Triple
T9838938
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Johan Frederik Koksma |
E239171
|
entity |
| Predicate | contributedTo |
P37
|
FINISHED |
| Object |
theory of uniform distribution modulo 1
The theory of uniform distribution modulo 1 is a branch of number theory that studies how sequences of real numbers distribute their fractional parts evenly in the unit interval.
|
E824093
|
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: theory of uniform distribution modulo 1 | Statement: [Johan Frederik Koksma, contributedTo, theory of uniform distribution modulo 1]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: theory of uniform distribution modulo 1 Context triple: [Johan Frederik Koksma, contributedTo, theory of uniform distribution modulo 1]
-
A.
Khintchine theorem
Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
-
B.
Erdős–Wintner theorem
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
C.
An Introduction to Diophantine Approximation
"An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
-
D.
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.
-
E.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
- 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: theory of uniform distribution modulo 1 Triple: [Johan Frederik Koksma, contributedTo, theory of uniform distribution modulo 1]
Generated description
The theory of uniform distribution modulo 1 is a branch of number theory that studies how sequences of real numbers distribute their fractional parts evenly in the unit interval.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: theory of uniform distribution modulo 1 Target entity description: The theory of uniform distribution modulo 1 is a branch of number theory that studies how sequences of real numbers distribute their fractional parts evenly in the unit interval.
-
A.
Khintchine theorem
Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
-
B.
Erdős–Wintner theorem
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
C.
An Introduction to Diophantine Approximation
"An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
-
D.
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.
-
E.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
- 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.