Triple

T3576748
Position Surface form Disambiguated ID Type / Status
Subject Bethe ansatz E75706 entity
Predicate solves P14252 FINISHED
Object Lieb–Liniger model
The Lieb–Liniger model is an exactly solvable quantum many-body system describing one-dimensional bosons with delta-function interactions, fundamental in the study of integrable systems and quantum gases.
E368994 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: Lieb–Liniger model | Statement: [Bethe ansatz, solves, Lieb–Liniger model]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lieb–Liniger model
Context triple: [Bethe ansatz, solves, Lieb–Liniger model]
  • A. Gross–Pitaevskii equation
    The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
  • B. Luttinger liquid theory
    Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
  • C. 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.
  • D. Fermi gas
    A Fermi gas is a quantum many-particle system composed of fermions that obey Fermi–Dirac statistics, often used to model electrons in metals, neutrons in neutron stars, and ultracold atomic gases.
  • E. Bose gas
    A Bose gas is a quantum-mechanical system of indistinguishable bosons whose collective behavior is governed by Bose–Einstein statistics, often leading to phenomena like Bose–Einstein condensation at low temperatures.
  • 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: Lieb–Liniger model
Triple: [Bethe ansatz, solves, Lieb–Liniger model]
Generated description
The Lieb–Liniger model is an exactly solvable quantum many-body system describing one-dimensional bosons with delta-function interactions, fundamental in the study of integrable systems and quantum gases.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lieb–Liniger model
Target entity description: The Lieb–Liniger model is an exactly solvable quantum many-body system describing one-dimensional bosons with delta-function interactions, fundamental in the study of integrable systems and quantum gases.
  • A. Gross–Pitaevskii equation
    The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
  • B. Luttinger liquid theory
    Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
  • C. 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.
  • D. Fermi gas
    A Fermi gas is a quantum many-particle system composed of fermions that obey Fermi–Dirac statistics, often used to model electrons in metals, neutrons in neutron stars, and ultracold atomic gases.
  • E. Bose gas
    A Bose gas is a quantum-mechanical system of indistinguishable bosons whose collective behavior is governed by Bose–Einstein statistics, often leading to phenomena like Bose–Einstein condensation at low temperatures.
  • 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_69ad85d5e3008190bdfe0bacdd1f5a1b completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc0dba238819083a1d09005c312b8 completed March 8, 2026, 6:32 p.m.
NED1 Entity disambiguation (via context triple) batch_69b3bbc3d4e88190b18ed318c55594cc completed March 13, 2026, 7:24 a.m.
NEDg Description generation batch_69b3bd01ba7881909a0987b7d5dad4c2 completed March 13, 2026, 7:30 a.m.
NED2 Entity disambiguation (via description) batch_69b3f5b6e66c81908700d5f3df0a864d completed March 13, 2026, 11:32 a.m.
Created at: March 8, 2026, 3:21 p.m.