Triple

T209670
Position Surface form Disambiguated ID Type / Status
Subject binomial theorem E4686 entity
Predicate forComplexExponent P4746 FINISHED
Object (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ — LITERAL 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: (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ | Statement: [binomial theorem, forComplexExponent, (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: forComplexExponent
Context triple: [binomial theorem, forComplexExponent, (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ]
  • A. logarithmBaseDetermines
    Indicates that the chosen base of a logarithm determines how a quantity is expressed or scaled in logarithmic terms.
  • B. mathematicallyUses chosen
    Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
  • C. usesComputationMethod
    Indicates that an entity performs its processing or decision-making by applying a specified computational method or algorithm.
  • D. exclusivePower
    Indicates that one entity holds sole authority or control over another entity or a specific domain, excluding others from sharing that power.
  • E. exercisedPowerOver
    Indicates that one entity exerted control, influence, or authority over another entity.
  • F. None of above.

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_69a25e8b9b908190b69a3f0594b95f7e completed Feb. 28, 2026, 3:18 a.m.
PD Predicate disambiguation batch_69a25b4e3c2881908d83e8218aa9f2d9 completed Feb. 28, 2026, 3:04 a.m.
Created at: Feb. 28, 2026, 2:51 a.m.