Triple

T37197123

Position	Surface form	Disambiguated ID	Type / Status
Subject	Frey curve construction	`E921624`	entity
Predicate	inspiredConjecture	`P38188`	FINISHED
Object	epsilon conjecture of Serre The epsilon conjecture of Serre is a deep conjecture in number theory, proposed by Jean-Pierre Serre, concerning subtle bounds in the behavior of Galois representations and modular forms, particularly in relation to the modularity of elliptic curves.	`E253116`	NE FINISHED

How this triple was built (3 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: epsilon conjecture of Serre | Statement: [Frey curve construction, inspiredConjecture, epsilon conjecture of Serre]

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: epsilon conjecture of Serre
Triple: [Frey curve construction, inspiredConjecture, epsilon conjecture of Serre]

Generated description

The epsilon conjecture of Serre is a deep conjecture in number theory, proposed by Jean-Pierre Serre, concerning subtle bounds in the behavior of Galois representations and modular forms, particularly in relation to the modularity of elliptic curves.

PD Predicate disambiguation gpt-5-mini-2025-08-07

Target predicate: inspiredConjecture
Context triple: [Frey curve construction, inspiredConjecture, epsilon conjecture of Serre]

A. associatedConjecture
Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
B. refinedConjecture
Indicates that a previously stated conjecture has been modified or made more precise, resulting in a refined version of the original conjecture.
C. conjecturedSign
Indicates that one entity is proposed or hypothesized to be the sign, symbol, or indicator of another entity, without confirmed certainty.
D. relatedConjecture chosen
Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
E. conjecturallySatisfy
Indicates that one entity is believed or hypothesized, but not proven, to fulfill or meet the conditions or requirements specified by another entity.
F. None of above.

Provenance (6 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_69f76ea313a08190a54404cd1e47da90`	completed	May 3, 2026, 3:49 p.m.
NER	Named-entity recognition	`batch_69fd76d1e5208190a6f26651492d1e3c`	completed	May 8, 2026, 5:38 a.m.
NED1	Entity disambiguation (via context triple)	`batch_6a4043b519fc8190952e775ebaf0b8cf`	completed	June 27, 2026, 9:42 p.m.
NEDg	Description generation	`batch_6a404461ff1c8190ae3ed2dbedc8dc48`	completed	June 27, 2026, 9:45 p.m.
NED2	Entity disambiguation (via description)	`batch_6a40457ebde88190b43dc9291ec1b2de`	completed	June 27, 2026, 9:49 p.m.
PD	Predicate disambiguation	`batch_69fd702a226c81908edfda00f4be4130`	completed	May 8, 2026, 5:10 a.m.

Created at: May 3, 2026, 4:15 p.m.