Triple

T13614830
Position Surface form Disambiguated ID Type / Status
Subject Hyperbolic Manifolds and Discrete Groups E325284 entity
Predicate topic P261 FINISHED
Object Mostow rigidity E898487 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: Mostow rigidity | Statement: [Hyperbolic Manifolds and Discrete Groups, topic, Mostow rigidity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Mostow rigidity
Context triple: [Hyperbolic Manifolds and Discrete Groups, topic, Mostow rigidity]
  • A. Mostow rigidity theorem chosen
    The Mostow rigidity theorem is a fundamental result in geometry and topology stating that, in dimensions greater than two, the large-scale geometry of a complete finite-volume hyperbolic manifold is uniquely determined by its fundamental group, implying strong rigidity for such structures.
  • B. 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.
  • C. Teichmüller space
    Teichmüller space is a parameter space in complex analysis and geometry that classifies all marked conformal or hyperbolic structures on a given topological surface up to equivalence.
  • D. Milnor–Wood inequality
    The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
  • E. Ahlfors finiteness theorem
    The Ahlfors finiteness theorem is a fundamental result in the theory of Kleinian groups stating that, under suitable discreteness and analyticity conditions, the quotient of the domain of discontinuity has finite topological type.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d8076aae28819092cf636190ee5529 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbb0ad0a7c81909c7972187202db96 completed April 12, 2026, 2:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69f77f9cbc388190972e949324144d2f completed May 3, 2026, 5:02 p.m.
Created at: April 9, 2026, 9:50 p.m.