Triple
T13660533
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Picard theorem |
E326981
|
entity |
| Predicate | hasProofMethod |
P7024
|
FINISHED |
| Object | Riemann surface theory |
E47348
|
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: Riemann surface theory | Statement: [Picard theorem, hasProofMethod, Riemann surface theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riemann surface theory Context triple: [Picard theorem, hasProofMethod, Riemann surface theory]
-
A.
Riemann surfaces
chosen
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
B.
Teichmüller theory
Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
-
C.
Teichmüller space
Teichmüller space is a parameter space in complex analysis and geometry that classifies all marked conformal or hyperbolic structures on a given topological surface up to equivalence.
-
D.
Complex Analysis
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
-
E.
Several Complex Variables
"Several Complex Variables" is a foundational mathematical text that systematically develops the theory of functions of several complex variables and has significantly influenced modern complex analysis.
- 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_69d8076d8270819092afc2f0e9c359a8 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69dbc620df208190afaccf3ddd10aa60 |
completed | April 12, 2026, 4:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f78b08d27c8190badc612c26423c0e |
completed | May 3, 2026, 5:51 p.m. |
Created at: April 9, 2026, 9:52 p.m.