Triple

T15515403
Position Surface form Disambiguated ID Type / Status
Subject George Gabriel Stokes E368821 entity
Predicate notableIdea P4 FINISHED
Object Stokes–Helmholtz decomposition
The Stokes–Helmholtz decomposition is a fundamental theorem in vector calculus stating that any sufficiently smooth vector field can be uniquely decomposed into an irrotational (curl-free) and a solenoidal (divergence-free) component under appropriate conditions.
E553414 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: Stokes–Helmholtz decomposition | Statement: [George Gabriel Stokes, notableIdea, Stokes–Helmholtz decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stokes–Helmholtz decomposition
Context triple: [George Gabriel Stokes, notableIdea, Stokes–Helmholtz decomposition]
  • A. Hodge decomposition
    Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
  • B. Helmholtz equation
    The Helmholtz equation is a fundamental partial differential equation that describes time-harmonic wave propagation in fields such as acoustics, electromagnetism, and optics.
  • C. Wiener–Hopf equations
    Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
  • D. Taylor–Proudman theorem
    The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
  • E. Topological Methods in Hydrodynamics
    Topological Methods in Hydrodynamics is a seminal mathematical monograph by Vladimir Arnold that applies topological and geometric techniques to the study of fluid flows and hydrodynamic phenomena.
  • 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: Stokes–Helmholtz decomposition
Triple: [George Gabriel Stokes, notableIdea, Stokes–Helmholtz decomposition]
Generated description
The Stokes–Helmholtz decomposition is a fundamental theorem in vector calculus stating that any sufficiently smooth vector field can be uniquely decomposed into an irrotational (curl-free) and a solenoidal (divergence-free) component under appropriate conditions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stokes–Helmholtz decomposition
Target entity description: The Stokes–Helmholtz decomposition is a fundamental theorem in vector calculus stating that any sufficiently smooth vector field can be uniquely decomposed into an irrotational (curl-free) and a solenoidal (divergence-free) component under appropriate conditions.
  • A. Hodge decomposition chosen
    Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
  • B. Helmholtz equation
    The Helmholtz equation is a fundamental partial differential equation that describes time-harmonic wave propagation in fields such as acoustics, electromagnetism, and optics.
  • C. Wiener–Hopf equations
    Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
  • D. Taylor–Proudman theorem
    The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
  • E. Topological Methods in Hydrodynamics
    Topological Methods in Hydrodynamics is a seminal mathematical monograph by Vladimir Arnold that applies topological and geometric techniques to the study of fluid flows and hydrodynamic phenomena.
  • F. None of above.

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_69d85a1794cc8190b0b428716296e63e completed April 10, 2026, 2:01 a.m.
NER Named-entity recognition batch_69e04031e62c8190953b61207142af15 completed April 16, 2026, 1:49 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3d4edee481908382ca5cd266f7b0 completed May 9, 2026, 1:57 p.m.
NEDg Description generation batch_69ff3f59213c8190a9c98350225b5151 completed May 9, 2026, 2:06 p.m.
NED2 Entity disambiguation (via description) batch_69ff3ff96a6c8190a4c9f20dabc86cef completed May 9, 2026, 2:08 p.m.
Created at: April 10, 2026, 4:02 a.m.