Triple

T5338226
Position Surface form Disambiguated ID Type / Status
Subject Hardy–Ramanujan asymptotic formula E123877 entity
Predicate instanceOf P0 FINISHED
Object theorem in analytic number theory C716 CONCEPT FINISHED

How this triple was built (1 step)

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.

CD Concept disambiguation gpt-5-mini-2025-08-07 
Target class: theorem in analytic number theory
Context triple: [Hardy–Ramanujan asymptotic formula, instanceOf, theorem in analytic number theory]
  • A. identity in analytic number theory
    Identity in analytic number theory is a rigorously proven equality, often involving series, integrals, or arithmetic functions, that reveals structural relationships between number-theoretic objects and underpins analytic techniques such as transforms, convolutions, and explicit formulas.
  • B. conjecture in number theory
    A conjecture in number theory is an unproven but plausibly true statement about the properties or relationships of integers, often motivated by patterns, partial results, or computational evidence.
  • C. Dirichlet series
    A Dirichlet series is an infinite series of the form ∑ₙ₌₁^∞ aₙ n^(-s), where s is a complex variable and aₙ are complex coefficients, used extensively in analytic number theory to study arithmetic functions and L-functions.
  • D. circle method
    The circle method is an analytic number theory technique that uses integration over the unit circle in the complex plane to estimate the number of representations of integers by various arithmetic functions.
  • E. mathematical theorem chosen
    A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.
  • F. None of above.

Provenance (1 batch)

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_69bd464b07f8819095aa76577c9829e4 completed March 20, 2026, 1:06 p.m.
Created at: March 20, 2026, 2 p.m.