Triple

T10055759
Position Surface form Disambiguated ID Type / Status
Subject Gröbner basis E208856 entity
Predicate relatedAlgorithm P25130 FINISHED
Object Buchberger algorithm E243471 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: Buchberger algorithm | Statement: [Gröbner basis, relatedAlgorithm, Buchberger algorithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Buchberger algorithm
Context triple: [Gröbner basis, relatedAlgorithm, Buchberger algorithm]
  • A. Buchberger algorithm chosen
    The Buchberger algorithm is a fundamental procedure in computational algebra for computing Gröbner bases of polynomial ideals, enabling systematic solutions to systems of polynomial equations.
  • B. Gröbner basis
    A Gröbner basis is a particular generating set of an ideal in a polynomial ring that allows algorithmic solutions to many problems in computational algebra, such as ideal membership and solving systems of polynomial equations.
  • C. Zassenhaus algorithm for factoring polynomials over the rationals
    The Zassenhaus algorithm for factoring polynomials over the rationals is a classical computational method that reduces rational polynomial factorization to modular factorization and then recombines the results using lifting techniques.
  • D. Knuth–Bendix completion algorithm
    The Knuth–Bendix completion algorithm is a procedure in term rewriting and automated theorem proving that transforms a set of equations into a confluent rewriting system, enabling decision of word problems in algebraic structures.
  • E. Cantor–Zassenhaus algorithm
    The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
  • 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_69ca836094408190a36a1ea7e9a86fcd completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cdcfacacd08190abe66f8bb17b92c7 completed April 2, 2026, 2:08 a.m.
NED1 Entity disambiguation (via context triple) batch_69d29a49cb208190b56d991a523efbac completed April 5, 2026, 5:22 p.m.
Created at: March 30, 2026, 8:57 p.m.