Triple

T6456443
Position Surface form Disambiguated ID Type / Status
Subject Lie group E142004 entity
Predicate instanceOf P0 FINISHED
Object smooth manifold C3506 CONCEPT FINISHED

How this triple was built (1 step)

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.

CD Concept disambiguation gpt-5-mini-2025-08-07 
Target class: smooth manifold
Context triple: [Lie group, instanceOf, smooth manifold]
  • A. Lorentzian manifold
    A Lorentzian manifold is a smooth manifold equipped with a metric tensor of signature \((-+\cdots+)\) (or its variants) that models spacetime in general relativity by distinguishing timelike, spacelike, and null directions.
  • B. four-dimensional manifold
    A four-dimensional manifold is a topological space that locally resembles four-dimensional Euclidean space, meaning each point has a neighborhood homeomorphic to an open subset of ℝ⁴.
  • C. pseudo-Riemannian manifold
    A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.
  • D. differential geometric object chosen
    A differential geometric object is a mathematical entity, such as a manifold, tensor, or connection, defined on smooth spaces and characterized by properties that are invariant under smooth coordinate transformations.
  • E. nonsingular curve
    A nonsingular curve is an algebraic curve with no singular points, meaning it is smooth everywhere and has a well-defined tangent line at every point.
  • F. None of above.

Provenance (1 batch)

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_69c008d2f91c8190a8178767a35e08fc completed March 22, 2026, 3:20 p.m.
Created at: March 22, 2026, 4:48 p.m.