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.