Triple

T10617349
Position Surface form Disambiguated ID Type / Status
Subject Alexander Beilinson E276155 entity
Predicate knownFor P22 FINISHED
Object 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.
E876105 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: Beilinson–Drinfeld Grassmannian | Statement: [Alexander Beilinson, knownFor, Beilinson–Drinfeld Grassmannian]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Beilinson–Drinfeld Grassmannian
Context triple: [Alexander Beilinson, knownFor, Beilinson–Drinfeld Grassmannian]
  • A. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • B. Kazhdan–Lusztig theory
    Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
  • 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. Gerbes
    Gerbes is a regional supermarket chain in the United States operating as a banner of Kroger and offering groceries and household goods.
  • E. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • 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: Beilinson–Drinfeld Grassmannian
Triple: [Alexander Beilinson, knownFor, Beilinson–Drinfeld Grassmannian]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Beilinson–Drinfeld Grassmannian
Target entity description: 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.
  • A. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • B. Kazhdan–Lusztig theory
    Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
  • 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. Gerbes
    Gerbes is a regional supermarket chain in the United States operating as a banner of Kroger and offering groceries and household goods.
  • E. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • 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_69d6aaf948d88190806cc3a8c47a3fb2 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d6df6e2df4819099a19b59d90d0dd1 completed April 8, 2026, 11:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69d96b7bb7108190b0f1cbe4117abec0 completed April 10, 2026, 9:28 p.m.
NEDg Description generation batch_69d96dee84f48190bf5b0cb1115a8bba completed April 10, 2026, 9:38 p.m.
NED2 Entity disambiguation (via description) batch_69d9708824208190acf75933962d690f completed April 10, 2026, 9:50 p.m.
Created at: April 8, 2026, 7:33 p.m.