Triple
T25550024
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mordell curve |
E640411
|
entity |
| Predicate | isIsomorphicOverAlgebraicClosureTo |
P29599
|
FINISHED |
| Object | curve y^2 = x^3 + 1 (for k ≠ 0) |
—
|
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: curve y^2 = x^3 + 1 (for k ≠ 0) | Statement: [Mordell curve, isIsomorphicOverAlgebraicClosureTo, curve y^2 = x^3 + 1 (for k ≠ 0)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isIsomorphicOverAlgebraicClosureTo Context triple: [Mordell curve, isIsomorphicOverAlgebraicClosureTo, curve y^2 = x^3 + 1 (for k ≠ 0)]
-
A.
isIsomorphicTo
chosen
Indicates that two structures have a one-to-one, structure-preserving correspondence between their elements, making them equivalent in form even if not identical in content.
-
B.
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.
-
C.
isAlgebraicOver
Indicates that one mathematical object satisfies a nontrivial polynomial equation whose coefficients lie in the other object (typically a field or ring), expressing algebraic dependence over that base.
-
D.
isAssociativeUpToIsomorphism
Indicates that a binary operation is associative in a structural sense, meaning any two ways of parenthesizing a finite product are related by a canonical isomorphism rather than strict equality.
-
E.
isBirationalTo
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.
- 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_69f5f8c583e48190a2a1f65d80a2b589 |
completed | May 2, 2026, 1:14 p.m. |
| PD | Predicate disambiguation | batch_69f468421ba08190880eac99135e5970 |
completed | May 1, 2026, 8:45 a.m. |
Created at: April 21, 2026, 3:36 p.m.