Triple

T9838927
Position Surface form Disambiguated ID Type / Status
Subject Johan Frederik Koksma E239171 entity
Predicate notableWork P4 FINISHED
Object Koksma–Hlawka inequality
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.
E824092 NE FINISHED

How this triple was built (4 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 | Statement: [Johan Frederik Koksma, notableWork, Koksma–Hlawka inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Koksma–Hlawka inequality
Context triple: [Johan Frederik Koksma, notableWork, Koksma–Hlawka inequality]
  • A. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • B. Hermite constant
    The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
  • C. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • D. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Koksma–Hlawka inequality
Triple: [Johan Frederik Koksma, notableWork, Koksma–Hlawka inequality]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Koksma–Hlawka inequality
Target entity description: 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.
  • A. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • B. Hermite constant
    The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
  • C. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • D. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • E. 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.
  • F. None of above. chosen

Provenance (5 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_69d1d5d145ac8190ad10a4328216ef54 completed April 5, 2026, 3:24 a.m.
NEDg Description generation batch_69d1d6bb23cc81909efbeccf147018e8 completed April 5, 2026, 3:27 a.m.
NED2 Entity disambiguation (via description) batch_69d1d726e58c819090135d1ff275d2d8 completed April 5, 2026, 3:29 a.m.
Created at: March 30, 2026, 8:33 p.m.