Triple

T32283287
Position Surface form Disambiguated ID Type / Status
Subject Ian Agol E824756 entity
Predicate notableConcept P201 FINISHED
Object virtual Haken theorem
The virtual Haken theorem is a landmark result in 3-manifold topology proving that every closed hyperbolic 3-manifold has a finite cover that is Haken, meaning it contains an incompressible surface.
 E2000863 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: virtual Haken theorem | Statement: [Ian Agol, notableConcept, virtual Haken 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: virtual Haken theorem
Triple: [Ian Agol, notableConcept, virtual Haken theorem]
Generated description
The virtual Haken theorem is a landmark result in 3-manifold topology proving that every closed hyperbolic 3-manifold has a finite cover that is Haken, meaning it contains an incompressible surface.

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_69f3490f404081908450db66884f4334 completed April 30, 2026, 12:20 p.m.
NER Named-entity recognition batch_69f6bccd1aa88190882a5dbb8100ca1e completed May 3, 2026, 3:11 a.m.
NED1 Entity disambiguation (via context triple) batch_6a2f46ec2ad881908ba78cb0d030c99c completed June 15, 2026, 12:27 a.m.
NEDg Description generation batch_6a2f481af6f081909c675376d09345df completed June 15, 2026, 12:32 a.m.
NED2 Entity disambiguation (via description) batch_6a301ae519348190a8563be3d2c124d0 completed June 15, 2026, 3:31 p.m.
Created at: May 1, 2026, 12:43 a.m.