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.