Triple
T21047245
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lindelöf theorem in complex analysis |
E518479
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Phragmén–Lindelöf principle |
—
|
NE NERFINISHED |
How this triple was built (3 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: Phragmén–Lindelöf principle | Statement: [Lindelöf theorem in complex analysis, usesConcept, Phragmén–Lindelöf principle]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Phragmén–Lindelöf principle Context triple: [Lindelöf theorem in complex analysis, usesConcept, Phragmén–Lindelöf principle]
-
A.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
-
B.
Lindelöf theorem in complex analysis
The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
-
C.
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.
-
D.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
-
E.
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.
- 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: Phragmén–Lindelöf principle Target entity description: The Phragmén–Lindelöf principle is a result in complex analysis that extends the maximum modulus principle to unbounded domains, giving growth bounds for holomorphic functions under certain boundary conditions.
-
A.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
-
B.
Lindelöf theorem in complex analysis
The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
-
C.
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.
-
D.
Schwarz lemma
Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
-
E.
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.
- F. None of above. chosen
Provenance (2 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_69e0b50438e08190917e2538bb8bc034 |
completed | April 16, 2026, 10:08 a.m. |
| NER | Named-entity recognition | batch_69e6fcf4d26481908b639996500a8319 |
completed | April 21, 2026, 4:28 a.m. |
Created at: April 16, 2026, 2:34 p.m.