Triple
T3410518
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Srinivasa Ramanujan |
E71880
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E355435
|
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: Ramanujan–Nagell equation | Statement: [Srinivasa Ramanujan, notableWork, Ramanujan–Nagell equation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ramanujan–Nagell equation Context triple: [Srinivasa Ramanujan, notableWork, Ramanujan–Nagell equation]
-
A.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
-
B.
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.
-
C.
Lagrange's four-square theorem
Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
-
D.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- 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: Ramanujan–Nagell equation Triple: [Srinivasa Ramanujan, notableWork, Ramanujan–Nagell equation]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ramanujan–Nagell equation Target entity description: 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.
-
A.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
-
B.
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.
-
C.
Lagrange's four-square theorem
Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
-
D.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- 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_69ad85ac312481909e7027ced1456a9f |
completed | March 8, 2026, 2:20 p.m. |
| NER | Named-entity recognition | batch_69adb9094b2881909262e58a470ed9d0 |
completed | March 8, 2026, 5:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b34bdd99248190823875cae2531609 |
completed | March 12, 2026, 11:27 p.m. |
| NEDg | Description generation | batch_69b34e4972008190af3b84f26b4a3629 |
completed | March 12, 2026, 11:37 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b34fc6c3f88190ba1a08243232df05 |
completed | March 12, 2026, 11:44 p.m. |
Created at: March 8, 2026, 3:15 p.m.