Triple

T209668
Position Surface form Disambiguated ID Type / Status
Subject binomial theorem E4686 entity
Predicate hasGeneralization P2372 FINISHED
Object Newton's generalized binomial theorem 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's generalized binomial theorem | Statement: [binomial theorem, hasGeneralization, Newton's generalized binomial theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Newton's generalized binomial theorem
Context triple: [binomial theorem, hasGeneralization, Newton's generalized binomial theorem]
  • A. 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.
  • B. 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.
  • 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. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • 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_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_69a3441cc15c8190910b1b9e5dbb4910 completed Feb. 28, 2026, 7:38 p.m.
Created at: Feb. 28, 2026, 2:51 a.m.