Triple
T9456624
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | spacetime algebra |
E228029
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Hestenes’ geometric algebra
Hestenes’ geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to efficiently describe geometry, physics, and spacetime transformations in a coordinate-free way.
|
E228029
|
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: Hestenes’ geometric algebra | Statement: [spacetime algebra, relatedTo, Hestenes’ geometric algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hestenes’ geometric algebra Context triple: [spacetime algebra, relatedTo, Hestenes’ geometric algebra]
-
A.
foundations of geometric algebra as a unified language for physics
Foundations of geometric algebra as a unified language for physics is a mathematical framework that reformulates and streamlines the description of physical theories—such as classical mechanics, electromagnetism, and quantum mechanics—within a single, coherent algebraic system.
-
B.
geometric calculus
Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
-
C.
spacetime algebra
Spacetime algebra is a mathematical framework based on geometric (Clifford) algebra that unifies and simplifies the description of spacetime and physical laws, particularly in relativity and electromagnetism.
-
D.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
-
E.
Vector Analysis (with Edwin Bidwell Wilson)
Vector Analysis (with Edwin Bidwell Wilson) is a foundational early 20th-century textbook that systematically developed the modern formalism of vector calculus and helped standardize its use in physics and engineering.
- 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: Hestenes’ geometric algebra Triple: [spacetime algebra, relatedTo, Hestenes’ geometric algebra]
Generated description
Hestenes’ geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to efficiently describe geometry, physics, and spacetime transformations in a coordinate-free way.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hestenes’ geometric algebra Target entity description: Hestenes’ geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to efficiently describe geometry, physics, and spacetime transformations in a coordinate-free way.
-
A.
foundations of geometric algebra as a unified language for physics
Foundations of geometric algebra as a unified language for physics is a mathematical framework that reformulates and streamlines the description of physical theories—such as classical mechanics, electromagnetism, and quantum mechanics—within a single, coherent algebraic system.
-
B.
geometric calculus
Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
-
C.
spacetime algebra
chosen
Spacetime algebra is a mathematical framework based on geometric (Clifford) algebra that unifies and simplifies the description of spacetime and physical laws, particularly in relativity and electromagnetism.
-
D.
Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
-
E.
Vector Analysis (with Edwin Bidwell Wilson)
Vector Analysis (with Edwin Bidwell Wilson) is a foundational early 20th-century textbook that systematically developed the modern formalism of vector calculus and helped standardize its use in physics and engineering.
- F. None of above.
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_69ca843b123881909b0e60028475d12d |
completed | March 30, 2026, 2:10 p.m. |
| NER | Named-entity recognition | batch_69cd7f90cf648190ab238ba6b4f03c4f |
completed | April 1, 2026, 8:26 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d122849fec81908a8e7363d6bab4ed |
completed | April 4, 2026, 2:39 p.m. |
| NEDg | Description generation | batch_69d123f710988190a876fab3a1e226d3 |
completed | April 4, 2026, 2:45 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d1252cd7508190a7d11fce51960290 |
completed | April 4, 2026, 2:50 p.m. |
Created at: March 30, 2026, 7:52 p.m.