Triple

T21783731
Position Surface form Disambiguated ID Type / Status
Subject Serge Lang E537781 entity
Predicate notableWork P4 FINISHED
Object Introduction to Diophantine Approximations — 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: Introduction to Diophantine Approximations | Statement: [Serge Lang, notableWork, Introduction to Diophantine Approximations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Introduction to Diophantine Approximations
Context triple: [Serge Lang, notableWork, Introduction to Diophantine Approximations]
  • A. An Introduction to Diophantine Approximation chosen
    "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.
  • B. 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.
  • C. Diophantine approximation
    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.
  • D. 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.
  • 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 (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_69e0c47198f881908cb0d237266c10e9 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69f046303d54819096b3fab4ab5678e6 completed April 28, 2026, 5:31 a.m.
Created at: April 16, 2026, 6:52 p.m.