Triple

T990118
Position Surface form Disambiguated ID Type / Status
Subject Hermann Weyl E21368 entity
Predicate notableWork P4 FINISHED
Object Gruppentheorie und Quantenmechanik
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
E117652 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: Gruppentheorie und Quantenmechanik | Statement: [Hermann Weyl, notableWork, Gruppentheorie und Quantenmechanik]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gruppentheorie und Quantenmechanik
Context triple: [Hermann Weyl, notableWork, Gruppentheorie und Quantenmechanik]
  • A. Mathematical Foundations of Quantum Mechanics
    Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
  • B. Vorlesungen über Atommechanik
    Vorlesungen über Atommechanik is a foundational early 20th-century textbook on quantum theory and atomic mechanics written by physicist Max Born.
  • C. Wigner’s theorem on symmetry transformations
    Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
  • D. 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.
  • E. matrix mechanics
    Matrix mechanics is an early formulation of quantum mechanics that represents physical observables as matrices and describes their time evolution through noncommutative algebra.
  • 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: Gruppentheorie und Quantenmechanik
Triple: [Hermann Weyl, notableWork, Gruppentheorie und Quantenmechanik]
Generated description
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gruppentheorie und Quantenmechanik
Target entity description: Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
  • A. Mathematical Foundations of Quantum Mechanics
    Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
  • B. Vorlesungen über Atommechanik
    Vorlesungen über Atommechanik is a foundational early 20th-century textbook on quantum theory and atomic mechanics written by physicist Max Born.
  • C. Wigner’s theorem on symmetry transformations
    Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
  • D. 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.
  • E. matrix mechanics
    Matrix mechanics is an early formulation of quantum mechanics that represents physical observables as matrices and describes their time evolution through noncommutative algebra.
  • 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_69a493c383dc8190a03257f22d4b4183 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b4ac27e081908f132115464667b2 completed March 1, 2026, 9:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac258d9f4c8190b285455410b30575 completed March 7, 2026, 1:18 p.m.
NEDg Description generation batch_69ac267e4fa08190895fa6809d0decb8 completed March 7, 2026, 1:22 p.m.
NED2 Entity disambiguation (via description) batch_69ac271c8ad081909c1f1629e0793c40 completed March 7, 2026, 1:24 p.m.
Created at: March 1, 2026, 7:41 p.m.