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.