Triple

T25590725
Position Surface form Disambiguated ID Type / Status
Subject Mordell–Weil theorem E641515 entity
Predicate involvesConcept P531 FINISHED
Object weak Mordell–Weil theorem
The weak Mordell–Weil theorem is a foundational result in arithmetic geometry stating that the group of rational points on an abelian variety over a number field is finitely generated modulo a finite index subgroup.
E641515 NE FINISHED

How this triple was built (2 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: weak Mordell–Weil theorem | Statement: [Mordell–Weil theorem, involvesConcept, weak Mordell–Weil theorem]
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: weak Mordell–Weil theorem
Triple: [Mordell–Weil theorem, involvesConcept, weak Mordell–Weil theorem]
Generated description
The weak Mordell–Weil theorem is a foundational result in arithmetic geometry stating that the group of rational points on an abelian variety over a number field is finitely generated modulo a finite index subgroup.

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_69e75dc60d108190b7e2419e36b0134b completed April 21, 2026, 11:21 a.m.
NER Named-entity recognition batch_69f5f96cc064819088071450af183d1c completed May 2, 2026, 1:17 p.m.
NED1 Entity disambiguation (via context triple) batch_6a10b76a0834819096b8c736b6d731df completed May 22, 2026, 8:07 p.m.
NEDg Description generation batch_6a10b8265e8c8190817bca20ada4c82a completed May 22, 2026, 8:10 p.m.
NED2 Entity disambiguation (via description) batch_6a10b96e57f081908a75a191ce7bafce completed May 22, 2026, 8:15 p.m.
Created at: April 21, 2026, 4:24 p.m.