Triple

T18397362
Position Surface form Disambiguated ID Type / Status
Subject Brahmagupta E449902 entity
Predicate knownFor P22 FINISHED
Object Brahmagupta–Fibonacci identity NE NERFINISHED

How this triple was built (2 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: Brahmagupta–Fibonacci identity | Statement: [Brahmagupta, knownFor, Brahmagupta–Fibonacci identity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Brahmagupta–Fibonacci identity
Context triple: [Brahmagupta, knownFor, Brahmagupta–Fibonacci identity]
  • A. Brahmagupta–Fibonacci identity chosen
    The Brahmagupta–Fibonacci identity is a classical algebraic formula showing that the product of two sums of two squares can itself be expressed as a sum of two squares, fundamental in number theory and the study of quadratic forms.
  • B. 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.
  • 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. 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.
  • E. Legendre's three-square theorem
    Legendre's three-square theorem is a result in number theory that characterizes exactly which positive integers can be expressed as the sum of three squares of integers.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b9fab8a8819086a9ddc0871715e0 completed April 10, 2026, 8:51 a.m.
NER Named-entity recognition batch_69e5184777548190818365ee52ac88b7 completed April 19, 2026, 6 p.m.
Created at: April 10, 2026, 10:46 a.m.