Triple

T14618899
Position Surface form Disambiguated ID Type / Status
Subject Oliver Penrose E343160 entity
Predicate notableWork P4 FINISHED
Object Penrose–Onsager criterion for Bose–Einstein condensation
The Penrose–Onsager criterion for Bose–Einstein condensation is a theoretical condition that identifies condensation through the emergence of macroscopic eigenvalues in the one-particle density matrix, providing a rigorous definition of Bose–Einstein condensation in interacting systems.
 E1110828 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Penrose–Onsager criterion for Bose–Einstein condensation | Statement: [Oliver Penrose, notableWork, Penrose–Onsager criterion for Bose–Einstein condensation]

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Penrose–Onsager criterion for Bose–Einstein condensation
Context triple: [Oliver Penrose, notableWork, Penrose–Onsager criterion for Bose–Einstein condensation]
  • A. Bose–Einstein Condensation (book)
    Bose–Einstein Condensation is a comprehensive monograph by Lev Pitaevskii and coauthors that presents the theoretical foundations and experimental developments of Bose–Einstein condensation in dilute quantum gases.
  • B. Bogoliubov theory of weakly interacting Bose gases
    Bogoliubov theory of weakly interacting Bose gases is a foundational quantum many-body framework that explains the excitation spectrum and collective behavior of dilute Bose–Einstein condensates by treating interactions as small perturbations around a condensed ground state.
  • C. Bose–Einstein condensate
    A Bose–Einstein condensate is an exotic state of matter formed when a dilute gas of bosons is cooled to temperatures near absolute zero, causing a large fraction of the particles to occupy the same quantum state and behave as a single quantum entity.
  • D. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • E. Ginzburg–Landau theory of superconductivity
    The Ginzburg–Landau theory of superconductivity is a phenomenological framework that describes superconductors using a complex order parameter and macroscopic equations to capture phase transitions, coherence length, and magnetic behavior.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Penrose–Onsager criterion for Bose–Einstein condensation
Target entity description: The Penrose–Onsager criterion for Bose–Einstein condensation is a theoretical condition that identifies condensation through the emergence of macroscopic eigenvalues in the one-particle density matrix, providing a rigorous definition of Bose–Einstein condensation in interacting systems.
  • A. Bose–Einstein Condensation (book)
    Bose–Einstein Condensation is a comprehensive monograph by Lev Pitaevskii and coauthors that presents the theoretical foundations and experimental developments of Bose–Einstein condensation in dilute quantum gases.
  • B. Bogoliubov theory of weakly interacting Bose gases
    Bogoliubov theory of weakly interacting Bose gases is a foundational quantum many-body framework that explains the excitation spectrum and collective behavior of dilute Bose–Einstein condensates by treating interactions as small perturbations around a condensed ground state.
  • C. Bose–Einstein condensate
    A Bose–Einstein condensate is an exotic state of matter formed when a dilute gas of bosons is cooled to temperatures near absolute zero, causing a large fraction of the particles to occupy the same quantum state and behave as a single quantum entity.
  • D. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • E. Ginzburg–Landau theory of superconductivity
    The Ginzburg–Landau theory of superconductivity is a phenomenological framework that describes superconductors using a complex order parameter and macroscopic equations to capture phase transitions, coherence length, and magnetic behavior.
  • F. None of above. chosen

How the object was described

The object's one-sentence description was generated by prompting gpt-5.1 with the object name and this triple as context.

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: Penrose–Onsager criterion for Bose–Einstein condensation
Triple: [Oliver Penrose, notableWork, Penrose–Onsager criterion for Bose–Einstein condensation]
Generated description
The Penrose–Onsager criterion for Bose–Einstein condensation is a theoretical condition that identifies condensation through the emergence of macroscopic eigenvalues in the one-particle density matrix, providing a rigorous definition of Bose–Einstein condensation in interacting systems.

Provenance (5 batches)

Stage Batch ID Job type Status
creating batch_69d822dffc3c8190aa173b90761bffda elicitation completed
NER batch_69deb46550e48190af45f426f02579bb ner completed
NED1 batch_69fda924c7308190931c03fbac57b0bf ned_source_triple completed
NED2 batch_69fdb36bd50c8190a8af992fe4b12bb6 ned_description completed
NEDg batch_69fdb234bc1c8190a85c802dfcfa7909 nedg completed
Created at: April 10, 2026, 1:25 a.m.