Triple

T426771
Position Surface form Disambiguated ID Type / Status
Subject Leonhard Euler E9625 entity
Predicate notableWork P4 FINISHED
Object Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
E54272 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: Euler’s method for numerical integration | Statement: [Leonhard Euler, notableWork, Euler’s method for numerical integration]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Euler’s method for numerical integration
Context triple: [Leonhard Euler, notableWork, Euler’s method for numerical integration]
  • A. Euler–Maruyama method
    The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
  • B. 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.
  • C. Riemann sums
    Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
  • D. von Neumann stability analysis
    Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
  • E. Differential analyzer
    The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
  • 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: Euler’s method for numerical integration
Triple: [Leonhard Euler, notableWork, Euler’s method for numerical integration]
Generated description
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Euler’s method for numerical integration
Target entity description: Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
  • A. Euler–Maruyama method
    The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
  • B. 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.
  • C. Riemann sums
    Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
  • D. von Neumann stability analysis
    Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
  • E. Differential analyzer
    The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
  • 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_69a2e801e1d48190b505d1dd336b52ac completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2eed691c4819092b7e57306114bbc completed Feb. 28, 2026, 1:34 p.m.
NED1 Entity disambiguation (via context triple) batch_69a42f665c2881908850bce36cdf74b8 completed March 1, 2026, 12:21 p.m.
NEDg Description generation batch_69a43038d2348190a348e6661d27dde4 completed March 1, 2026, 12:25 p.m.
NED2 Entity disambiguation (via description) batch_69a430f6c6f88190b5aecfe3c4c8957d completed March 1, 2026, 12:28 p.m.
Created at: Feb. 28, 2026, 1:11 p.m.