Triple

T3748401
Position Surface form Disambiguated ID Type / Status
Subject Erhard Schmidt E81265 entity
Predicate notableWork P4 FINISHED
Object Schmidt orthogonalization
Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
 E384564 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: Schmidt orthogonalization | Statement: [Erhard Schmidt, notableWork, Schmidt orthogonalization]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Schmidt orthogonalization
Context triple: [Erhard Schmidt, notableWork, Schmidt orthogonalization]
  • A. Richardson iteration
    Richardson iteration is an early iterative method for solving linear systems and other operator equations, based on repeated relaxation steps to progressively improve an approximate solution.
  • B. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • C. Gaussian elimination
    Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
  • D. Jacobi method
    The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
  • E. Gauss–Seidel method
    The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
  • 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: Schmidt orthogonalization
Triple: [Erhard Schmidt, notableWork, Schmidt orthogonalization]
Generated description
Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Schmidt orthogonalization
Target entity description: Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
  • A. Richardson iteration
    Richardson iteration is an early iterative method for solving linear systems and other operator equations, based on repeated relaxation steps to progressively improve an approximate solution.
  • B. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • C. Gaussian elimination
    Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
  • D. Jacobi method
    The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
  • E. Gauss–Seidel method
    The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
  • 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_69ad8b19b7b08190a6188804e99c53e9 completed March 8, 2026, 2:43 p.m.
NER Named-entity recognition batch_69adcb6ac5ac8190934ec1a6c887a8f5 completed March 8, 2026, 7:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4db2f5e9881908c10feafbb569f48 completed March 14, 2026, 3:51 a.m.
NEDg Description generation batch_69b4df1cfd348190831cc472de055436 completed March 14, 2026, 4:07 a.m.
NED2 Entity disambiguation (via description) batch_69b4df7b2da881908aef158d79c2834c completed March 14, 2026, 4:09 a.m.
Created at: March 8, 2026, 3:35 p.m.