Triple

T7078849
Position Surface form Disambiguated ID Type / Status
Subject Klaus Roth E164891 entity
Predicate knownFor P22 FINISHED
Object Roth's theorem on Diophantine approximation E637307 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: Roth's theorem on Diophantine approximation | Statement: [Klaus Roth, knownFor, Roth's theorem on Diophantine approximation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Roth's theorem on Diophantine approximation
Context triple: [Klaus Roth, knownFor, Roth's theorem on Diophantine approximation]
  • A. Baker theorem on linear forms in logarithms
    The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
  • B. Roth theorem chosen
    Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
  • C. Khintchine theorem
    Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
  • D. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • 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 (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_69c6887cbc6c8190bdfac42d940f4d8a completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e4ef47d48190b31125d1b57f7bec completed March 27, 2026, 8:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7947294d4819094d7cfb34efde915 completed March 28, 2026, 8:42 a.m.
Created at: March 27, 2026, 2:40 p.m.