Triple

T1060236
Position Surface form Disambiguated ID Type / Status
Subject G. H. Hardy E22889 entity
Predicate notableWork P4 FINISHED
Object Inequalities
"Inequalities" is a classic mathematical monograph by G. H. Hardy (with J. E. Littlewood and G. Pólya) that systematically develops the theory and applications of mathematical inequalities.
E120388 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: Inequalities | Statement: [G. H. Hardy, notableWork, Inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Inequalities
Context triple: [G. H. Hardy, notableWork, Inequalities]
  • A. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • B. Jensen inequality
    Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
  • C. Inequality Reexamined
    Inequality Reexamined is a philosophical and economic work by Amartya Sen that critically analyzes traditional views of inequality and justice through his capabilities approach.
  • D. Without Equal
    "Without Equal" is the English motto expressing the unmatched excellence and elite status of the U.S. Army Special Operations Command.
  • E. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • 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: Inequalities
Triple: [G. H. Hardy, notableWork, Inequalities]
Generated description
"Inequalities" is a classic mathematical monograph by G. H. Hardy (with J. E. Littlewood and G. Pólya) that systematically develops the theory and applications of mathematical inequalities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Inequalities
Target entity description: "Inequalities" is a classic mathematical monograph by G. H. Hardy (with J. E. Littlewood and G. Pólya) that systematically develops the theory and applications of mathematical inequalities.
  • A. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • B. Jensen inequality
    Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
  • C. Inequality Reexamined
    Inequality Reexamined is a philosophical and economic work by Amartya Sen that critically analyzes traditional views of inequality and justice through his capabilities approach.
  • D. Without Equal
    "Without Equal" is the English motto expressing the unmatched excellence and elite status of the U.S. Army Special Operations Command.
  • E. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • 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_69a493dada0481909c43649f9843ea91 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b8f3f98c819096338198d9f30491 completed March 1, 2026, 10:08 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac3bd3400c8190b84e88073f19beba completed March 7, 2026, 2:53 p.m.
NEDg Description generation batch_69ac3ca9b5d88190816980f964f7e947 completed March 7, 2026, 2:56 p.m.
NED2 Entity disambiguation (via description) batch_69ac3d61a0c48190b619b3049df33512 completed March 7, 2026, 2:59 p.m.
Created at: March 1, 2026, 7:42 p.m.