Triple
T20509327
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weyl denominator |
E503517
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Weyl numerator
The Weyl numerator is the polynomial in the Weyl character formula that encodes the contribution of a highest weight representation before division by the Weyl denominator.
|
E1436437
|
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: Weyl numerator | Statement: [Weyl denominator, relatedTo, Weyl numerator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl numerator Context triple: [Weyl denominator, relatedTo, Weyl numerator]
-
A.
Weyl denominator
The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
-
B.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
C.
Weyl dimension formula
The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
-
D.
Weyl vector
The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
-
E.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory 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: Weyl numerator Triple: [Weyl denominator, relatedTo, Weyl numerator]
Generated description
The Weyl numerator is the polynomial in the Weyl character formula that encodes the contribution of a highest weight representation before division by the Weyl denominator.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weyl numerator Target entity description: The Weyl numerator is the polynomial in the Weyl character formula that encodes the contribution of a highest weight representation before division by the Weyl denominator.
-
A.
Weyl denominator
The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
-
B.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
C.
Weyl dimension formula
The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
-
D.
Weyl vector
The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
-
E.
Weyl integration formula
The Weyl integration formula is a fundamental result in representation theory and Lie group theory that expresses integration of class functions over a compact Lie group in terms of integration over a maximal torus with a specific Jacobian factor.
- 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.