Triple
T21494618
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fermat surface |
E530319
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object | Fermat curve |
—
|
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: Fermat curve | Statement: [Fermat surface, generalizes, Fermat curve]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fermat curve Context triple: [Fermat surface, generalizes, Fermat curve]
-
A.
Fermat curve
chosen
A Fermat curve is an algebraic curve defined by an equation of the form \(x^n + y^n = 1\), studied in number theory and algebraic geometry for its rich arithmetic and geometric properties.
-
B.
Fermat surface
A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
-
C.
Mordell curve
A Mordell curve is an elliptic curve of the form \(y^2 = x^3 + k\) over a field, central to number theory and Diophantine geometry.
-
D.
Tate curve
The Tate curve is a type of elliptic curve defined over non-archimedean local fields, central to John Tate’s work on p-adic uniformization and the study of elliptic curves with bad reduction.
-
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 (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_69e0c45bd15481909fba5910765cdda2 |
completed | April 16, 2026, 11:13 a.m. |
| NER | Named-entity recognition | batch_69e9ea567244819091863350fedae3ae |
completed | April 23, 2026, 9:45 a.m. |
Created at: April 16, 2026, 6:23 p.m.