Triple
T209694
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | binomial theorem |
E4686
|
entity |
| Predicate | relatedConcept |
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: [binomial theorem, relatedConcept, Pascal's rule]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pascal's rule Context triple: [binomial theorem, relatedConcept, 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.
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.
multinomial theorem
The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
-
E.
Jakob Bernoulli
Jakob Bernoulli was a pioneering Swiss mathematician of the late 17th century, renowned for his foundational work in calculus and probability theory, including the early formulation of the law of large numbers.
- 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_69a25737567c81908f9c505300239181 |
completed | Feb. 28, 2026, 2:47 a.m. |
| NER | Named-entity recognition | batch_69a25c082fa08190b4d097bf68300222 |
completed | Feb. 28, 2026, 3:07 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a33e3dc3008190a021d1b18438b773 |
completed | Feb. 28, 2026, 7:13 p.m. |
Created at: Feb. 28, 2026, 2:51 a.m.