Triple

T22965061
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Lang conjecture E571015 entity
Predicate expressedIn P4596 FINISHED
Object Diophantine approximation language — NE NERFINISHED

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 language | Statement: [Bombieri–Lang conjecture, expressedIn, Diophantine approximation language]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Diophantine approximation language
Context triple: [Bombieri–Lang conjecture, expressedIn, Diophantine approximation language]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. arithmetization of syntax
    Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.