Triple
T10236304
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Buchberger algorithm |
E243471
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Gröbner basis |
E208856
|
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: Gröbner basis | Statement: [Buchberger algorithm, relatedTo, Gröbner basis]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gröbner basis Context triple: [Buchberger algorithm, relatedTo, Gröbner basis]
-
A.
Gröbner basis
chosen
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.
-
B.
Buchberger algorithm
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.
-
C.
Gröbner fan
A Gröbner fan is a polyhedral fan that encodes all initial ideals (and thus all Gröbner bases) of an ideal with respect to different term orders.
-
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.
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.
- 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_69d381b0f97c819085c9b45799a5fb7c |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d4d219ab04819094a17c96bf1d65ae |
completed | April 7, 2026, 9:44 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d6f762732481909246dcb768074643 |
completed | April 9, 2026, 12:48 a.m. |
Created at: April 6, 2026, 11:22 a.m.