Triple

T13035698
Position Surface form Disambiguated ID Type / Status
Subject Monge–Ampère equation E326554 entity
Predicate relatedTo P37 FINISHED
Object Abreu equation
The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
E1017919 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: Abreu equation | Statement: [Monge–Ampère equation, relatedTo, Abreu equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Abreu equation
Context triple: [Monge–Ampère equation, relatedTo, Abreu equation]
  • A. Bhabha–Corben equations
    The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
  • B. Charney equation
    The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
  • C. Carothers equation
    The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
  • D. Karplus equation
    The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
  • E. Goodman–Martínez–Thompson correlation
    The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
  • 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: Abreu equation
Triple: [Monge–Ampère equation, relatedTo, Abreu equation]
Generated description
The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Abreu equation
Target entity description: The Abreu equation is a fourth-order nonlinear partial differential equation arising in Kähler and toric geometry, particularly in the study of extremal and constant scalar curvature Kähler metrics.
  • A. Bhabha–Corben equations
    The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
  • B. Charney equation
    The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
  • C. Carothers equation
    The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
  • D. Karplus equation
    The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
  • E. Goodman–Martínez–Thompson correlation
    The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
  • 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_69d8076cc45c81908123123f43e69266 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69d97effca908190ab89fdb034e02680 completed April 10, 2026, 10:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6cbcf11f88190ab1746f973132af1 completed May 3, 2026, 4:15 a.m.
NEDg Description generation batch_69f6cee0a27081909203e3331186b4ca completed May 3, 2026, 4:28 a.m.
NED2 Entity disambiguation (via description) batch_69f6cf987f68819084edcd6613832fe8 completed May 3, 2026, 4:31 a.m.
Created at: April 9, 2026, 8:55 p.m.