Triple
T20509232
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kazhdan–Lusztig theory |
E503515
|
entity |
| Predicate | hasPart |
P35
|
FINISHED |
| Object | R-polynomials |
—
|
NE NERFINISHED |
How this triple was built (3 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: R-polynomials | Statement: [Kazhdan–Lusztig theory, hasPart, R-polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: R-polynomials Context triple: [Kazhdan–Lusztig theory, hasPart, R-polynomials]
-
A.
Symanzik polynomials
Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
-
B.
Jack polynomials
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
-
C.
Carlitz polynomials
Carlitz polynomials are a family of polynomials in the theory of function fields over finite fields that serve as analogues of classical Bernoulli polynomials and play a key role in Carlitz module and Drinfeld module theory.
-
D.
Tutte polynomial
The Tutte polynomial is a fundamental graph invariant in combinatorics that encodes extensive structural information about a graph, unifying and generalizing numerous other graph invariants such as the chromatic and flow polynomials.
-
E.
Macdonald polynomials
Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: R-polynomials Target entity description: R-polynomials are certain recursively defined polynomials associated with pairs of elements in a Coxeter group that play a key role in the combinatorial and representation-theoretic structure underlying Kazhdan–Lusztig theory.
-
A.
Symanzik polynomials
Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
-
B.
Jack polynomials
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
-
C.
Carlitz polynomials
Carlitz polynomials are a family of polynomials in the theory of function fields over finite fields that serve as analogues of classical Bernoulli polynomials and play a key role in Carlitz module and Drinfeld module theory.
-
D.
Tutte polynomial
The Tutte polynomial is a fundamental graph invariant in combinatorics that encodes extensive structural information about a graph, unifying and generalizing numerous other graph invariants such as the chromatic and flow polynomials.
-
E.
Macdonald polynomials
Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
- F. None of above. chosen
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_69e0b4b1e52c8190894281cf7e3283ab |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e69dc9de788190882ce471966ef2b4 |
completed | April 20, 2026, 9:42 p.m. |
Created at: April 16, 2026, 11:36 a.m.