Triple

T9838943
Position Surface form Disambiguated ID Type / Status
Subject Johan Frederik Koksma E239171 entity
Predicate notableConcept P201 FINISHED
Object Koksma–Hlawka inequality in numerical integration E824092 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: Koksma–Hlawka inequality in numerical integration | Statement: [Johan Frederik Koksma, notableConcept, Koksma–Hlawka inequality in numerical integration]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Koksma–Hlawka inequality in numerical integration
Context triple: [Johan Frederik Koksma, notableConcept, Koksma–Hlawka inequality in numerical integration]
  • A. Koksma–Hlawka inequality chosen
    The Koksma–Hlawka inequality is a fundamental result in numerical analysis and discrepancy theory that bounds the error of quasi-Monte Carlo integration by the product of a function’s variation and the discrepancy of the sampling points.
  • B. Gaussian quadrature rules
    Gaussian quadrature rules are numerical integration methods that approximate definite integrals by optimally choosing evaluation points and weights to achieve exactness for polynomials up to a high degree.
  • C. van der Corput method for estimating exponential sums
    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.
  • D. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • E. van der Corput method
    The van der Corput method is a technique in analytic number theory used to estimate exponential sums and derive bounds for problems such as the distribution of prime numbers and lattice point counting.
  • 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_69ca84e314108190978324a4bdb959f8 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb34921b881909836ba0f5b42a27b completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1e429682c8190a94339b96d4081f6 completed April 5, 2026, 4:25 a.m.
Created at: March 30, 2026, 8:33 p.m.