Triple
T10991842
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schwarz lemma |
E259769
|
entity |
| Predicate | relatedResult |
P96512
|
FINISHED |
| Object | Little Picard theorem |
E326981
|
NE FINISHED |
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: Little Picard theorem | Statement: [Schwarz lemma, relatedResult, Little Picard theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Little Picard theorem Context triple: [Schwarz lemma, relatedResult, Little Picard theorem]
-
A.
Picard theorem
chosen
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.
-
B.
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.
-
C.
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.
-
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.
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.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: relatedResult Context triple: [Schwarz lemma, relatedResult, Little Picard theorem]
-
A.
relatedTo
Indicates a general, non-specific relationship or association exists between two entities.
-
B.
relatedType
Indicates that one entity is connected to another through a specified type or category of relationship.
-
C.
relatedTest
Indicates that there exists some form of connection or association between one test and another.
-
D.
relatedField
Indicates that one field, topic, or area of study is connected or relevant to another in subject matter or application.
-
E.
moreCloselyRelatedTo
Indicates that one entity has a stronger or closer relationship, connection, or similarity to a second entity than to some other reference entity.
- 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_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_69e34504ebec8190a78e4795765b0c24 |
completed | April 18, 2026, 8:47 a.m. |
| PD | Predicate disambiguation | batch_69d72e93ac648190b46c5d12bf3eb1e9 |
completed | April 9, 2026, 4:44 a.m. |
| PDg | Predicate description generation | batch_69d732242fdc8190be77d1f730a42935 |
completed | April 9, 2026, 4:59 a.m. |
Created at: April 8, 2026, 9:24 p.m.