Triple

T13070902
Position Surface form Disambiguated ID Type / Status
Subject Bernard Malgrange E329452 entity
Predicate notableFor P22 FINISHED
Object Malgrange–Ehrenpreis theorem
The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
E1021737 NE FINISHED

How this triple was built (4 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: Malgrange–Ehrenpreis theorem | Statement: [Bernard Malgrange, notableFor, Malgrange–Ehrenpreis theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Malgrange–Ehrenpreis theorem
Context triple: [Bernard Malgrange, notableFor, Malgrange–Ehrenpreis theorem]
  • A. Malgrange preparation theorem
    The Malgrange preparation theorem is a fundamental result in analysis and singularity theory that generalizes the Weierstrass preparation theorem to smooth functions, providing a local factorization of such functions near singular points.
  • B. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • C. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • D. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
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: Malgrange–Ehrenpreis theorem
Triple: [Bernard Malgrange, notableFor, Malgrange–Ehrenpreis theorem]
Generated description
The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Malgrange–Ehrenpreis theorem
Target entity description: The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
  • A. Malgrange preparation theorem
    The Malgrange preparation theorem is a fundamental result in analysis and singularity theory that generalizes the Weierstrass preparation theorem to smooth functions, providing a local factorization of such functions near singular points.
  • B. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • C. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • D. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • E. 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.
  • F. None of above. chosen

Provenance (5 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_69d80771749c81909a6d9197b9504872 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69d980ee6130819095d835e7ff6a8c5b completed April 10, 2026, 10:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6e26e5d6881908663444bca67b01e completed May 3, 2026, 5:51 a.m.
NEDg Description generation batch_69f6e32bf5508190b4dc58971f8f64d0 completed May 3, 2026, 5:54 a.m.
NED2 Entity disambiguation (via description) batch_69f6e40a13c8819084daf9b77b46a181 completed May 3, 2026, 5:58 a.m.
Created at: April 9, 2026, 9 p.m.