Triple
T10991847
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schwarz lemma |
E259769
|
entity |
| Predicate | alsoKnownAs |
P39
|
FINISHED |
| Object | Schwarz’s lemma |
E259769
|
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: Schwarz’s lemma | Statement: [Schwarz lemma, alsoKnownAs, Schwarz’s lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schwarz’s lemma Context triple: [Schwarz lemma, alsoKnownAs, Schwarz’s lemma]
-
A.
Schwarz lemma
chosen
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.
-
B.
Schwarz–Pick theorem
The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
-
C.
Bieberbach conjecture
The Bieberbach conjecture, now a theorem, is a landmark result in complex analysis that characterizes the size of Taylor coefficients of normalized univalent (injective) holomorphic functions on the unit disk.
-
D.
Rouché's theorem
Rouché's theorem is a result in complex analysis that provides conditions under which two holomorphic functions have the same number of zeros inside a given contour.
-
E.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
- 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_69d6aa8a6a548190a750f944ccdc8064 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d795d1e918819090c71f5a077fa15a |
completed | April 9, 2026, 12:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e3c8190c888190ba8d6fb2f4f3eb05 |
completed | April 18, 2026, 6:06 p.m. |
Created at: April 8, 2026, 9:24 p.m.