Triple
T2228057
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | André Weil |
E48698
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
Weil pairing
The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
|
E244846
|
NE FINISHED |
How this triple was built (4 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: Weil pairing | Statement: [André Weil, notableConcept, Weil pairing]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weil pairing Context triple: [André Weil, notableConcept, Weil pairing]
-
A.
Hasse bound for elliptic curves
The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
-
B.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
C.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
D.
Weierstrass elliptic functions
Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
-
E.
Deuring reduction theorem
The Deuring reduction theorem is a result in number theory that relates the reduction of elliptic curves with complex multiplication modulo primes to the theory of quaternion algebras and endomorphism rings.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Weil pairing Triple: [André Weil, notableConcept, Weil pairing]
Generated description
The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weil pairing Target entity description: The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
-
A.
Hasse bound for elliptic curves
The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
-
B.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
C.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
D.
Weierstrass elliptic functions
Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
-
E.
Deuring reduction theorem
The Deuring reduction theorem is a result in number theory that relates the reduction of elliptic curves with complex multiplication modulo primes to the theory of quaternion algebras and endomorphism rings.
- F. None of above. chosen
Provenance (5 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_69a88aa51b388190949868ec9766e587 |
completed | March 4, 2026, 7:40 p.m. |
| NER | Named-entity recognition | batch_69abc0670ce48190b98814064bff0517 |
completed | March 7, 2026, 6:06 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae6567b64c8190ab718f20bbf033df |
completed | March 9, 2026, 6:15 a.m. |
| NEDg | Description generation | batch_69ae666bd32c81909ff15201757a6c76 |
completed | March 9, 2026, 6:19 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae66d8ba688190a2102c00fc6231c4 |
completed | March 9, 2026, 6:21 a.m. |
Created at: March 4, 2026, 7:47 p.m.