Triple
T7030753
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Multiplicative Number Theory |
E163262
|
entity |
| Predicate | hasClassicResult |
P74560
|
FINISHED |
| Object |
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.
|
E637299
|
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: Erdős–Wintner theorem | Statement: [Multiplicative Number Theory, hasClassicResult, Erdős–Wintner theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Erdős–Wintner theorem Context triple: [Multiplicative Number Theory, hasClassicResult, Erdős–Wintner theorem]
-
A.
Erdős–Kac theorem
The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
-
B.
Dirichlet's theorem on arithmetic progressions
Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
-
C.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
-
D.
Bateman–Horn conjecture
The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
-
E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta 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: Erdős–Wintner theorem Triple: [Multiplicative Number Theory, hasClassicResult, Erdős–Wintner theorem]
Generated description
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Erdős–Wintner theorem Target entity description: The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
A.
Erdős–Kac theorem
The Erdős–Kac theorem is a fundamental result in probabilistic number theory stating that the number of distinct prime factors of a typical integer behaves like a normally distributed random variable.
-
B.
Dirichlet's theorem on arithmetic progressions
Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
-
C.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
-
D.
Bateman–Horn conjecture
The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
-
E.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta 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_69c6885d691c81908cf7d31083113886 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6e77415e88190ab65137382f1b155 |
completed | March 27, 2026, 8:24 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c775980920819081d31b8d2843fb3d |
completed | March 28, 2026, 6:30 a.m. |
| NEDg | Description generation | batch_69c77aa1c704819088a9561ac55f9037 |
completed | March 28, 2026, 6:52 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c77b082f3c8190a649297ce0f816bb |
completed | March 28, 2026, 6:54 a.m. |
Created at: March 27, 2026, 2:35 p.m.