Triple

T20509241
Position Surface form Disambiguated ID Type / Status
Subject Kazhdan–Lusztig theory E503515 entity
Predicate relatedTo P37 FINISHED
Object Schubert calculus
Schubert calculus is a branch of algebraic geometry and combinatorics that studies the intersection theory of Schubert varieties in flag manifolds, often using symmetric functions and representation-theoretic tools.
E1436433 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: Schubert calculus | Statement: [Kazhdan–Lusztig theory, relatedTo, Schubert calculus]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schubert calculus
Context triple: [Kazhdan–Lusztig theory, relatedTo, Schubert calculus]
  • A. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • B. Bott residue formula
    The Bott residue formula is a fundamental result in differential and algebraic geometry that expresses global invariants, such as characteristic numbers, as sums of local contributions at the fixed points of a holomorphic vector field or group action.
  • C. Hilbert scheme theory
    Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
  • D. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • E. Hirzebruch genera
    Hirzebruch genera are topological invariants in algebraic topology and differential geometry that generalize characteristic classes to classify and study manifolds.
  • 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: Schubert calculus
Triple: [Kazhdan–Lusztig theory, relatedTo, Schubert calculus]
Generated description
Schubert calculus is a branch of algebraic geometry and combinatorics that studies the intersection theory of Schubert varieties in flag manifolds, often using symmetric functions and representation-theoretic tools.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Schubert calculus
Target entity description: Schubert calculus is a branch of algebraic geometry and combinatorics that studies the intersection theory of Schubert varieties in flag manifolds, often using symmetric functions and representation-theoretic tools.
  • A. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • B. Bott residue formula
    The Bott residue formula is a fundamental result in differential and algebraic geometry that expresses global invariants, such as characteristic numbers, as sums of local contributions at the fixed points of a holomorphic vector field or group action.
  • C. Hilbert scheme theory
    Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
  • D. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • E. Hirzebruch genera
    Hirzebruch genera are topological invariants in algebraic topology and differential geometry that generalize characteristic classes to classify and study manifolds.
  • 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_69e0b4b1e52c8190894281cf7e3283ab completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69dc9de788190882ce471966ef2b4 completed April 20, 2026, 9:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a089d34c4ac8190a4ff8d8442dac927 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089dc1a5688190ba700d78fb1b1940 completed May 16, 2026, 4:39 p.m.
NED2 Entity disambiguation (via description) batch_6a08a16aa21c8190aa7d79578aca0698 completed May 16, 2026, 4:55 p.m.
Created at: April 16, 2026, 11:36 a.m.