Triple

T22423374
Position Surface form Disambiguated ID Type / Status
Subject Erdős–Turán conjecture E554303 entity
Predicate relatedTo P37 FINISHED
Object Erdős–Turán inequality
The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
E1537105 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: Erdős–Turán inequality | Statement: [Erdős–Turán conjecture, relatedTo, Erdős–Turán inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős–Turán inequality
Context triple: [Erdős–Turán conjecture, relatedTo, Erdős–Turán inequality]
  • A. 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.
  • B. 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.
  • C. Pólya–Vinogradov inequality
    The Pólya–Vinogradov inequality is a fundamental result in analytic number theory that gives a strong upper bound on character sums, playing a key role in the study of Dirichlet characters and the distribution of primes in arithmetic progressions.
  • D. 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.
  • E. 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.
  • 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: Erdős–Turán inequality
Triple: [Erdős–Turán conjecture, relatedTo, Erdős–Turán inequality]
Generated description
The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Erdős–Turán inequality
Target entity description: The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
  • A. 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.
  • B. 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.
  • C. Pólya–Vinogradov inequality
    The Pólya–Vinogradov inequality is a fundamental result in analytic number theory that gives a strong upper bound on character sums, playing a key role in the study of Dirichlet characters and the distribution of primes in arithmetic progressions.
  • D. 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.
  • E. 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.
  • 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_69e11e4f2d0c819091aa3558ea2ee630 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15a2af620819083338127e78137dc completed April 29, 2026, 1:08 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0b0c66eaa88190a58d646620de8612 completed May 18, 2026, 12:56 p.m.
NEDg Description generation batch_6a0b0d8a6024819093541ef45e3a22b4 completed May 18, 2026, 1 p.m.
NED2 Entity disambiguation (via description) batch_6a0b0de37c208190ac16ec35b1a8edee completed May 18, 2026, 1:02 p.m.
Created at: April 16, 2026, 8:47 p.m.