Triple

T4552383
Position Surface form Disambiguated ID Type / Status
Subject Hardy–Littlewood circle method E120394 entity
Predicate relatedTo P37 FINISHED
Object Hardy–Littlewood conjectures E120396 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 conjectures | Statement: [Hardy–Littlewood circle method, relatedTo, Hardy–Littlewood conjectures]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy–Littlewood conjectures
Context triple: [Hardy–Littlewood circle method, relatedTo, Hardy–Littlewood conjectures]
  • A. Hardy–Littlewood conjectures chosen
    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.
  • B. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • C. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • 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_69bd4636f1648190a701445c2fcd9c17 completed March 20, 2026, 1:05 p.m.
NER Named-entity recognition batch_69bd57f7b9748190af29d02fc77b02e0 completed March 20, 2026, 2:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdc56c0ce08190beb9d4f468b988f7 completed March 20, 2026, 10:08 p.m.
Created at: March 20, 2026, 1:09 p.m.