Triple

T846899
Position Surface form Disambiguated ID Type / Status
Subject Leopold Kronecker E18296 entity
Predicate notableWork P4 FINISHED
Object 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.
E100234 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: Kronecker delta | Statement: [Leopold Kronecker, notableWork, Kronecker delta]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kronecker delta
Context triple: [Leopold Kronecker, notableWork, Kronecker delta]
  • A. 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.
  • B. Kretschmann scalar
    The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
  • C. Kac
    Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
  • D. Wigner–Eckart theorem
    The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
  • E. Einstein tensor
    The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
  • 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: Kronecker delta
Triple: [Leopold Kronecker, notableWork, Kronecker delta]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kronecker delta
Target entity description: 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.
  • A. 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.
  • B. Kretschmann scalar
    The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
  • C. Kac
    Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
  • D. Wigner–Eckart theorem
    The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
  • E. Einstein tensor
    The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
  • 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_69a4938b04208190b82e1df6b572c548 completed March 1, 2026, 7:29 p.m.
NER Named-entity recognition batch_69a4ac0ba6b4819089c15ed7e1765502 completed March 1, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69a7929e65d08190bcea03f581288cc4 completed March 4, 2026, 2:02 a.m.
NEDg Description generation batch_69a7937c2ce481908c04e08e2be02985 completed March 4, 2026, 2:05 a.m.
NED2 Entity disambiguation (via description) batch_69a79761ee34819094a0558ef195d8a0 completed March 4, 2026, 2:22 a.m.
Created at: March 1, 2026, 7:38 p.m.