Triple
T21145330
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kobayashi metric |
E521038
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Teichmüller metric |
—
|
NE NERFINISHED |
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: [Kobayashi metric, relatedConcept, Teichmüller metric]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Teichmüller metric Context triple: [Kobayashi metric, relatedConcept, Teichmüller metric]
-
A.
Teichmüller metric
chosen
The Teichmüller metric is a natural Finsler metric on Teichmüller space that measures the minimal quasiconformal distortion needed to deform one Riemann surface into another.
-
B.
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.
-
C.
Weil–Petersson metric
The Weil–Petersson metric is a natural Kähler metric on Teichmüller space, arising from the \(L^2\)-pairing of quadratic differentials and playing a central role in the geometry of moduli spaces of Riemann surfaces.
-
D.
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.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e0b50c6a848190a4e525a77a319b8a |
completed | April 16, 2026, 10:08 a.m. |
| NER | Named-entity recognition | batch_69e723fcdb7c8190ae04d6ad9dff3187 |
completed | April 21, 2026, 7:15 a.m. |
Created at: April 16, 2026, 2:58 p.m.