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.