Triple
T7194300
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Vandermonde's identity |
E167770
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Chu–Vandermonde identity
The Chu–Vandermonde identity is a classical combinatorial and hypergeometric summation formula that generalizes Vandermonde's identity to rising factorials (Pochhammer symbols) and binomial-type coefficients.
|
E167770
|
NE FINISHED |
How this triple was built (4 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: Chu–Vandermonde identity | Statement: [Vandermonde's identity, relatedTo, Chu–Vandermonde identity]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chu–Vandermonde identity Context triple: [Vandermonde's identity, relatedTo, Chu–Vandermonde identity]
-
A.
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.
-
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.
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.
-
E.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Chu–Vandermonde identity Triple: [Vandermonde's identity, relatedTo, Chu–Vandermonde identity]
Generated description
The Chu–Vandermonde identity is a classical combinatorial and hypergeometric summation formula that generalizes Vandermonde's identity to rising factorials (Pochhammer symbols) and binomial-type coefficients.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chu–Vandermonde identity Target entity description: The Chu–Vandermonde identity is a classical combinatorial and hypergeometric summation formula that generalizes Vandermonde's identity to rising factorials (Pochhammer symbols) and binomial-type coefficients.
-
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.
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.
-
E.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
- F. None of above.
Provenance (5 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_69c7cbe7d42c8190915fd0713523cbb0 |
completed | March 28, 2026, 12:39 p.m. |
| NEDg | Description generation | batch_69c7cc787a9881908c44b1b94b748e9c |
completed | March 28, 2026, 12:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7cd0eb36c8190bc8e4265033d214f |
completed | March 28, 2026, 12:43 p.m. |
Created at: March 27, 2026, 2:50 p.m.