Triple
T23235090
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Casimir operator |
E581262
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Casimir invariants
Casimir invariants are special central elements of a Lie algebra’s universal enveloping algebra that label and distinguish its irreducible representations by taking constant values within each representation.
|
E581262
|
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: Casimir invariants | Statement: [Casimir operator, relatedTo, Casimir invariants]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Casimir invariants Context triple: [Casimir operator, relatedTo, Casimir invariants]
-
A.
Casimir operator
The Casimir operator is a distinguished central element in the universal enveloping algebra of a Lie algebra that acts as a scalar on each irreducible representation and is used to classify and label those representations.
-
B.
Coleman–Mandula theorem
The Coleman–Mandula theorem is a foundational result in theoretical physics that severely restricts how spacetime and internal symmetries can be combined in a unified quantum field theory, showing that only a direct product of these symmetries is generally allowed.
-
C.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
D.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
-
E.
Haag–Łopuszański–Sohnius theorem
The Haag–Łopuszański–Sohnius theorem is a foundational result in theoretical physics that classifies all possible symmetries of relativistic quantum field theories by showing that supersymmetry provides the unique nontrivial extension of the Poincaré symmetry consistent with a nontrivial S-matrix.
- 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: Casimir invariants Triple: [Casimir operator, relatedTo, Casimir invariants]
Generated description
Casimir invariants are special central elements of a Lie algebra’s universal enveloping algebra that label and distinguish its irreducible representations by taking constant values within each representation.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Casimir invariants Target entity description: Casimir invariants are special central elements of a Lie algebra’s universal enveloping algebra that label and distinguish its irreducible representations by taking constant values within each representation.
-
A.
Casimir operator
chosen
The Casimir operator is a distinguished central element in the universal enveloping algebra of a Lie algebra that acts as a scalar on each irreducible representation and is used to classify and label those representations.
-
B.
Coleman–Mandula theorem
The Coleman–Mandula theorem is a foundational result in theoretical physics that severely restricts how spacetime and internal symmetries can be combined in a unified quantum field theory, showing that only a direct product of these symmetries is generally allowed.
-
C.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
D.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
-
E.
Haag–Łopuszański–Sohnius theorem
The Haag–Łopuszański–Sohnius theorem is a foundational result in theoretical physics that classifies all possible symmetries of relativistic quantum field theories by showing that supersymmetry provides the unique nontrivial extension of the Poincaré symmetry consistent with a nontrivial S-matrix.
- 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_69e2460556f88190be1744a84a84173f |
completed | April 17, 2026, 2:39 p.m. |
| NER | Named-entity recognition | batch_69f192e8c7548190b53434eeb2620a6e |
completed | April 29, 2026, 5:11 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0c3f59de808190afb414450ac32d0d |
completed | May 19, 2026, 10:45 a.m. |
| NEDg | Description generation | batch_6a0c4008c4a881908ad49e733b549036 |
completed | May 19, 2026, 10:48 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0c40bece448190bb9fd1a3058a1f06 |
completed | May 19, 2026, 10:51 a.m. |
Created at: April 17, 2026, 4:09 p.m.