Triple

T9030830
Position Surface form Disambiguated ID Type / Status
Subject Alan Baker E216165 entity
Predicate notablePublication P4 FINISHED
Object 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.
E772535 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: Transcendental Number Theory | Statement: [Alan Baker, notablePublication, Transcendental Number Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Transcendental Number Theory
Context triple: [Alan Baker, notablePublication, Transcendental Number Theory]
  • A. 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.
  • B. 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.
  • C. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • D. Liouville numbers
    Liouville numbers are real numbers that can be approximated extremely closely by rationals, making them a classic example of transcendental numbers in number theory.
  • E. 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.
  • 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: Transcendental Number Theory
Triple: [Alan Baker, notablePublication, Transcendental Number Theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Transcendental Number Theory
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • D. Liouville numbers
    Liouville numbers are real numbers that can be approximated extremely closely by rationals, making them a classic example of transcendental numbers in number theory.
  • E. 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.
  • 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_69ca83a5fa88819088144801b4dd7245 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cc6a9e0aa881908886f453c51ecd0e completed April 1, 2026, 12:45 a.m.
NED1 Entity disambiguation (via context triple) batch_69cfdbc662208190a3f4e6e593208c5c completed April 3, 2026, 3:24 p.m.
NEDg Description generation batch_69cfdceaa44c81909384939d651b9a61 completed April 3, 2026, 3:29 p.m.
NED2 Entity disambiguation (via description) batch_69cfdd75761c8190b17f97184ae07810 completed April 3, 2026, 3:32 p.m.
Created at: March 30, 2026, 7:08 p.m.