Triple

T2169630
Position Surface form Disambiguated ID Type / Status
Subject N. G. de Bruijn E46991 entity
Predicate notableWork P4 FINISHED
Object de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
E239170 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: de Bruijn–van Aardenne–Ehrenfest theorem | Statement: [N. G. de Bruijn, notableWork, de Bruijn–van Aardenne–Ehrenfest theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: de Bruijn–van Aardenne–Ehrenfest theorem
Context triple: [N. G. de Bruijn, notableWork, de Bruijn–van Aardenne–Ehrenfest theorem]
  • A. 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.
  • B. Sprague–Grundy theorem
    The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
  • C. H-theorem
    The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
  • D. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • E. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • 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: de Bruijn–van Aardenne–Ehrenfest theorem
Triple: [N. G. de Bruijn, notableWork, de Bruijn–van Aardenne–Ehrenfest theorem]
Generated description
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: de Bruijn–van Aardenne–Ehrenfest theorem
Target entity description: The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
  • A. 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.
  • B. Sprague–Grundy theorem
    The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
  • C. H-theorem
    The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
  • D. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • E. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • 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_69a88a184cbc8190877791f6552c2484 completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abbeaeb58881908ad34f7b253bac2a completed March 7, 2026, 5:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae58f511a08190880fbde8900d59df completed March 9, 2026, 5:21 a.m.
NEDg Description generation batch_69ae59a9b010819081491e988184b386 completed March 9, 2026, 5:24 a.m.
NED2 Entity disambiguation (via description) batch_69ae5a12f11c81908cc345905f0a485e completed March 9, 2026, 5:26 a.m.
Created at: March 4, 2026, 7:45 p.m.