Triple

T10389306
Position Surface form Disambiguated ID Type / Status
Subject Weil representation E244847 entity
Predicate constructedVia P3565 FINISHED
Object Stone–von Neumann theorem
The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
E860124 NE FINISHED

How this triple was built (5 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: Stone–von Neumann theorem | Statement: [Weil representation, constructedVia, Stone–von Neumann theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stone–von Neumann theorem
Context triple: [Weil representation, constructedVia, Stone–von Neumann theorem]
  • A. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • B. Stone’s theorem on one-parameter unitary groups
    Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • C. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • D. 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.
  • E. 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.
  • 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: Stone–von Neumann theorem
Triple: [Weil representation, constructedVia, Stone–von Neumann theorem]
Generated description
The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stone–von Neumann theorem
Target entity description: The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
  • A. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • B. Stone’s theorem on one-parameter unitary groups
    Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • C. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • D. 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.
  • E. 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.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: constructedVia
Context triple: [Weil representation, constructedVia, Stone–von Neumann theorem]
  • A. constructedAs chosen
    Indicates that one entity is built, formed, or created in the manner, structure, or configuration specified by another entity.
  • B. constructedTo
    Indicates that one entity has been built, created, or designed for the purpose of serving, supporting, or enabling another entity.
  • C. constructedUnder
    Indicates that something was built, created, or assembled while subject to the authority, direction, or conditions imposed by a particular agent, rule, plan, or regime.
  • D. createdByConstructionOf
    Indicates that something comes into existence as a result of a construction process or building activity performed by an agent.
  • E. constructedDuring
    Indicates that one entity was built or created within the time period defined by another entity or event.
  • F. None of above.

Provenance (6 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9b40dd8819080ac839487020a44 completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d795b2423c8190a7c0e9b6fcbcc6db completed April 9, 2026, 12:04 p.m.
NEDg Description generation batch_69d7998acbf881909b6f063c4bf2d0a6 completed April 9, 2026, 12:20 p.m.
NED2 Entity disambiguation (via description) batch_69d79aa0cc5481908bc14cda8fb6e8b1 completed April 9, 2026, 12:25 p.m.
PD Predicate disambiguation batch_69d4dfb0e7a88190bec0b7a52c70dfe2 completed April 7, 2026, 10:42 a.m.
Created at: April 6, 2026, 12:05 p.m.