Triple
T10543866
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carl Ludwig Siegel |
E248763
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Siegel–Walfisz theorem
The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
|
E871402
|
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: Siegel–Walfisz theorem | Statement: [Carl Ludwig Siegel, notableWork, Siegel–Walfisz theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Siegel–Walfisz theorem Context triple: [Carl Ludwig Siegel, notableWork, Siegel–Walfisz theorem]
-
A.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
-
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.
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.
-
D.
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.
-
E.
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.
- 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: Siegel–Walfisz theorem Triple: [Carl Ludwig Siegel, notableWork, Siegel–Walfisz theorem]
Generated description
The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Siegel–Walfisz theorem Target entity description: The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
-
A.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
-
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.
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.
-
D.
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.
-
E.
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.
- 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_69d381c733c08190ab1dd6239f5f34ae |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d51911b10481909e6e548879e8de36 |
completed | April 7, 2026, 2:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d9343c5c308190952596e5254b6a65 |
completed | April 10, 2026, 5:32 p.m. |
| NEDg | Description generation | batch_69d938c697f481908a93296ee7f82eae |
completed | April 10, 2026, 5:52 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d940176c988190b7583ce9f2c21898 |
completed | April 10, 2026, 6:23 p.m. |
Created at: April 6, 2026, 12:32 p.m.