Triple
T4552365
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy–Littlewood circle method |
E120394
|
entity |
| Predicate | appliedTo |
P1129
|
FINISHED |
| Object |
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.
|
E451524
|
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: Goldbach conjecture | Statement: [Hardy–Littlewood circle method, appliedTo, Goldbach conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Goldbach conjecture Context triple: [Hardy–Littlewood circle method, appliedTo, Goldbach conjecture]
-
A.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for 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.
Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
-
D.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
-
E.
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.
- 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: Goldbach conjecture Triple: [Hardy–Littlewood circle method, appliedTo, Goldbach conjecture]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Goldbach conjecture Target entity description: 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.
-
A.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for 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.
Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
-
D.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
-
E.
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.
- 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_69bd4636f1648190a701445c2fcd9c17 |
completed | March 20, 2026, 1:05 p.m. |
| NER | Named-entity recognition | batch_69bd57f7b9748190af29d02fc77b02e0 |
completed | March 20, 2026, 2:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bdb95b01b0819094a600752e41aa09 |
completed | March 20, 2026, 9:17 p.m. |
| NEDg | Description generation | batch_69bdbdbf73508190b64a78ff9274ee6d |
completed | March 20, 2026, 9:35 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bdbe1bcd8c819094adea59c91c6f5b |
completed | March 20, 2026, 9:37 p.m. |
Created at: March 20, 2026, 1:09 p.m.