Triple

T228925
Position Surface form Disambiguated ID Type / Status
Subject Carl Friedrich Gauss E4368 entity
Predicate notableWork P4 FINISHED
Object 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.
E29365 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: Gaussian integral | Statement: [Carl Friedrich Gauss, notableWork, Gaussian integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gaussian integral
Context triple: [Carl Friedrich Gauss, notableWork, Gaussian integral]
  • A. Feynman path integral
    The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
  • B. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • C. Born–Huang expansion
    The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
  • D. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • E. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • 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: Gaussian integral
Triple: [Carl Friedrich Gauss, notableWork, Gaussian integral]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gaussian integral
Target entity description: 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.
  • A. Feynman path integral
    The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
  • B. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • C. Born–Huang expansion
    The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
  • D. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • E. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • 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_69a257363ffc81909757bde7ab3404da completed Feb. 28, 2026, 2:47 a.m.
NER Named-entity recognition batch_69a25c9140c48190b90647400854b37e completed Feb. 28, 2026, 3:10 a.m.
NED1 Entity disambiguation (via context triple) batch_69a35b66359481908daf0412badd76bc completed Feb. 28, 2026, 9:17 p.m.
NEDg Description generation batch_69a35d280c8c81909dd05d5c45ffe616 completed Feb. 28, 2026, 9:24 p.m.
NED2 Entity disambiguation (via description) batch_69a35dc9ad808190a93a4a4c062ce69c completed Feb. 28, 2026, 9:27 p.m.
Created at: Feb. 28, 2026, 2:53 a.m.