Triple
T18479853
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bateman–Horn conjecture |
E451528
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Bunyakovsky conjecture
The Bunyakovsky conjecture is an unproven statement in number theory asserting that certain irreducible integer polynomials with positive leading coefficient take on infinitely many prime values.
|
E1326000
|
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: Bunyakovsky conjecture | Statement: [Bateman–Horn conjecture, generalizes, Bunyakovsky conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bunyakovsky conjecture Context triple: [Bateman–Horn conjecture, generalizes, Bunyakovsky conjecture]
-
A.
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.
-
B.
Hardy–Littlewood conjectures
The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
-
C.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
D.
Goldbach conjecture
The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
-
E.
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.
- 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: Bunyakovsky conjecture Triple: [Bateman–Horn conjecture, generalizes, Bunyakovsky conjecture]
Generated description
The Bunyakovsky conjecture is an unproven statement in number theory asserting that certain irreducible integer polynomials with positive leading coefficient take on infinitely many prime values.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bunyakovsky conjecture Target entity description: The Bunyakovsky conjecture is an unproven statement in number theory asserting that certain irreducible integer polynomials with positive leading coefficient take on infinitely many prime values.
-
A.
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.
-
B.
Hardy–Littlewood conjectures
The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
-
C.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
-
D.
Goldbach conjecture
The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
-
E.
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.
- 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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53066a7108190a50eda9b489c90ca |
completed | April 19, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a043f2f64848190808075254008e6e1 |
completed | May 13, 2026, 9:06 a.m. |
| NEDg | Description generation | batch_6a043fb7db388190bb50cfade4f025f9 |
completed | May 13, 2026, 9:09 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a044063c6048190b65620af8ceed897 |
completed | May 13, 2026, 9:12 a.m. |
Created at: April 10, 2026, 11:35 a.m.