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.