Triple
T209661
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | binomial theorem |
E4686
|
entity |
| Predicate | relatesTo |
P37
|
FINISHED |
| Object |
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.
|
E26830
|
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: Pascal's triangle | Statement: [binomial theorem, relatesTo, Pascal's triangle]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pascal's triangle Context triple: [binomial theorem, relatesTo, Pascal's triangle]
-
A.
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.
-
B.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
-
C.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
D.
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.
-
E.
Numbers
Numbers is the fourth book of the Hebrew Bible and the Christian Old Testament, recounting the Israelites’ wilderness wanderings and organizing laws and censuses.
- 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: Pascal's triangle Triple: [binomial theorem, relatesTo, Pascal's triangle]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Pascal's triangle Target entity description: 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.
-
A.
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.
-
B.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
-
C.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
D.
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.
-
E.
Numbers
Numbers is the fourth book of the Hebrew Bible and the Christian Old Testament, recounting the Israelites’ wilderness wanderings and organizing laws and censuses.
- F. None of above. chosen
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_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_69a332c9e99081909026bf5bfeb6c86c |
completed | Feb. 28, 2026, 6:24 p.m. |
| NEDg | Description generation | batch_69a33326c71c81908c02320901915ce3 |
completed | Feb. 28, 2026, 6:25 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69a3338948808190b6fd60524c721fd5 |
completed | Feb. 28, 2026, 6:27 p.m. |
Created at: Feb. 28, 2026, 2:51 a.m.