Triple
T10991669
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kleinian group |
E259766
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object | Fuchsian group |
E500439
|
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: Fuchsian group | Statement: [Kleinian group, generalizes, Fuchsian group]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fuchsian group Context triple: [Kleinian group, generalizes, Fuchsian group]
-
A.
Fuchsian group
chosen
A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
-
B.
Kleinian group
A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
-
C.
modular group PSL(2,Z)
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
-
D.
Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
-
E.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
- 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_69e374639f1481908ea372b81a834f6f |
completed | April 18, 2026, 12:09 p.m. |
Created at: April 8, 2026, 9:24 p.m.