Triple

T8669825
Position Surface form Disambiguated ID Type / Status
Subject Pál Turán E205766 entity
Predicate knownFor P22 FINISHED
Object Turán–Kubilius inequality
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
E750083 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: Turán–Kubilius inequality | Statement: [Pál Turán, knownFor, Turán–Kubilius inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Turán–Kubilius inequality
Context triple: [Pál Turán, knownFor, Turán–Kubilius inequality]
  • A. Erdős–Kac theorem
    The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
  • B. 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.
  • C. Erdős–Turán conjecture
    The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
  • D. Selberg–Delange method results
    Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
  • E. Erdős–Wintner theorem
    The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
  • 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: Turán–Kubilius inequality
Triple: [Pál Turán, knownFor, Turán–Kubilius inequality]
Generated description
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Turán–Kubilius inequality
Target entity description: The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • A. Erdős–Kac theorem
    The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
  • B. 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.
  • C. Erdős–Turán conjecture
    The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
  • D. Selberg–Delange method results
    Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
  • E. Erdős–Wintner theorem
    The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
  • 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_69ca83516ae88190aefe034b3bc589e3 completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc4917cb9881909a73b74e54250613 completed March 31, 2026, 10:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69cecd2b996481908da33fbd95494376 completed April 2, 2026, 8:10 p.m.
NEDg Description generation batch_69cece8fcbcc8190832a66287bc8f833 completed April 2, 2026, 8:16 p.m.
NED2 Entity disambiguation (via description) batch_69cecff48600819086a15700cb947056 completed April 2, 2026, 8:22 p.m.
Created at: March 30, 2026, 6:31 p.m.