Triple
T18729743
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Friedrich Richelot |
E458003
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Richelot isogeny
The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
|
E1340022
|
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: Richelot isogeny | Statement: [Friedrich Richelot, notableWork, Richelot isogeny]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Richelot isogeny Context triple: [Friedrich Richelot, notableWork, Richelot isogeny]
-
A.
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.
-
B.
Gross–Koblitz formula
The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
-
C.
Cassels–Tate pairing
The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
-
D.
Schoof–Elkies–Atkin (SEA) point-counting algorithm
The Schoof–Elkies–Atkin (SEA) point-counting algorithm is an efficient method in computational number theory and elliptic curve cryptography for determining the number of points on an elliptic curve over a finite field.
-
E.
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.
- 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: Richelot isogeny Triple: [Friedrich Richelot, notableWork, Richelot isogeny]
Generated description
The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Richelot isogeny Target entity description: The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
-
A.
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.
-
B.
Gross–Koblitz formula
The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
-
C.
Cassels–Tate pairing
The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
-
D.
Schoof–Elkies–Atkin (SEA) point-counting algorithm
The Schoof–Elkies–Atkin (SEA) point-counting algorithm is an efficient method in computational number theory and elliptic curve cryptography for determining the number of points on an elliptic curve over a finite field.
-
E.
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.
- 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_69d8d393ba9c8190a8b03b04ddbb0a09 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e56d7660488190b4f70db963d05ef6 |
completed | April 20, 2026, 12:04 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a05325b685c8190a2889755ed931973 |
completed | May 14, 2026, 2:24 a.m. |
| NEDg | Description generation | batch_6a053410a8188190992d9fa6130ab372 |
completed | May 14, 2026, 2:31 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a05349009e481909fb757415468aa70 |
completed | May 14, 2026, 2:33 a.m. |
Created at: April 10, 2026, 11:50 a.m.