Triple

T9844095
Position Surface form Disambiguated ID Type / Status
Subject Cauchy matrix E239295 entity
Predicate relatedTo P37 FINISHED
Object Vandermonde matrix E620657 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: Vandermonde matrix | Statement: [Cauchy matrix, relatedTo, Vandermonde matrix]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Vandermonde matrix
Context triple: [Cauchy matrix, relatedTo, Vandermonde matrix]
  • A. Vandermonde matrix chosen
    A Vandermonde matrix is a structured matrix whose rows (or columns) are geometric progressions of given numbers, widely used in polynomial interpolation, determinant theory, and numerical analysis.
  • B. Cauchy matrix
    A Cauchy matrix is a structured matrix whose entries are defined by the reciprocals of pairwise differences of two sequences, widely used in numerical analysis, interpolation, and algebra.
  • C. Sylvester matrix
    The Sylvester matrix is a structured matrix constructed from the coefficients of two polynomials, commonly used to compute their resultant and study common roots in algebra.
  • D. Vandermonde's identity
    Vandermonde's identity is a fundamental combinatorial formula that expresses a binomial coefficient with a sum index as a sum of products of binomial coefficients, often visualized via counting arguments or generating functions.
  • E. Sylvester determinant
    The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
  • 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_69ca84e3f0c48190ada72a65ebd50efd completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb35dc29c819080203be5b904dc9d completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5dda4b0819092703270e87bee5a completed April 5, 2026, 3:24 a.m.
Created at: March 30, 2026, 8:33 p.m.