Triple

T7194324
Position Surface form Disambiguated ID Type / Status
Subject Vandermonde's identity E167770 entity
Predicate hasAlternativeName P39 FINISHED
Object Vandermonde convolution identity E167770 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 convolution identity | Statement: [Vandermonde's identity, hasAlternativeName, Vandermonde convolution identity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Vandermonde convolution identity
Context triple: [Vandermonde's identity, hasAlternativeName, Vandermonde convolution identity]
  • A. Vandermonde's identity chosen
    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.
  • B. Pascal's identity
    Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
  • C. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • D. generalized binomial theorem
    The generalized binomial theorem extends the classical binomial theorem by allowing real or complex exponents, expressing powers of a binomial as an infinite series using generalized binomial coefficients.
  • E. 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.
  • 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_69c6888b5248819090499a884ee3ec39 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e9050164819081fd6a11d10f9833 completed March 27, 2026, 8:31 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7db0401f481909cc09c2b8c23cd24 completed March 28, 2026, 1:43 p.m.
Created at: March 27, 2026, 2:50 p.m.