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.