Triple

T8669853
Position Surface form Disambiguated ID Type / Status
Subject Pál Turán E205766 entity
Predicate hasInequalityNamedAfter P83997 FINISHED
Object Turán–Kubilius inequality E750083 NE FINISHED

How this triple was built (3 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, hasInequalityNamedAfter, Turán–Kubilius inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Turán–Kubilius inequality
Context triple: [Pál Turán, hasInequalityNamedAfter, Turán–Kubilius inequality]
  • A. Turán–Kubilius inequality chosen
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasInequalityNamedAfter
Context triple: [Pál Turán, hasInequalityNamedAfter, Turán–Kubilius inequality]
  • A. hasSymbolNamedAfter
    Indicates that one entity has a symbol whose name is derived from or dedicated to another entity.
  • B. namedAfterField
    Indicates that one entity has been given a name derived from or in honor of another entity, typically a person, place, or thing.
  • C. namedAfterSuccessor
    Indicates that an entity is named after another entity that succeeds or follows it in time, position, or sequence.
  • D. hasPeakNamedAfter
    Indicates that a mountain or peak bears a name derived from or dedicated to a particular person, place, or entity.
  • E. hasCollectionNamedAfter
    Indicates that an entity has a collection (e.g., of works, items, or artifacts) that is named in honor of or after another entity.
  • 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_69cef3898bf88190959b361638d032de completed April 2, 2026, 10:54 p.m.
PD Predicate disambiguation batch_69cc4564e018819081036722f3e42a71 completed March 31, 2026, 10:06 p.m.
PDg Predicate description generation batch_69cc46c330bc8190a9b644078881c6ff completed March 31, 2026, 10:12 p.m.
Created at: March 30, 2026, 6:31 p.m.