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.