Triple

T6512788
Position Surface form Disambiguated ID Type / Status
Subject John Edensor Littlewood E126367 entity
Predicate knownFor P22 FINISHED
Object Hardy–Littlewood Tauberian theorem E451517 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 Tauberian theorem | Statement: [John Edensor Littlewood, knownFor, Hardy–Littlewood Tauberian theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood Tauberian theorem
Context triple: [John Edensor Littlewood, knownFor, Hardy–Littlewood Tauberian theorem]
  • A. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • 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. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • D. Mertens’ theorems
    Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
  • E. Hardy–Littlewood circle method
    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.
  • 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_69c687e68e748190baceb9298f32d3ed completed March 27, 2026, 1:36 p.m.
NER Named-entity recognition batch_69c69f3c5eb88190a56723acd8096dd8 completed March 27, 2026, 3:16 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6cb69ca0c8190954dbe6c627981f3 completed March 27, 2026, 6:24 p.m.
Created at: March 27, 2026, 1:44 p.m.