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.