Triple

T21046407
Position Surface form Disambiguated ID Type / Status
Subject Thurston’s classification of surface diffeomorphisms E518460 entity
Predicate relatedTo P37 FINISHED
Object JSJ decomposition of 3-manifolds — NE NERFINISHED

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: JSJ decomposition of 3-manifolds | Statement: [Thurston’s classification of surface diffeomorphisms, relatedTo, JSJ decomposition of 3-manifolds]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: JSJ decomposition of 3-manifolds
Context triple: [Thurston’s classification of surface diffeomorphisms, relatedTo, JSJ decomposition of 3-manifolds]
  • A. JSJ decomposition chosen
    The JSJ decomposition is a fundamental tool in 3-manifold topology that splits a 3-manifold along tori into simpler, canonical pieces that are either Seifert fibered or atoroidal, forming a key step toward its geometric classification.
  • B. Seifert fibered spaces
    Seifert fibered spaces are three-dimensional manifolds that can be decomposed into a disjoint union of circles arranged in a highly structured, fibered way over a two-dimensional orbifold.
  • C. Thurston hyperbolization theorem
    The Thurston hyperbolization theorem is a fundamental result in 3-manifold topology that characterizes when certain 3-manifolds admit complete hyperbolic structures, forming a cornerstone of Thurston’s geometrization program.
  • D. Foliations of Three-Manifolds Which Are Circle Bundles
    "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
  • E. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.