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.