Triple

T228964
Position Surface form Disambiguated ID Type / Status
Subject Carl Friedrich Gauss E4368 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Gauss–Markov theorem
The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
E29373 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: Gauss–Markov theorem | Statement: [Carl Friedrich Gauss, hasConceptNamedAfter, Gauss–Markov theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gauss–Markov theorem
Context triple: [Carl Friedrich Gauss, hasConceptNamedAfter, Gauss–Markov theorem]
  • A. central limit theorem
    The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
  • B. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • C. Shannon–Khinchin axioms
    The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
  • D. 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.
  • E. expected utility theory (with John von Neumann)
    Expected utility theory (with John von Neumann) is a foundational framework in economics and decision theory that models how rational agents make choices under uncertainty by maximizing the expected value of a utility function.
  • 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: Gauss–Markov theorem
Triple: [Carl Friedrich Gauss, hasConceptNamedAfter, Gauss–Markov theorem]
Generated description
The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gauss–Markov theorem
Target entity description: The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
  • A. central limit theorem
    The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
  • B. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • C. Shannon–Khinchin axioms
    The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
  • D. 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.
  • E. expected utility theory (with John von Neumann)
    Expected utility theory (with John von Neumann) is a foundational framework in economics and decision theory that models how rational agents make choices under uncertainty by maximizing the expected value of a utility function.
  • 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_69a260c42060819089eb772202e504f5 completed Feb. 28, 2026, 3:28 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.