Triple

T738097
Position Surface form Disambiguated ID Type / Status
Subject von Neumann stability analysis E14978 entity
Predicate relatedTo P37 FINISHED
Object Lax equivalence theorem
The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
E87776 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: Lax equivalence theorem | Statement: [von Neumann stability analysis, relatedTo, Lax equivalence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lax equivalence theorem
Context triple: [von Neumann stability analysis, relatedTo, Lax equivalence theorem]
  • A. 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.
  • B. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • C. Euler equations
    The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
  • D. local existence and uniqueness theorem
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • E. 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.
  • 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: Lax equivalence theorem
Triple: [von Neumann stability analysis, relatedTo, Lax equivalence theorem]
Generated description
The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lax equivalence theorem
Target entity description: The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
  • A. 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.
  • B. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • C. Euler equations
    The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
  • D. local existence and uniqueness theorem
    The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
  • E. 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.
  • 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_69a4934d9930819099eed80096b0597d completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a5f1c9888190b2817138c6893cfe completed March 1, 2026, 8:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69a64a618c248190ab1bcecba04d3da8 completed March 3, 2026, 2:41 a.m.
NEDg Description generation batch_69a64b4c8bb88190aa413a4bed256129 completed March 3, 2026, 2:45 a.m.
NED2 Entity disambiguation (via description) batch_69a64beaafa0819099b02cca0f6c79b7 completed March 3, 2026, 2:48 a.m.
Created at: March 1, 2026, 7:37 p.m.