Triple
T13070901
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernard Malgrange |
E329452
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
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.
|
E1020443
|
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 preparation theorem | Statement: [Bernard Malgrange, notableFor, Malgrange preparation theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Malgrange preparation theorem Context triple: [Bernard Malgrange, notableFor, Malgrange preparation theorem]
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Puiseux series
Puiseux series are formal power series in fractional powers of a variable, widely used in algebraic geometry and singularity theory to locally parametrize algebraic curves.
- 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 preparation theorem Triple: [Bernard Malgrange, notableFor, Malgrange preparation theorem]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Malgrange preparation theorem Target entity description: 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.
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Puiseux series
Puiseux series are formal power series in fractional powers of a variable, widely used in algebraic geometry and singularity theory to locally parametrize algebraic curves.
- 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_69f6d60510dc81909e0cba8b63a50d9c |
completed | May 3, 2026, 4:58 a.m. |
| NEDg | Description generation | batch_69f6dbb4b8848190825102be81ff693a |
completed | May 3, 2026, 5:23 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f6dc705f28819087e5d374f83d3acc |
completed | May 3, 2026, 5:26 a.m. |
Created at: April 9, 2026, 9 p.m.