Triple

T1249045
Position Surface form Disambiguated ID Type / Status
Subject multinomial theorem E26831 entity
Predicate generalizationOf P2372 FINISHED
Object Newton binomial formula E27434 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: Newton binomial formula | Statement: [multinomial theorem, generalizationOf, Newton binomial formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Newton binomial formula
Context triple: [multinomial theorem, generalizationOf, Newton binomial formula]
  • 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. generalized binomial theorem chosen
    The generalized binomial theorem extends the classical binomial theorem by allowing real or complex exponents, expressing powers of a binomial as an infinite series using generalized binomial coefficients.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69a49487a9c48190ba9b05348fd1b53f completed March 1, 2026, 7:33 p.m.
NER Named-entity recognition batch_69a4bf83b32c81908648e5748b897247 completed March 1, 2026, 10:36 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac93c420f08190a6eda4d0aa498a3a completed March 7, 2026, 9:08 p.m.
Created at: March 1, 2026, 7:47 p.m.