Triple

T4597282
Position Surface form Disambiguated ID Type / Status
Subject Kronecker delta E100234 entity
Predicate usedIn P98 FINISHED
Object tensor calculus
Tensor calculus is a branch of mathematics that generalizes vector calculus to tensors, providing the language and tools to formulate and analyze physical laws in a coordinate-independent way, especially in differential geometry and general relativity.
E247936 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: tensor calculus | Statement: [Kronecker delta, usedIn, tensor calculus]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: tensor calculus
Context triple: [Kronecker delta, usedIn, tensor calculus]
  • A. Ricci calculus
    Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
  • B. Riemann curvature tensor
    The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
  • C. 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.
  • D. Ricci-Curbastro
    Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
  • E. Ricci curvature tensor
    The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
  • 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: tensor calculus
Triple: [Kronecker delta, usedIn, tensor calculus]
Generated description
Tensor calculus is a branch of mathematics that generalizes vector calculus to tensors, providing the language and tools to formulate and analyze physical laws in a coordinate-independent way, especially in differential geometry and general relativity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: tensor calculus
Target entity description: Tensor calculus is a branch of mathematics that generalizes vector calculus to tensors, providing the language and tools to formulate and analyze physical laws in a coordinate-independent way, especially in differential geometry and general relativity.
  • A. Ricci calculus chosen
    Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
  • B. Riemann curvature tensor
    The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
  • C. 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.
  • D. Ricci-Curbastro
    Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
  • E. Ricci curvature tensor
    The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
  • 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_69bd43cbc014819098b45f435908f88a completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd59420c108190b5c2c5039e964da5 completed March 20, 2026, 2:27 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdfa4a99c88190b7332fd2e1799b3a completed March 21, 2026, 1:54 a.m.
NEDg Description generation batch_69bdfb83b5d08190b2d8502e763a0841 completed March 21, 2026, 1:59 a.m.
NED2 Entity disambiguation (via description) batch_69bdfc0e456c81908efa3858d981ccc0 completed March 21, 2026, 2:01 a.m.
Created at: March 20, 2026, 1:11 p.m.