Triple
T13894068
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hadamard three-circle theorem |
E334042
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Phragmén–Lindelöf principle |
E518479
|
NE FINISHED |
How this triple was built (2 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: [Hadamard three-circle theorem, relatedTo, Phragmén–Lindelöf principle]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Phragmén–Lindelöf principle Context triple: [Hadamard three-circle theorem, relatedTo, Phragmén–Lindelöf principle]
-
A.
Lindelöf theorem in complex analysis
chosen
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.
-
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.
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.
-
D.
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.
-
E.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d81c5dd2d48190b7a5fc1e009de936 |
completed | April 9, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69de23a741908190bdf46d76c5f1411a |
completed | April 14, 2026, 11:23 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f7c71ca8a881908ac02687fbfe62fb |
completed | May 3, 2026, 10:07 p.m. |
Created at: April 9, 2026, 10:15 p.m.