Triple

T9838944
Position Surface form Disambiguated ID Type / Status
Subject Johan Frederik Koksma E239171 entity
Predicate areaOfInfluence P9 FINISHED
Object Dutch school of number theory
The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
E824094 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: Dutch school of number theory | Statement: [Johan Frederik Koksma, areaOfInfluence, Dutch school of number theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dutch school of number theory
Context triple: [Johan Frederik Koksma, areaOfInfluence, Dutch school of number theory]
  • A. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • B. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • C. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • D. Polish School of Mathematics
    The Polish School of Mathematics was a renowned early 20th-century mathematical tradition centered in cities like Warsaw and Lwów, noted for its groundbreaking work in areas such as functional analysis, topology, and logic.
  • E. Lwów School of Mathematics
    The Lwów School of Mathematics was a renowned early 20th-century Polish mathematical community centered in Lwów, famous for its groundbreaking work in functional analysis, set theory, and probability, and for its collaborative problem-solving culture documented in the Scottish Book.
  • 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: Dutch school of number theory
Triple: [Johan Frederik Koksma, areaOfInfluence, Dutch school of number theory]
Generated description
The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dutch school of number theory
Target entity description: The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
  • A. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • B. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • C. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • D. Polish School of Mathematics
    The Polish School of Mathematics was a renowned early 20th-century mathematical tradition centered in cities like Warsaw and Lwów, noted for its groundbreaking work in areas such as functional analysis, topology, and logic.
  • E. Lwów School of Mathematics
    The Lwów School of Mathematics was a renowned early 20th-century Polish mathematical community centered in Lwów, famous for its groundbreaking work in functional analysis, set theory, and probability, and for its collaborative problem-solving culture documented in the Scottish Book.
  • 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_69ca84e314108190978324a4bdb959f8 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb34921b881909836ba0f5b42a27b completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5d145ac8190ad10a4328216ef54 completed April 5, 2026, 3:24 a.m.
NEDg Description generation batch_69d1d6bb23cc81909efbeccf147018e8 completed April 5, 2026, 3:27 a.m.
NED2 Entity disambiguation (via description) batch_69d1d726e58c819090135d1ff275d2d8 completed April 5, 2026, 3:29 a.m.
Created at: March 30, 2026, 8:33 p.m.