Triple

T373790
Position Surface form Disambiguated ID Type / Status
Subject Bernhard Riemann E8325 entity
Predicate knownFor P22 FINISHED
Object 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.
E47353 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: Riemann sums | Statement: [Bernhard Riemann, knownFor, Riemann sums]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann sums
Context triple: [Bernhard Riemann, knownFor, Riemann sums]
  • A. Minkowski sum
    The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
  • B. 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.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Gaussian integral
    The Gaussian integral is a fundamental result in mathematics that evaluates the integral of the exponential of a negative quadratic function over the entire real line, yielding a value proportional to the square root of π and underpinning the normal distribution in probability theory.
  • E. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • 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: Riemann sums
Triple: [Bernhard Riemann, knownFor, Riemann sums]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Riemann sums
Target entity description: 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.
  • A. Minkowski sum
    The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
  • B. 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.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Gaussian integral
    The Gaussian integral is a fundamental result in mathematics that evaluates the integral of the exponential of a negative quadratic function over the entire real line, yielding a value proportional to the square root of π and underpinning the normal distribution in probability theory.
  • E. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • 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_69a2e7f2ec648190b42bc7db424f8109 completed Feb. 28, 2026, 1:04 p.m.
NER Named-entity recognition batch_69a2ec13b9b48190b294d998c6720132 completed Feb. 28, 2026, 1:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69a3f0a9608481908bee4d83768e6497 completed March 1, 2026, 7:54 a.m.
NEDg Description generation batch_69a3f131d1f88190ac131204c5402687 completed March 1, 2026, 7:56 a.m.
NED2 Entity disambiguation (via description) batch_69a3f202f308819098affb41d502d5fb completed March 1, 2026, 8 a.m.
Created at: Feb. 28, 2026, 1:08 p.m.