Triple

T15502758
Position Surface form Disambiguated ID Type / Status
Subject Continued Fractions E379001 entity
Predicate subject P450 FINISHED
Object Diophantine approximation E163264 NE FINISHED

How this triple was built (2 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: Diophantine approximation | Statement: [Continued Fractions, subject, Diophantine approximation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Diophantine approximation
Context triple: [Continued Fractions, subject, Diophantine approximation]
  • A. Diophantine approximation chosen
    Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
  • B. An Introduction to Diophantine Approximation
    "An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
  • C. Liouville's inequality in Diophantine approximation
    Liouville's inequality in Diophantine approximation is a foundational result that gives explicit lower bounds on how closely algebraic numbers can be approximated by rationals, leading to the first examples of transcendental numbers.
  • D. Dirichlet approximation theorem
    The Dirichlet approximation theorem is a fundamental result in Diophantine approximation that guarantees, for any real number and positive integer, the existence of a nearby rational number with bounded denominator and small approximation error.
  • E. Transcendental Number Theory
    Transcendental Number Theory is a mathematical monograph by Alan Baker that develops methods for studying transcendental and algebraic numbers, particularly through linear forms in logarithms.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d85cd53a7c819080f5b9042c4c199e completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e03fcc5bb88190b8a9a81419a9a38b completed April 16, 2026, 1:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3669f908819087162b1b8a4e4320 completed May 9, 2026, 1:28 p.m.
Created at: April 10, 2026, 3:54 a.m.