Triple

T8669826
Position Surface form Disambiguated ID Type / Status
Subject Pál Turán E205766 entity
Predicate knownFor P22 FINISHED
Object Turán's method
Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
E750084 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's method | Statement: [Pál Turán, knownFor, Turán's method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Turán's method
Context triple: [Pál Turán, knownFor, Turán's method]
  • A. Erdős–Stone theorem
    The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
  • B. Erdős on Graphs: His Legacy
    Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
  • C. 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.
  • D. Erdős–Ko–Rado theorem
    The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
  • E. Erdős–Gallai theorem
    The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
  • 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's method
Triple: [Pál Turán, knownFor, Turán's method]
Generated description
Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Turán's method
Target entity description: Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
  • A. Erdős–Stone theorem
    The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
  • B. Erdős on Graphs: His Legacy
    Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
  • C. 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.
  • D. Erdős–Ko–Rado theorem
    The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
  • E. Erdős–Gallai theorem
    The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
  • 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.