Triple
T16720466
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Indian mathematics |
E406333
|
entity |
| Predicate | developedMethod |
P73
|
FINISHED |
| Object |
chakravala method for solving indeterminate equations
The chakravala method for solving indeterminate equations is an ancient Indian cyclic algorithm, notably used to solve Pell-type quadratic Diophantine equations with remarkable efficiency and generality.
|
E1230018
|
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: chakravala method for solving indeterminate equations | Statement: [Indian mathematics, developedMethod, chakravala method for solving indeterminate equations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: chakravala method for solving indeterminate equations Context triple: [Indian mathematics, developedMethod, chakravala method for solving indeterminate equations]
-
A.
Bhaskara’s Bhedabheda
Bhaskara’s Bhedabheda is a sub-school of Vedanta that teaches the soul’s simultaneous difference and non-difference from Brahman, emphasizing both their unity and real distinction.
-
B.
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.
-
C.
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.
-
D.
Lebesgue–Nagell equation
The Lebesgue–Nagell equation is a Diophantine equation of the form \(x^2 + D = y^n\) (with fixed integers \(D\) and \(n \ge 3\)) studied in number theory for its finite and often explicitly determinable set of integer solutions.
-
E.
On Pythagorean Numbers
On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
- 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: chakravala method for solving indeterminate equations Triple: [Indian mathematics, developedMethod, chakravala method for solving indeterminate equations]
Generated description
The chakravala method for solving indeterminate equations is an ancient Indian cyclic algorithm, notably used to solve Pell-type quadratic Diophantine equations with remarkable efficiency and generality.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: chakravala method for solving indeterminate equations Target entity description: The chakravala method for solving indeterminate equations is an ancient Indian cyclic algorithm, notably used to solve Pell-type quadratic Diophantine equations with remarkable efficiency and generality.
-
A.
Bhaskara’s Bhedabheda
Bhaskara’s Bhedabheda is a sub-school of Vedanta that teaches the soul’s simultaneous difference and non-difference from Brahman, emphasizing both their unity and real distinction.
-
B.
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.
-
C.
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.
-
D.
Lebesgue–Nagell equation
The Lebesgue–Nagell equation is a Diophantine equation of the form \(x^2 + D = y^n\) (with fixed integers \(D\) and \(n \ge 3\)) studied in number theory for its finite and often explicitly determinable set of integer solutions.
-
E.
On Pythagorean Numbers
On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
- 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_69d8838f242881908abd8bc138795886 |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e3874270748190ad7c3b3531293b60 |
completed | April 18, 2026, 1:29 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a009d41cb6c8190bfa164ad20f009d9 |
completed | May 10, 2026, 2:59 p.m. |
| NEDg | Description generation | batch_6a009deba8448190a9f480e6807ea6be |
completed | May 10, 2026, 3:02 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a009e5daf808190ae75d8c3e22aaef2 |
completed | May 10, 2026, 3:03 p.m. |
Created at: April 10, 2026, 5:20 a.m.