Triple

T9844056
Position Surface form Disambiguated ID Type / Status
Subject Cauchy principal value E239294 entity
Predicate relatedConcept P37 FINISHED
Object Hadamard finite part
The Hadamard finite part is a generalized method of assigning finite values to divergent integrals or series by systematically isolating and discarding their singular components.
 E239294 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: Hadamard finite part | Statement: [Cauchy principal value, relatedConcept, Hadamard finite part]

Disambiguation candidates (2 decisions)

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: Hadamard finite part
Context triple: [Cauchy principal value, relatedConcept, Hadamard finite part]
  • A. Hadamard fractional integral
    The Hadamard fractional integral is a generalization of the classical integral that defines fractional-order integration using logarithmic kernels, particularly suited to functions defined on multiplicative (e.g., positive real) domains.
  • B. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • C. Cauchy principal value
    The Cauchy principal value is a method in mathematical analysis for assigning finite values to certain improper or divergent integrals and series by symmetrically balancing their singularities.
  • D. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Hadamard finite part
Target entity description: The Hadamard finite part is a generalized method of assigning finite values to divergent integrals or series by systematically isolating and discarding their singular components.
  • A. Hadamard fractional integral
    The Hadamard fractional integral is a generalization of the classical integral that defines fractional-order integration using logarithmic kernels, particularly suited to functions defined on multiplicative (e.g., positive real) domains.
  • B. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • C. Cauchy principal value chosen
    The Cauchy principal value is a method in mathematical analysis for assigning finite values to certain improper or divergent integrals and series by symmetrically balancing their singularities.
  • D. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • F. None of above.

How the object was described

The object's one-sentence description was generated by prompting gpt-5.1 with the object name and this triple as context.

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: Hadamard finite part
Triple: [Cauchy principal value, relatedConcept, Hadamard finite part]
Generated description
The Hadamard finite part is a generalized method of assigning finite values to divergent integrals or series by systematically isolating and discarding their singular components.

Provenance (5 batches)

Stage Batch ID Job type Status
creating batch_69ca84e3f0c48190ada72a65ebd50efd elicitation completed
NER batch_69cdb35dc29c819080203be5b904dc9d ner completed
NED1 batch_69d1d5dda4b0819092703270e87bee5a ned_source_triple completed
NED2 batch_69d1d74e7a148190a9470745bfd7ad42 ned_description completed
NEDg batch_69d1d6815e28819081788393cda63bc0 nedg completed
Created at: March 30, 2026, 8:33 p.m.