Triple

T9844121
Position Surface form Disambiguated ID Type / Status
Subject Cauchy determinant E239296 entity
Predicate appliesTo P1129 FINISHED
Object Cauchy matrix E239295 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: Cauchy matrix | Statement: [Cauchy determinant, appliesTo, Cauchy matrix]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cauchy matrix
Context triple: [Cauchy determinant, appliesTo, Cauchy matrix]
  • A. Cauchy matrix chosen
    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.
  • B. Cauchy determinant
    The Cauchy determinant is a classical determinant formula in linear algebra that gives a closed-form expression for matrices with entries of the form 1/(x_i + y_j), named after the French mathematician Augustin-Louis Cauchy.
  • C. Vandermonde matrix
    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.
  • D. Cauchy–Binet formula
    The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
  • 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_69d1e429682c8190a94339b96d4081f6 completed April 5, 2026, 4:25 a.m.
Created at: March 30, 2026, 8:33 p.m.