Triple

T2093723
Position Surface form Disambiguated ID Type / Status
Subject Arnold Sommerfeld E32730 entity
Predicate knownFor P22 FINISHED
Object Sommerfeld expansion in statistical mechanics
The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
E234761 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: Sommerfeld expansion in statistical mechanics | Statement: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sommerfeld expansion in statistical mechanics
Context triple: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
  • A. Kirkwood approximation in statistical mechanics
    The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
  • B. Fermi–Dirac statistics
    Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
  • C. Maxwell–Boltzmann statistics
    Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
  • D. Bose–Einstein statistics
    Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
  • E. 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.
  • 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: Sommerfeld expansion in statistical mechanics
Triple: [Arnold Sommerfeld, knownFor, Sommerfeld expansion in statistical mechanics]
Generated description
The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Sommerfeld expansion in statistical mechanics
Target entity description: The Sommerfeld expansion in statistical mechanics is an asymptotic method used to approximate integrals involving Fermi–Dirac distributions at low temperatures, widely applied to calculate thermodynamic properties of degenerate electron gases in metals.
  • A. Kirkwood approximation in statistical mechanics
    The Kirkwood approximation in statistical mechanics is a method for approximating many-particle correlation functions by expressing higher-order correlations in terms of lower-order ones, simplifying the description of interacting particle systems.
  • B. Fermi–Dirac statistics
    Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
  • C. Maxwell–Boltzmann statistics
    Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
  • D. Bose–Einstein statistics
    Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
  • E. 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.
  • 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_69a885eba0708190999696a45cbec816 completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69abba98c32081908a243bc7088a1510 completed March 7, 2026, 5:41 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae305aacc08190904a358fc4207075 completed March 9, 2026, 2:28 a.m.
NEDg Description generation batch_69ae30e0411c81908cd19bf8d3525056 completed March 9, 2026, 2:30 a.m.
NED2 Entity disambiguation (via description) batch_69ae31871d408190a4ae64372660fa79 completed March 9, 2026, 2:33 a.m.
Created at: March 4, 2026, 7:43 p.m.