Triple

T6512791
Position Surface form Disambiguated ID Type / Status
Subject John Edensor Littlewood E126367 entity
Predicate knownFor P22 FINISHED
Object Littlewood’s three principles of real analysis
Littlewood’s three principles of real analysis are a set of heuristic guidelines that clarify how measurable sets and functions can be approximated and simplified, emphasizing that they are nearly finite, nearly countable, and nearly continuous.
E600840 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: Littlewood’s three principles of real analysis | Statement: [John Edensor Littlewood, knownFor, Littlewood’s three principles of real analysis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Littlewood’s three principles of real analysis
Context triple: [John Edensor Littlewood, knownFor, Littlewood’s three principles of real analysis]
  • A. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • B. Problems and Theorems in Analysis (with George Pólya)
    "Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
  • C. Singular Integrals and Differentiability Properties of Functions
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • D. Du Bois-Reymond theory of orders of infinity
    The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
  • E. A Course of Pure Mathematics
    A Course of Pure Mathematics is a classic early 20th-century textbook that rigorously introduces the foundations of mathematical analysis and helped shape modern university-level mathematics education.
  • 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: Littlewood’s three principles of real analysis
Triple: [John Edensor Littlewood, knownFor, Littlewood’s three principles of real analysis]
Generated description
Littlewood’s three principles of real analysis are a set of heuristic guidelines that clarify how measurable sets and functions can be approximated and simplified, emphasizing that they are nearly finite, nearly countable, and nearly continuous.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Littlewood’s three principles of real analysis
Target entity description: Littlewood’s three principles of real analysis are a set of heuristic guidelines that clarify how measurable sets and functions can be approximated and simplified, emphasizing that they are nearly finite, nearly countable, and nearly continuous.
  • A. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • B. Problems and Theorems in Analysis (with George Pólya)
    "Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
  • C. Singular Integrals and Differentiability Properties of Functions
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • D. Du Bois-Reymond theory of orders of infinity
    The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
  • E. A Course of Pure Mathematics
    A Course of Pure Mathematics is a classic early 20th-century textbook that rigorously introduces the foundations of mathematical analysis and helped shape modern university-level mathematics education.
  • 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_69c687e68e748190baceb9298f32d3ed completed March 27, 2026, 1:36 p.m.
NER Named-entity recognition batch_69c69f3c5eb88190a56723acd8096dd8 completed March 27, 2026, 3:16 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6cb69ca0c8190954dbe6c627981f3 completed March 27, 2026, 6:24 p.m.
NEDg Description generation batch_69c6cc96edd08190b0c0f1b49dd64160 completed March 27, 2026, 6:29 p.m.
NED2 Entity disambiguation (via description) batch_69c6cd8d15ec8190be5a8c5e3f201139 completed March 27, 2026, 6:33 p.m.
Created at: March 27, 2026, 1:44 p.m.