Triple

T846898
Position Surface form Disambiguated ID Type / Status
Subject Leopold Kronecker E18296 entity
Predicate notableWork P4 FINISHED
Object Kronecker product
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
E102485 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 product | Statement: [Leopold Kronecker, notableWork, Kronecker product]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kronecker product
Context triple: [Leopold Kronecker, notableWork, Kronecker product]
  • A. 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.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. LinearAlgebra
    LinearAlgebra is Julia’s standard library module providing core functionality for vectors, matrices, and advanced linear algebra operations.
  • D. Matrix
    Matrix is a professional haircare and hair color brand widely used in salons and owned by the cosmetics company L'Oréal.
  • E. Matrix
    The Matrix is a vast, sentient data repository and virtual reality construct on Gallifrey that stores the knowledge, memories, and consciousness of Time Lords in the Doctor Who universe.
  • 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 product
Triple: [Leopold Kronecker, notableWork, Kronecker product]
Generated description
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kronecker product
Target entity description: The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
  • A. 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.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. LinearAlgebra
    LinearAlgebra is Julia’s standard library module providing core functionality for vectors, matrices, and advanced linear algebra operations.
  • D. Matrix
    Matrix is a professional haircare and hair color brand widely used in salons and owned by the cosmetics company L'Oréal.
  • E. Matrix
    The Matrix is a vast, sentient data repository and virtual reality construct on Gallifrey that stores the knowledge, memories, and consciousness of Time Lords in the Doctor Who universe.
  • 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_69a7a3bd8b588190b7a9eb72dce93d07 completed March 4, 2026, 3:15 a.m.
NEDg Description generation batch_69a7a8da0c3481909f34d435ccf62ea7 completed March 4, 2026, 3:36 a.m.
NED2 Entity disambiguation (via description) batch_69a7a97688fc8190818957701913738f completed March 4, 2026, 3:39 a.m.
Created at: March 1, 2026, 7:38 p.m.