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.