Triple
T2408518
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alfred Clebsch |
E50330
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
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.
|
E262456
|
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: Clebsch representation | Statement: [Alfred Clebsch, notableConcept, Clebsch representation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Clebsch representation Context triple: [Alfred Clebsch, notableConcept, Clebsch representation]
-
A.
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.
-
B.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
C.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
D.
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.
-
E.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
- 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: Clebsch representation Triple: [Alfred Clebsch, notableConcept, Clebsch representation]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Clebsch representation Target entity description: 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.
-
A.
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.
-
B.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
C.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
D.
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.
-
E.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
- 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_69a88b0339a88190a1207333cd271cc9 |
completed | March 4, 2026, 7:41 p.m. |
| NER | Named-entity recognition | batch_69abc92408308190ad2d331ebee71d15 |
completed | March 7, 2026, 6:43 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69aeb3eba9d08190a2c63e590e08b4df |
completed | March 9, 2026, 11:50 a.m. |
| NEDg | Description generation | batch_69aeb4a5e9c481908426fe51343a1342 |
completed | March 9, 2026, 11:53 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69aeb52bec1881909c589aea2af3684c |
completed | March 9, 2026, 11:55 a.m. |
Created at: March 4, 2026, 7:58 p.m.