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.