Triple

T4416462
Position Surface form Disambiguated ID Type / Status
Subject Knuth–Bendix completion algorithm E94985 entity
Predicate relatedTo P37 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: [Knuth–Bendix completion algorithm, relatedTo, Buchberger algorithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Buchberger algorithm
Context triple: [Knuth–Bendix completion algorithm, relatedTo, 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. 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.
  • D. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • E. Berlekamp’s algorithm for factoring polynomials over finite fields
    Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory 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_69b3453a36908190b95a79a297ca083c completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b3551afb448190a2ce2000193808ac completed March 13, 2026, 12:06 a.m.
NED1 Entity disambiguation (via context triple) batch_69b5f61b56a8819099b5302f1b53f76d completed March 14, 2026, 11:58 p.m.
Created at: March 12, 2026, 11:29 p.m.