Triple

T21494266
Position Surface form Disambiguated ID Type / Status
Subject Chinese remainder theorem E530312 entity
Predicate relatedTo P37 FINISHED
Object Bezout's identity E646780 NE FINISHED

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: Bezout's identity | Statement: [Chinese remainder theorem, relatedTo, Bezout's identity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bezout's identity
Context triple: [Chinese remainder theorem, relatedTo, Bezout's identity]
  • A. EGCD
    EGCD is the ICAO airport code for Woodford Aerodrome, a former airfield in Woodford, Greater Manchester, England.
  • B. Bézout’s theorem
    Bézout’s theorem is a fundamental result in algebraic geometry stating that, over an algebraically closed field, the number of intersection points of two projective plane curves (counted with multiplicity) equals the product of their degrees.
  • C. Brahmagupta–Fibonacci identity
    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.
  • D. Euclidean algorithm for polynomials chosen
    The Euclidean algorithm for polynomials is a procedure that repeatedly applies polynomial division to compute the greatest common divisor of two polynomials over a given field or ring.
  • E. Chinese remainder theorem
    The Chinese remainder theorem is a fundamental result in number theory that provides conditions and a method for solving systems of simultaneous congruences with pairwise coprime moduli.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
NED1 Entity disambiguation (via context triple) batch_6a09e1398efc8190a6465defb1715c2b completed May 17, 2026, 3:39 p.m.
Created at: April 16, 2026, 6:23 p.m.