Triple

T9456693
Position Surface form Disambiguated ID Type / Status
Subject Foundations of geometric algebra as a unified language for physics E228031 entity
Predicate hasCoreConcept P533 FINISHED
Object geometric algebra
Geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to elegantly describe geometry, transformations, and physical laws in a single coherent language.
E801055 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 algebra | Statement: [Foundations of geometric algebra as a unified language for physics, hasCoreConcept, geometric algebra]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: geometric algebra
Context triple: [Foundations of geometric algebra as a unified language for physics, hasCoreConcept, geometric algebra]
  • A. geometric calculus
    Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
  • B. 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.
  • 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. 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.
  • E. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • 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 algebra
Triple: [Foundations of geometric algebra as a unified language for physics, hasCoreConcept, geometric algebra]
Generated description
Geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to elegantly describe geometry, transformations, and physical laws in a single coherent language.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: geometric algebra
Target entity description: Geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to elegantly describe geometry, transformations, and physical laws in a single coherent language.
  • A. geometric calculus
    Geometric calculus is a mathematical framework that extends geometric algebra to handle differentiation and integration in a coordinate-free, geometrically intuitive way.
  • B. 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.
  • 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. 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.
  • E. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • 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_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.