Triple

T21953161
Position Surface form Disambiguated ID Type / Status
Subject Cartan–Killing form E542117 entity
Predicate instanceOf P0 FINISHED
Object symmetric bilinear form C3716 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: symmetric bilinear form
Context triple: [Cartan–Killing form, instanceOf, symmetric bilinear form]
  • A. quadratic form
    A quadratic form is a homogeneous polynomial of degree two in several variables, typically expressed as xᵀAx for a symmetric matrix A, that defines a scalar-valued function capturing curvature and geometric properties such as lengths, angles, and conic sections.
  • B. symmetric tensor
    A symmetric tensor is a multilinear map or multidimensional array whose components remain unchanged under any permutation of its indices.
  • C. alternating form
    An alternating form is a multilinear map on a vector space that changes sign whenever two of its arguments are swapped, and hence vanishes whenever any two arguments are equal.
  • D. inner product space
    An inner product space is a vector space equipped with an inner product, a function that assigns a scalar to each pair of vectors in a way that generalizes the dot product and induces notions of length and angle.
  • E. (0,2)-tensor chosen
    A (0,2)-tensor is a bilinear map that takes two vectors as input and returns a scalar, often representing objects like metrics or covariant tensor fields on a vector space or manifold.
  • 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_69e0c47ef0e48190a50e1bcc43f4b3fd completed April 16, 2026, 11:14 a.m.
Created at: April 16, 2026, 7:59 p.m.