Triple
T5446369
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carathéodory metric |
E122257
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Teichmüller metric |
E259765
|
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: Teichmüller metric | Statement: [Carathéodory metric, relatedTo, Teichmüller metric]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Teichmüller metric Context triple: [Carathéodory metric, relatedTo, Teichmüller metric]
-
A.
Teichmüller theory
chosen
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.
-
B.
Carathéodory metric
The Carathéodory metric is an intrinsic distance function in complex analysis that measures how far apart points are in a domain based on holomorphic mappings into the unit disk.
-
C.
Teichmüller curve
A Teichmüller curve is a complex geodesic in the moduli space of Riemann surfaces that arises from flat surface structures and has rich connections to dynamics, geometry, and number theory.
-
D.
uniformization theorem
The uniformization theorem is a fundamental result in complex analysis stating that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the complex plane, or the unit disk.
-
E.
Milnor–Wood inequality
The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
- 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_69bd4640f52c81909e653ec361f66d76 |
completed | March 20, 2026, 1:06 p.m. |
| NER | Named-entity recognition | batch_69bd91cf5d488190868ffefad02c7a04 |
completed | March 20, 2026, 6:28 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bf413573c08190beae400c485d2132 |
completed | March 22, 2026, 1:09 a.m. |
Created at: March 20, 2026, 2:07 p.m.