Triple

T8733512

Position	Surface form	Disambiguated ID	Type / Status
Subject	Hasse bound for elliptic curves	`E207314`	entity
Predicate	usedIn	`P98`	FINISHED
Object	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.	`E753155`	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: Schoof–Elkies–Atkin (SEA) point-counting algorithm | Statement: [Hasse bound for elliptic curves, usedIn, Schoof–Elkies–Atkin (SEA) point-counting algorithm]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Schoof–Elkies–Atkin (SEA) point-counting algorithm
Context triple: [Hasse bound for elliptic curves, usedIn, Schoof–Elkies–Atkin (SEA) point-counting algorithm]

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. Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
C. 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.
D. Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
E. Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
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: Schoof–Elkies–Atkin (SEA) point-counting algorithm
Triple: [Hasse bound for elliptic curves, usedIn, Schoof–Elkies–Atkin (SEA) point-counting algorithm]

Generated description

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.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Schoof–Elkies–Atkin (SEA) point-counting algorithm
Target entity description: 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.

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. Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
C. 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.
D. Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
E. Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
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_69ca8358e4008190898471a59b96c301`	completed	March 30, 2026, 2:06 p.m.
NER	Named-entity recognition	`batch_69cc5d2a26988190acfda17f232e610a`	completed	March 31, 2026, 11:47 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69cf292d71ec819082095cb7b8b2d39c`	completed	April 3, 2026, 2:42 a.m.
NEDg	Description generation	`batch_69cf2bd4f50c8190bad328e82d299ae0`	completed	April 3, 2026, 2:54 a.m.
NED2	Entity disambiguation (via description)	`batch_69cf2cbf60808190a006ee4fb26cde41`	completed	April 3, 2026, 2:58 a.m.

Created at: March 30, 2026, 6:37 p.m.