Triple

T21494103
Position Surface form Disambiguated ID Type / Status
Subject abc conjecture E530309 entity
Predicate subfield P450 FINISHED
Object Diophantine analysis — 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 analysis | Statement: [abc conjecture, subfield, Diophantine analysis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Diophantine analysis
Context triple: [abc conjecture, subfield, Diophantine analysis]
  • A. Diophantine equations
    Diophantine equations are polynomial equations for which only integer or rational solutions are sought, forming a central and often notoriously difficult area of 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. Diophantine geometry chosen
    Diophantine geometry is the branch of number theory that studies solutions to polynomial equations with integer or rational coefficients using geometric methods, particularly those from algebraic geometry.
  • D. Pell-type equations
    Pell-type equations are a class of quadratic Diophantine equations, typically of the form x² − Ny² = 1, that have been studied extensively in number theory since ancient times, including in Indian mathematics.
  • E. 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.
  • 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
Created at: April 16, 2026, 6:23 p.m.