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.