Triple

T2037064
Position Surface form Disambiguated ID Type / Status
Subject David Hestenes E44654 entity
Predicate developed P73 FINISHED
Object geometric calculus
Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
E228030 NE FINISHED

How this triple was built (4 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: geometric calculus | Statement: [David Hestenes, developed, geometric calculus]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: geometric calculus
Context triple: [David Hestenes, developed, geometric calculus]
  • A. Lie sphere geometry
    Lie sphere geometry is a branch of differential geometry that studies the properties and transformations of spheres (and related objects like planes and points) using the methods of Lie groups and projective geometry.
  • B. Lorentzian geometry
    Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
  • C. Stokes' theorem
    Stokes' theorem is a fundamental result in vector calculus that relates the surface integral of the curl of a vector field over a surface to the line integral of the field around the surface’s boundary.
  • D. Cartan structure equations
    Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
  • E. Christoffel symbols
    Christoffel symbols are mathematical objects in differential geometry that represent how coordinate bases change from point to point on a curved space or spacetime, and are used to define covariant derivatives and geodesics.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
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: geometric calculus
Triple: [David Hestenes, developed, geometric calculus]
Generated description
Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: geometric calculus
Target entity description: Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
  • A. Lie sphere geometry
    Lie sphere geometry is a branch of differential geometry that studies the properties and transformations of spheres (and related objects like planes and points) using the methods of Lie groups and projective geometry.
  • B. Lorentzian geometry
    Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
  • C. Stokes' theorem
    Stokes' theorem is a fundamental result in vector calculus that relates the surface integral of the curl of a vector field over a surface to the line integral of the field around the surface’s boundary.
  • D. Cartan structure equations
    Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
  • E. Christoffel symbols
    Christoffel symbols are mathematical objects in differential geometry that represent how coordinate bases change from point to point on a curved space or spacetime, and are used to define covariant derivatives and geodesics.
  • F. None of above. chosen

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_69a889159ec481908f9e4472d9f480c7 completed March 4, 2026, 7:33 p.m.
NER Named-entity recognition batch_69abb9363b608190b42aa6d3f3fd78c4 completed March 7, 2026, 5:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae1ff38fb881909558e4d715a4d314 completed March 9, 2026, 1:18 a.m.
NEDg Description generation batch_69ae20946a288190a3bd2a19e3608e86 completed March 9, 2026, 1:21 a.m.
NED2 Entity disambiguation (via description) batch_69ae2109d17c819094a298a822064052 completed March 9, 2026, 1:23 a.m.
Created at: March 4, 2026, 7:39 p.m.