilbert correspondence]
  • A. Riemann–Hilbert correspondence chosen
    The Riemann–Hilbert correspondence is a fundamental result in mathematics that establishes an equivalence between certain differential equations (or flat connections) on complex manifolds and representations of their fundamental groups, linking analytic and topological data.
  • B. Beilinson–Drinfeld Grassmannian
    The Beilinson–Drinfeld Grassmannian is a geometric object in algebraic geometry and representation theory that generalizes the affine Grassmannian to configurations of multiple points, playing a central role in the geometric Langlands program.
  • C. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • D. Beilinson–Bernstein localization theorem
    The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
  • E. Hitchin fibration
    The Hitchin fibration is a fundamental geometric structure in the theory of Higgs bundles that organizes their moduli space into an algebraically completely integrable system with deep connections to representation theory and the geometric Langlands program.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e0b4a81bec8190b69adfdc1336a015 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6799161c48190825eca3027d1aa51 completed April 20, 2026, 7:08 p.m.
Created at: April 16, 2026, 11:29 a.m.