Triple

T7030815
Position Surface form Disambiguated ID Type / Status
Subject Diophantine approximation E163264 entity
Predicate hasSubfield P5461 FINISHED
Object metric Diophantine approximation E163264 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: metric Diophantine approximation | Statement: [Diophantine approximation, hasSubfield, metric Diophantine approximation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: metric Diophantine approximation
Context triple: [Diophantine approximation, hasSubfield, metric Diophantine approximation]
  • A. 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.
  • B. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • C. Khinchin–Lévy constant
    The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
  • D. Diophantine geometry
    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.
  • E. Hermite constant
    The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
  • 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_69c6885d691c81908cf7d31083113886 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e20ee1208190811be10a84e7d8a4 completed March 27, 2026, 8:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c775980920819081d31b8d2843fb3d completed March 28, 2026, 6:30 a.m.
Created at: March 27, 2026, 2:35 p.m.