Triple
T7030868
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | George Pólya |
E163265
|
entity |
| Predicate | notableIdea |
P4
|
FINISHED |
| Object |
Pólya’s conjecture
Pólya’s conjecture is a disproven hypothesis in number theory that proposed a specific long-term sign pattern for the summatory Möbius function, suggesting it would eventually remain nonpositive.
|
E637315
|
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: Pólya’s conjecture | Statement: [George Pólya, notableIdea, Pólya’s conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pólya’s conjecture Context triple: [George Pólya, notableIdea, Pólya’s conjecture]
-
A.
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.
-
B.
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.
-
C.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
D.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
E.
Vinogradov's three-primes theorem
Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three 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: Pólya’s conjecture Triple: [George Pólya, notableIdea, Pólya’s conjecture]
Generated description
Pólya’s conjecture is a disproven hypothesis in number theory that proposed a specific long-term sign pattern for the summatory Möbius function, suggesting it would eventually remain nonpositive.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Pólya’s conjecture Target entity description: Pólya’s conjecture is a disproven hypothesis in number theory that proposed a specific long-term sign pattern for the summatory Möbius function, suggesting it would eventually remain nonpositive.
-
A.
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.
-
B.
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.
-
C.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
D.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
E.
Vinogradov's three-primes theorem
Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three 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_69c6885d691c81908cf7d31083113886 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6e20ee1208190811be10a84e7d8a4 |
completed | March 27, 2026, 8:01 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.