Triple
T32516888
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Twisted Edwards curve |
E831082
|
entity |
| Predicate | isBirationallyEquivalentTo |
P97268
|
FINISHED |
| Object | Weierstrass elliptic 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: Weierstrass elliptic curve | Statement: [Twisted Edwards curve, isBirationallyEquivalentTo, Weierstrass elliptic curve]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isBirationallyEquivalentTo Context triple: [Twisted Edwards curve, isBirationallyEquivalentTo, Weierstrass elliptic curve]
-
A.
isBirationalTo
chosen
Indicates that there exists a birational map between two algebraic varieties, meaning they are isomorphic outside lower-dimensional subsets and share the same function field.
-
B.
isBiholomorphismOf
Indicates that one complex-analytic map is a biholomorphic equivalence between two complex manifolds, i.e., a holomorphic bijection whose inverse is also holomorphic.
-
C.
isDiffeomorphicTo
Indicates that there exists a smooth, bijective map between two spaces whose inverse is also smooth, so the spaces are equivalent in the sense of differential topology.
-
D.
isRationalSurface
Indicates that a given algebraic surface is birationally equivalent to the projective plane, i.e., it has the rationality property.
-
E.
isIsogenousTo
Indicates that two mathematical structures, typically elliptic curves or abelian varieties, are related by an isogeny, i.e., a non-constant morphism with finite kernel that preserves their group structure.
- F. None of above.
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_69f3492318348190ba37fb6b5f1d67f4 |
completed | April 30, 2026, 12:20 p.m. |
| NER | Named-entity recognition | batch_69f6c4aabff08190ad437b687dd41f8d |
completed | May 3, 2026, 3:44 a.m. |
| PD | Predicate disambiguation | batch_69f6bd2a14b081908162923dfbf0a6f4 |
completed | May 3, 2026, 3:12 a.m. |
Created at: May 1, 2026, 1 a.m.