Triple
T6788315
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stokes' theorem |
E155868
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Green's theorem
Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
|
E620783
|
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: Green's theorem | Statement: [Stokes' theorem, generalizes, Green's theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Green's theorem Context triple: [Stokes' theorem, generalizes, Green's theorem]
-
A.
Stokes' theorem
Stokes' theorem is a fundamental result in vector calculus that relates the surface integral of the curl of a vector field over a surface to the line integral of the field around the surface’s boundary.
-
B.
Cauchy integral theorem
The Cauchy integral theorem is a fundamental result in complex analysis stating that the integral of a holomorphic function over any closed contour in a simply connected domain is zero.
-
C.
Fubini's theorem
Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
-
D.
Poincaré lemma
The Poincaré lemma is a fundamental result in differential geometry and topology stating that every closed differential form on a star-shaped (or more generally, contractible) domain is locally exact.
-
E.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
- 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: Green's theorem Triple: [Stokes' theorem, generalizes, Green's theorem]
Generated description
Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Green's theorem Target entity description: Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
-
A.
Stokes' theorem
Stokes' theorem is a fundamental result in vector calculus that relates the surface integral of the curl of a vector field over a surface to the line integral of the field around the surface’s boundary.
-
B.
Cauchy integral theorem
The Cauchy integral theorem is a fundamental result in complex analysis stating that the integral of a holomorphic function over any closed contour in a simply connected domain is zero.
-
C.
Fubini's theorem
Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
-
D.
Poincaré lemma
The Poincaré lemma is a fundamental result in differential geometry and topology stating that every closed differential form on a star-shaped (or more generally, contractible) domain is locally exact.
-
E.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
- 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_69c6881770fc8190972b2906390380f5 |
completed | March 27, 2026, 1:37 p.m. |
| NER | Named-entity recognition | batch_69c6d2aa2e0c8190b994261826ae001d |
completed | March 27, 2026, 6:55 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c71a8998408190b741417ce6f21f55 |
completed | March 28, 2026, 12:02 a.m. |
| NEDg | Description generation | batch_69c71e2ad0b08190a24f8865b8074b35 |
completed | March 28, 2026, 12:17 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c71e9ec7148190a5f1df4951990f64 |
completed | March 28, 2026, 12:19 a.m. |
Created at: March 27, 2026, 2:14 p.m.