Triple
T5211903
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gruppentheorie und Quantenmechanik |
E117652
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Weyl representation
The Weyl representation is a specific way of realizing group elements as linear operators on a Hilbert space, widely used in quantum mechanics and representation theory to study symmetries and their action on quantum states.
|
E140812
|
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 representation | Statement: [Gruppentheorie und Quantenmechanik, relatedConcept, Weyl representation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl representation Context triple: [Gruppentheorie und Quantenmechanik, relatedConcept, Weyl representation]
-
A.
Clebsch representation
The Clebsch representation is a mathematical formulation in fluid dynamics and vector calculus that expresses a three-dimensional vector field, particularly a velocity field, in terms of scalar potential functions.
-
B.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
-
C.
Lie algebra representation
A Lie algebra representation is a way of expressing a Lie algebra as linear transformations of a vector space, enabling the study of its structure through matrices and linear operators.
-
D.
Dirac spinors
Dirac spinors are four-component mathematical objects in relativistic quantum mechanics that describe spin-½ particles, such as electrons, incorporating both their spin and particle–antiparticle degrees of freedom.
-
E.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
- 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 representation Triple: [Gruppentheorie und Quantenmechanik, relatedConcept, Weyl representation]
Generated description
The Weyl representation is a specific way of realizing group elements as linear operators on a Hilbert space, widely used in quantum mechanics and representation theory to study symmetries and their action on quantum states.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weyl representation Target entity description: The Weyl representation is a specific way of realizing group elements as linear operators on a Hilbert space, widely used in quantum mechanics and representation theory to study symmetries and their action on quantum states.
-
A.
Clebsch representation
The Clebsch representation is a mathematical formulation in fluid dynamics and vector calculus that expresses a three-dimensional vector field, particularly a velocity field, in terms of scalar potential functions.
-
B.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
-
C.
Lie algebra representation
chosen
A Lie algebra representation is a way of expressing a Lie algebra as linear transformations of a vector space, enabling the study of its structure through matrices and linear operators.
-
D.
Dirac spinors
Dirac spinors are four-component mathematical objects in relativistic quantum mechanics that describe spin-½ particles, such as electrons, incorporating both their spin and particle–antiparticle degrees of freedom.
-
E.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
- F. None of above.
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_69bd4464ba3c8190bc16b2ebbe42ddb0 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7a7166848190805152142e184529 |
completed | March 20, 2026, 4:48 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69beefd9e0b481908db7d6e2907b3b2b |
completed | March 21, 2026, 7:22 p.m. |
| NEDg | Description generation | batch_69bef0b1fe9c8190bfc1be621c7c1c76 |
completed | March 21, 2026, 7:25 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bef16739148190b9700228be7d07f9 |
completed | March 21, 2026, 7:28 p.m. |
Created at: March 20, 2026, 1:47 p.m.