Triple
T5896712
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Pál Erdős |
E131117
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Erdős–Moser equation
The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
|
E554305
|
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–Moser equation | Statement: [Pál Erdős, knownFor, Erdős–Moser equation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Erdős–Moser equation Context triple: [Pál Erdős, knownFor, Erdős–Moser equation]
-
A.
Ramanujan–Nagell equation
The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
-
B.
Beal conjecture
The Beal conjecture is an unsolved problem in number theory proposing that if A^x + B^y = C^z with A, B, C, x, y, z positive integers and exponents greater than 2, then A, B, and C must share a common prime factor.
-
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.
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.
Waring's problem
Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
- 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–Moser equation Triple: [Pál Erdős, knownFor, Erdős–Moser equation]
Generated description
The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Erdős–Moser equation Target entity description: The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
-
A.
Ramanujan–Nagell equation
The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
-
B.
Beal conjecture
The Beal conjecture is an unsolved problem in number theory proposing that if A^x + B^y = C^z with A, B, C, x, y, z positive integers and exponents greater than 2, then A, B, and C must share a common prime factor.
-
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.
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.
Waring's problem
Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
- 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_69c00857439c819095950754176aa58a |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c036f4b56c8190aa52c9460eae8fbe |
completed | March 22, 2026, 6:37 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c0b159cb908190b78b78d1e854212b |
completed | March 23, 2026, 3:19 a.m. |
| NEDg | Description generation | batch_69c0b22d661c8190a055abd3ca6fa92f |
completed | March 23, 2026, 3:23 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c0b608a10881908c9bca7d09a99b05 |
completed | March 23, 2026, 3:39 a.m. |
Created at: March 22, 2026, 3:58 p.m.