Triple
T14430233
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kurt Friedrichs |
E357805
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Friedrichs extension
The Friedrichs extension is a fundamental construction in functional analysis that associates a unique self-adjoint extension to certain symmetric, semibounded operators, playing a key role in the mathematical formulation of quantum mechanics and partial differential equations.
|
E1100053
|
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: Friedrichs extension | Statement: [Kurt Friedrichs, notableWork, Friedrichs extension]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Friedrichs extension Context triple: [Kurt Friedrichs, notableWork, Friedrichs extension]
-
A.
Haag’s theorem
Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
-
B.
Naimark dilation theorem
The Naimark dilation theorem is a fundamental result in operator theory and quantum measurement theory stating that every positive operator-valued measure can be realized as the compression of a projection-valued measure on a larger Hilbert space.
-
C.
Schrödinger operators
Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
-
D.
Gelfand–Naimark–Segal construction
The Gelfand–Naimark–Segal construction is a fundamental procedure in functional analysis that represents abstract C*-algebras as concrete operators on a Hilbert space via states, forming the basis of the GNS representation.
-
E.
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).
- 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: Friedrichs extension Triple: [Kurt Friedrichs, notableWork, Friedrichs extension]
Generated description
The Friedrichs extension is a fundamental construction in functional analysis that associates a unique self-adjoint extension to certain symmetric, semibounded operators, playing a key role in the mathematical formulation of quantum mechanics and partial differential equations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Friedrichs extension Target entity description: The Friedrichs extension is a fundamental construction in functional analysis that associates a unique self-adjoint extension to certain symmetric, semibounded operators, playing a key role in the mathematical formulation of quantum mechanics and partial differential equations.
-
A.
Haag’s theorem
Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
-
B.
Naimark dilation theorem
The Naimark dilation theorem is a fundamental result in operator theory and quantum measurement theory stating that every positive operator-valued measure can be realized as the compression of a projection-valued measure on a larger Hilbert space.
-
C.
Schrödinger operators
Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
-
D.
Gelfand–Naimark–Segal construction
The Gelfand–Naimark–Segal construction is a fundamental procedure in functional analysis that represents abstract C*-algebras as concrete operators on a Hilbert space via states, forming the basis of the GNS representation.
-
E.
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).
- 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_69d8279402a88190821ffa39ae15bccf |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de914570f08190b1c7c1c57a0cb476 |
completed | April 14, 2026, 7:11 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd5bd1c4d0819085edb9ed22128b68 |
completed | May 8, 2026, 3:43 a.m. |
| NEDg | Description generation | batch_69fd5d42e1b48190b41ecafcf9ca9a3b |
completed | May 8, 2026, 3:49 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd5e1ca1e081908441508d651ecc63 |
completed | May 8, 2026, 3:53 a.m. |
Created at: April 10, 2026, 1:18 a.m.