Triple

T15977085
Position Surface form Disambiguated ID Type / Status
Subject Cauchy functional equation E387476 entity
Predicate alsoKnownAs P39 FINISHED
Object additive Cauchy equation E387476 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: additive Cauchy equation | Statement: [Cauchy functional equation, alsoKnownAs, additive Cauchy equation]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: additive Cauchy equation
Context triple: [Cauchy functional equation, alsoKnownAs, additive Cauchy equation]
  • A. Cauchy functional equation chosen
    The Cauchy functional equation is a fundamental equation in functional analysis and real analysis, typically of the form f(x + y) = f(x) + f(y), whose solutions characterize additive functions and illustrate the contrast between regular (e.g., continuous) and highly pathological behaviors.
  • B. Cauchy–Euler equation
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • C. Cauchy’s mean value theorem
    Cauchy’s mean value theorem is a fundamental result in real analysis that generalizes the standard mean value theorem by relating the rates of change of two differentiable functions on an interval.
  • D. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • E. Ulam stability
    Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69d86da94ccc819083d187f5dc6a123e elicitation completed
NER batch_69e157521f6c8190a54023b5ee6fc033 ner completed
NED1 batch_69ffbe8e4124819084c2937f532f5ab5 ned_source_triple completed
Created at: April 10, 2026, 4:54 a.m.