Triple

T6117017
Position Surface form Disambiguated ID Type / Status
Subject G. H. Hardy E136383 entity
Predicate notableFor P22 FINISHED
Object Hardy–Littlewood circle method E120394 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: Hardy–Littlewood circle method | Statement: [G. H. Hardy, notableFor, Hardy–Littlewood circle method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood circle method
Context triple: [G. H. Hardy, notableFor, Hardy–Littlewood circle method]
  • A. Hardy–Littlewood circle method chosen
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • B. Hardy–Ramanujan asymptotic formula
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • C. Dirichlet hyperbola method
    The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
  • D. Selberg sieve
    The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
  • E. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • 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_69c0089f851c81909e5e189a617dcff6 completed March 22, 2026, 3:19 p.m.
NER Named-entity recognition batch_69c05beb4cfc8190ab67a5338ec59cea completed March 22, 2026, 9:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69c1256ddb38819095f582b6468db407 completed March 23, 2026, 11:35 a.m.
Created at: March 22, 2026, 4:14 p.m.