Triple
T7194302
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Vandermonde's identity |
E167770
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Pascal's rule |
E27128
|
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: Pascal's rule | Statement: [Vandermonde's identity, relatedTo, Pascal's rule]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pascal's rule Context triple: [Vandermonde's identity, relatedTo, Pascal's rule]
-
A.
Pascal's identity
chosen
Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
-
B.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
C.
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.
-
D.
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.
-
E.
Catalan numbers
Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
- 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_69c7bf9b8ff48190a561035f754922e9 |
completed | March 28, 2026, 11:46 a.m. |
Created at: March 27, 2026, 2:50 p.m.