Triple
T25550028
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mordell curve |
E640411
|
entity |
| Predicate | hasRationalPoints |
P64879
|
FINISHED |
| Object | solutions (x,y) ∈ ℚ² of y^2 = x^3 + k |
—
|
LITERAL 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: solutions (x,y) ∈ ℚ² of y^2 = x^3 + k | Statement: [Mordell curve, hasRationalPoints, solutions (x,y) ∈ ℚ² of y^2 = x^3 + k]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasRationalPoints Context triple: [Mordell curve, hasRationalPoints, solutions (x,y) ∈ ℚ² of y^2 = x^3 + k]
-
A.
trivialRationalPoints
Indicates that the only rational points satisfying the given condition or lying on the given object are the trivial or obvious ones (typically those forced by the structure, such as points at infinity or simple coordinate values).
-
B.
rationalPointsProperty
chosen
Indicates that a mathematical object (typically a variety or curve) has a specified property concerning its rational points, such as their existence, distribution, or structure over a given field.
-
C.
isRationalSurface
Indicates that a given algebraic surface is birationally equivalent to the projective plane, i.e., it has the rationality property.
-
D.
hasWeierstrassPoints
Indicates that a given algebraic curve possesses one or more Weierstrass points, i.e., special points where the gap sequence of holomorphic differentials deviates from the generic case.
-
E.
isBelyiCurve
Indicates that a given algebraic curve is a Belyi curve, i.e., it admits a holomorphic map to the projective line branched over at most three points.
- 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_69e75dc101a881909fd33b02174e9768 |
completed | April 21, 2026, 11:21 a.m. |
| NER | Named-entity recognition | batch_69f638d11c988190af7fd4572b08e038 |
completed | May 2, 2026, 5:48 p.m. |
| PD | Predicate disambiguation | batch_69f63706b6008190993577193c85ff50 |
completed | May 2, 2026, 5:40 p.m. |
Created at: April 21, 2026, 3:36 p.m.