Triple

T17993985
Position Surface form Disambiguated ID Type / Status
Subject Elliott H. Lieb E430452 entity
Predicate notableWork P4 FINISHED
Object Lieb–Thirring inequality
The Lieb–Thirring inequality is a fundamental result in mathematical physics and analysis that provides bounds on sums of negative eigenvalues of Schrödinger operators, with deep applications to quantum mechanics and stability of matter.
E1300504 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: Lieb–Thirring inequality | Statement: [Elliott H. Lieb, notableWork, Lieb–Thirring inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lieb–Thirring inequality
Context triple: [Elliott H. Lieb, notableWork, Lieb–Thirring inequality]
  • A. Bogoliubov inequality
    The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
  • B. Hardy inequality
    The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
  • C. Morawetz inequalities
    Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
  • D. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • E. Weyl inequalities
    Weyl inequalities are fundamental results in linear algebra that bound the eigenvalues of sums of Hermitian (or symmetric) matrices in terms of the eigenvalues of the individual matrices.
  • 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: Lieb–Thirring inequality
Triple: [Elliott H. Lieb, notableWork, Lieb–Thirring inequality]
Generated description
The Lieb–Thirring inequality is a fundamental result in mathematical physics and analysis that provides bounds on sums of negative eigenvalues of Schrödinger operators, with deep applications to quantum mechanics and stability of matter.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lieb–Thirring inequality
Target entity description: The Lieb–Thirring inequality is a fundamental result in mathematical physics and analysis that provides bounds on sums of negative eigenvalues of Schrödinger operators, with deep applications to quantum mechanics and stability of matter.
  • A. Bogoliubov inequality
    The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
  • B. Hardy inequality
    The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
  • C. Morawetz inequalities
    Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
  • D. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • E. Weyl inequalities
    Weyl inequalities are fundamental results in linear algebra that bound the eigenvalues of sums of Hermitian (or symmetric) matrices in terms of the eigenvalues of the individual matrices.
  • 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_69d8b90364248190a37381adea932f42 completed April 10, 2026, 8:46 a.m.
NER Named-entity recognition batch_69e4b3e29490819090ff221e7d7a9ddd completed April 19, 2026, 10:52 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0337ae62588190b1a6464fb703cc8f completed May 12, 2026, 2:22 p.m.
NEDg Description generation batch_6a033ca6a2608190a391694153070cc8 completed May 12, 2026, 2:43 p.m.
NED2 Entity disambiguation (via description) batch_6a033d6bf3f48190ac141febc04608f6 completed May 12, 2026, 2:47 p.m.
Created at: April 10, 2026, 10:23 a.m.