Triple

T18865108
Position Surface form Disambiguated ID Type / Status
Subject Bogoliubov inequality E461417 entity
Predicate relatedTo P37 FINISHED
Object Griffiths inequalities
Griffiths inequalities are fundamental correlation inequalities in statistical mechanics that constrain spin correlations in ferromagnetic Ising-type models and underpin many rigorous results about phase transitions and monotonicity.
E1347495 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: Griffiths inequalities | Statement: [Bogoliubov inequality, relatedTo, Griffiths inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Griffiths inequalities
Context triple: [Bogoliubov inequality, relatedTo, Griffiths inequalities]
  • 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. Meyer inequalities
    Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
  • C. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • D. 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.
  • E. Chebyshev inequalities
    Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
  • 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: Griffiths inequalities
Triple: [Bogoliubov inequality, relatedTo, Griffiths inequalities]
Generated description
Griffiths inequalities are fundamental correlation inequalities in statistical mechanics that constrain spin correlations in ferromagnetic Ising-type models and underpin many rigorous results about phase transitions and monotonicity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Griffiths inequalities
Target entity description: Griffiths inequalities are fundamental correlation inequalities in statistical mechanics that constrain spin correlations in ferromagnetic Ising-type models and underpin many rigorous results about phase transitions and monotonicity.
  • 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. Meyer inequalities
    Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
  • C. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • D. 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.
  • E. Chebyshev inequalities
    Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
  • 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_69d8dcfb7b9c8190854e7b171b98ea2e completed April 10, 2026, 11:20 a.m.
NER Named-entity recognition batch_69e5c2a5074481908941fcbb3b3eefa2 completed April 20, 2026, 6:07 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0575b902ec8190bcda2ab33b87bea4 completed May 14, 2026, 7:11 a.m.
NEDg Description generation batch_6a057927ddd881908809c9c27e1ae5a2 completed May 14, 2026, 7:26 a.m.
NED2 Entity disambiguation (via description) batch_6a0579982b4c8190a7cff4d2946bc15d completed May 14, 2026, 7:28 a.m.
Created at: April 10, 2026, 11:57 a.m.