Triple

T7150595
Position Surface form Disambiguated ID Type / Status
Subject density functional theory E166680 entity
Predicate hasTheorem P38252 FINISHED
Object Hohenberg–Kohn theorem
The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
E645114 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: Hohenberg–Kohn theorem | Statement: [density functional theory, hasTheorem, Hohenberg–Kohn theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hohenberg–Kohn theorem
Context triple: [density functional theory, hasTheorem, Hohenberg–Kohn 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. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. 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.
  • D. Hartree–Fock method
    The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
  • E. Born–Oppenheimer approximation
    The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
  • 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: Hohenberg–Kohn theorem
Triple: [density functional theory, hasTheorem, Hohenberg–Kohn theorem]
Generated description
The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hohenberg–Kohn theorem
Target entity description: The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
  • 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. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. 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.
  • D. Hartree–Fock method
    The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
  • E. Born–Oppenheimer approximation
    The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
  • 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_69c68886779c8190a8e3fbabffe68253 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e7f28b188190b1732ca711666531 completed March 27, 2026, 8:26 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7ada940e08190b16e97e363801e75 completed March 28, 2026, 10:30 a.m.
NEDg Description generation batch_69c7ae5767408190860c1c7bc3a769fa completed March 28, 2026, 10:32 a.m.
NED2 Entity disambiguation (via description) batch_69c7aeb68c3481909c6dff8ee51349ab completed March 28, 2026, 10:34 a.m.
Created at: March 27, 2026, 2:46 p.m.