Triple

T18479720
Position Surface form Disambiguated ID Type / Status
Subject Vinogradov's three-primes theorem E451525 entity
Predicate usesConcept P531 FINISHED
Object Weyl differencing — 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: Weyl differencing | Statement: [Vinogradov's three-primes theorem, usesConcept, Weyl differencing]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weyl differencing
Context triple: [Vinogradov's three-primes theorem, usesConcept, Weyl differencing]
  • A. van der Corput method for estimating exponential sums chosen
    The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
  • B. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • C. Cartwright–Littlewood theory on nonlinear differential equations
    Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
  • D. 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.
  • E. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.