Triple

T10829551
Position Surface form Disambiguated ID Type / Status
Subject Nigel Hitchin E255580 entity
Predicate notableFor P22 FINISHED
Object Hitchin system
The Hitchin system is an influential integrable system in algebraic geometry and mathematical physics, arising from the study of Higgs bundles on Riemann surfaces and playing a key role in areas such as mirror symmetry and the geometric Langlands program.
E886933 NE FINISHED

How this triple was built (4 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: Hitchin system | Statement: [Nigel Hitchin, notableFor, Hitchin system]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hitchin system
Context triple: [Nigel Hitchin, notableFor, Hitchin system]
  • A. 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.
  • B. Hurwitz space
    A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
  • C. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • D. 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.
  • E. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Hitchin system
Triple: [Nigel Hitchin, notableFor, Hitchin system]
Generated description
The Hitchin system is an influential integrable system in algebraic geometry and mathematical physics, arising from the study of Higgs bundles on Riemann surfaces and playing a key role in areas such as mirror symmetry and the geometric Langlands program.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hitchin system
Target entity description: The Hitchin system is an influential integrable system in algebraic geometry and mathematical physics, arising from the study of Higgs bundles on Riemann surfaces and playing a key role in areas such as mirror symmetry and the geometric Langlands program.
  • A. 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.
  • B. Hurwitz space
    A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
  • C. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • D. 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.
  • E. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • F. None of above. chosen

Provenance (5 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_69d6aa8081448190a9324184f2bd1c26 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d74420fa188190b5b3c59e1a9f551d completed April 9, 2026, 6:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69de85a068b08190948c3ca32cdda147 completed April 14, 2026, 6:21 p.m.
NEDg Description generation batch_69de8956d9f081909d076c5e413c1f74 completed April 14, 2026, 6:37 p.m.
NED2 Entity disambiguation (via description) batch_69de8e80fe80819088ac76bb5abc58f0 completed April 14, 2026, 6:59 p.m.
Created at: April 8, 2026, 9:19 p.m.