Triple

T10511993
Position Surface form Disambiguated ID Type / Status
Subject Ricci calculus E247936 entity
Predicate relatedTo P37 FINISHED
Object Einstein notation
Einstein notation is a concise index-based convention in tensor calculus that simplifies expressions by implying summation over repeated indices.
E869109 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: Einstein notation | Statement: [Ricci calculus, relatedTo, Einstein notation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Einstein notation
Context triple: [Ricci calculus, relatedTo, Einstein notation]
  • A. Levi-Civita symbol
    The Levi-Civita symbol is an antisymmetric tensor used in mathematics and physics to represent orientations, cross products, and determinants in multiple dimensions.
  • B. Ricci calculus
    Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
  • C. Minkowski metric η_{μν}
    The Minkowski metric η_{μν} is the flat spacetime metric of special relativity, describing a four-dimensional spacetime with Lorentzian signature that serves as the background for many formulations of relativistic physics.
  • D. Ricci-Curbastro
    Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
  • E. Kronecker delta
    The Kronecker delta is a function of two variables that equals 1 when the variables are equal and 0 otherwise, widely used in linear algebra, tensor calculus, and discrete mathematics to represent identity relations.
  • 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: Einstein notation
Triple: [Ricci calculus, relatedTo, Einstein notation]
Generated description
Einstein notation is a concise index-based convention in tensor calculus that simplifies expressions by implying summation over repeated indices.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Einstein notation
Target entity description: Einstein notation is a concise index-based convention in tensor calculus that simplifies expressions by implying summation over repeated indices.
  • A. Levi-Civita symbol
    The Levi-Civita symbol is an antisymmetric tensor used in mathematics and physics to represent orientations, cross products, and determinants in multiple dimensions.
  • B. Ricci calculus
    Ricci calculus is a mathematical framework for tensor analysis on manifolds that underpins much of modern differential geometry and general relativity.
  • C. Minkowski metric η_{μν}
    The Minkowski metric η_{μν} is the flat spacetime metric of special relativity, describing a four-dimensional spacetime with Lorentzian signature that serves as the background for many formulations of relativistic physics.
  • D. Ricci-Curbastro
    Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
  • E. Kronecker delta
    The Kronecker delta is a function of two variables that equals 1 when the variables are equal and 0 otherwise, widely used in linear algebra, tensor calculus, and discrete mathematics to represent identity relations.
  • 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_69d381c4aa948190942e1d803143fb0e completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d509b5fcb8819087a23a2b26aecd70 completed April 7, 2026, 1:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69d90de6e9508190a1cdf348ec542dd5 completed April 10, 2026, 2:49 p.m.
NEDg Description generation batch_69d9107c75108190994939ab46aa642f completed April 10, 2026, 3 p.m.
NED2 Entity disambiguation (via description) batch_69d9154c922c81909991f87f89c083cd completed April 10, 2026, 3:20 p.m.
Created at: April 6, 2026, 12:27 p.m.