Triple

T2815530

Position	Surface form	Disambiguated ID	Type / Status
Subject	Euler’s method for numerical integration	`E54272`	entity
Predicate	isGeneralizedBy	`P2372`	FINISHED
Object	Heun’s method Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.	`E300767`	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: Heun’s method | Statement: [Euler’s method for numerical integration, isGeneralizedBy, Heun’s method]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Heun’s method
Context triple: [Euler’s method for numerical integration, isGeneralizedBy, Heun’s method]

A. 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.
B. Milstein method
The Milstein method is a numerical scheme for solving stochastic differential equations that improves on the Euler–Maruyama method by including derivative terms of the diffusion coefficient for higher accuracy.
C. Halley’s method for solving equations
Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
D. 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.
E. Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
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: Heun’s method
Triple: [Euler’s method for numerical integration, isGeneralizedBy, Heun’s method]

Generated description

Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Heun’s method
Target entity description: Heun’s method is a second-order Runge–Kutta numerical integration technique that improves on Euler’s method by using a predictor-corrector approach to achieve greater accuracy.

A. 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.
B. Milstein method
The Milstein method is a numerical scheme for solving stochastic differential equations that improves on the Euler–Maruyama method by including derivative terms of the diffusion coefficient for higher accuracy.
C. Halley’s method for solving equations
Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
D. 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.
E. Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
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_69ab49de0af08190b3da69683be1e728`	completed	March 6, 2026, 9:40 p.m.
NER	Named-entity recognition	`batch_69abde4d29488190a32461906dd9ea7e`	completed	March 7, 2026, 8:14 a.m.
NED1	Entity disambiguation (via context triple)	`batch_69afce9f964081909e422aaf1f026dbb`	completed	March 10, 2026, 7:56 a.m.
NEDg	Description generation	`batch_69afcf12e3a0819098f28d31434a0c5f`	completed	March 10, 2026, 7:58 a.m.
NED2	Entity disambiguation (via description)	`batch_69afcf9c2d308190b111aa8038c9227a`	completed	March 10, 2026, 8 a.m.

Created at: March 6, 2026, 9:59 p.m.